Research ArticleA Dynamic Analysis of a Motor Vehicle Pollutant EmissionReduction Management Model Based on the SD-GM Approach

Shuwei Jia

College of Information and Management Science Henan Agricultural University Zhengzhou 450002 China

Correspondence should be addressed to Shuwei Jia shuweijia999666163com

Received 6 November 2017 Revised 29 June 2018 Accepted 12 July 2018 Published 1 August 2018

Academic Editor Rodica Luca

Copyright copy 2018 Shuwei Jia This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The present study constructed a motor vehicle pollution charging management model by primarily reducing the trip volume ofmotor vehicles introducing the charging mechanism and employing integration of the system dynamics and grey model theory(SD-GM) from the perspective of the environment and society To optimize the chosen parameters the dynamic growth rategraphical function of the gross domestic product (GDP) was firstly generated based on the GM(11) prediction theory In additionverification was conducted in accordance with the degree of grey incidence Secondly the net migration rate was estimated basedon the attraction degree of the city and the average net migration rate The degree of PMx and NOx pollution was finally definedand endowed with different weights to define the degree of air pollution in accordance with the actual degree of air pollution inBeijing In terms of model testing and verification we conducted extreme condition tests and sensitivity tests and checked theresidual error Finally this study analyzed and compared different policies which indicate that the amount of motor vehicle trips(AMVT) the amount of PMx generation (APMG) the amount of NOx generation (ANOG) and the degree of air pollution (DAP)decreased by 3101 2652 2129 and 1250 respectively

1 Introduction

With the continuous improvement of living standards andaccelerated urbanization in China transportation demandshave rapidly increased In addition urban residents havegradually come to prefer automobiles as a means of trans-portation The population of Chinese vehicles has rapidlyincreased since 2006 thereby boosting automobile quantitiesfaster than the traffic capacity of urban roads In additiontraffic jams and vehicle-induced exhaust gas pollution havebecome increasingly serious and not only influence trafficsafety and the normal travel of residents but also result in airpollution such as haze

To solve these problems scholars characterized exhaustgas emissions and air pollution to generate different methodsof alleviating traffic jams and air pollution In terms ofenergy conservation and emission reduction of vehicles Liuet al (2015) examined the passenger transport energy con-sumption and emissions in Beijing using scenario analysesand proposed measures to reduce vehicle emissions therebyproviding references for policy makers [1] Xu et al (2016)

utilized provincial panel data from 2001 to 2012 and usedthe stochastic impacts by regression on population affluenceand technology (STIRPAT) model to explore the drivingforces of PM25 emissions in China [2] The empirical resultsindicated that the inverted ldquoU-shapedrdquo impact of privatevehicles may be due to the different roles of structural scaleand technical effects at different stages Leinert et al (2013)studied the influence of automobile taxation policies on NOxemission which provides policy references for research onvehicle emission reduction [3] Cheng et al (2017) useddynamic spatial panel models to analyze the driving factorsof Chinarsquos haze pollution based on 2001 to 2012 data coveringPM25 concentrations in 285 cities [4] The results identify ahigh proportion of haze pollution due to secondary industrya coal-dominated energy structure and increasing trafficintensity as key driving factors of urban PM25 pollutionin China In terms of the environmental perspective Kaida(2015) examined the spillover effect of congestion charg-ing on proenvironmental behavior [5] Penabaena-Niebleset al (2015) researched the impact of transitions betweensignal timing plans in the social cost based on delays fuel

HindawiDiscrete Dynamics in Nature and SocietyVolume 2018 Article ID 2512350 18 pageshttpsdoiorg10115520182512350

2 Discrete Dynamics in Nature and Society

consumption and air emissions [6] Some scholars alsoexamined various other problems such as traffic congestion[7 8] and emissions [9ndash12] transportation networks [13] car-bon taxation [14] and air quality [15ndash17] In addition certainscholars adopted economic means such as the congestionpricing policy [18 19] to characterize vehicle-induced trafficjams and exhaust gas emissions

Nevertheless scholars seldom employ system dynam-ics and dynamic simulation analyses for vehicle emissionreduction research Therefore it is necessary to introducethe system dynamics approach because it emphasizes systembehavior structure and causal feedback relationships Inaddition this paper also introduces the charging mechanismand increased vehicle trip costs by charging to reduce vehicletrips and PMx and NOx emissions More importantly it pro-poses a reduction management model for vehicle pollutantemissions on the basis of integrated system dynamics and thegrey model theory (SD-GM approach) which can realize along-term and dynamic simulation analysis

2 Methods

21 SystemDynamicsMethod The system dynamicsmethodwhich is based on the system theory and computer simulationtechnology characterizes the different behavior patterns of acomplex system that are generated through time In additionthemethod analyzes the causal relationship between variablesthrough the information feedback mechanism to determinethe key problem variables that influence the system therebyverifying the reasonability and stability of the constructedmodel throughmodel tests and inspectionsThe effectivenessand practicability of the model are also validated basedon the sensitivity analyses of parameters and the dynamicsimulation of different policies to provide policy suggestionsfor solving problems

211 Task Investigation and Objective Analysis The contin-uous increase of exhaust emissions due to the continuousincrease of motor vehicle ownership has resulted in thefrequent presence of ldquohazerdquo pollution in cities Pollutiondegrees are generallymore serious inmetropolitan areas suchas Beijing Shanghai and Guangzhou According to researchdata motor vehicle exhaust emission is one of the mainsources of air pollution in China As a result a series ofmeasures have been implemented to reduce the amount ofmotor vehicle trips (AMVT) to alleviate urban traffic jamsand further constrain the degree of air pollution (DAP)

212 Stock-Flow Diagram and Causal Loop Diagram Thecorresponding stock-flow diagram was generated based onthe above analysis using the system dynamics softwareVensim as shown in Figure 1 Detailed descriptions weregiven in Appendix A This stock-flow diagram presents twomain loops that were derived based on the AMVT reductionand PMx (NOx) emission reduction analyses as presented inFigure 2

Loop 1 is a negative feedback loop An increase in theinitial NOx (PMx) emissions intensifies the degree of airpollution thereby strengthening the air pollution control

and increasing the cost of motor vehicle trips by the imple-mentation of policies such as the air pollution charging fee(APCF) An increase in the cost ofmotor vehicle trips reducesthe attraction degree of vehicle trips and the growth ofvehicles thereby reducing the growth rate of motor vehiclesIn addition a reduction in the growth rate of motor vehicleseffectively restrains the increase of motor vehicles reducesthe AMVT and finally reduces NOx (PMx) emissionsAccording to the loop an initial increase in NOx (PMx)emissions reduces the final emissions values Similarly theanalysis of loop 2 is presented in Figure 2

22 Data Sources and Parameters Determination The datasource patterns were roughly divided into three kinds analy-sis of the statistics existing literature and SD-GM approach

221 Data of Official Website (M1) The use of a referencedata model and the presence of strong data stability can beused to calculate the arithmetic mean value among otherthings based on historical statistical data and materials suchas Statistical Yearbook of All Provinces and Cities StatisticalYearbook of China and China Automotive Industry Yearbook

(1) According to Table 1 the initial amount of motorvehicles initial value of population and gross domesticproduct (GDP) gross are respectively listed as 4019 millionvehicles 186 million persons and 12153 trillion yuan

(2) Initial value of amount of NOx generation (ANOG)asymp 002 times 4019 times 104 = 80380 tons initial value of amount ofPMx generation (APMG) asymp004 times 4019 times 104 = 160760 tons

(3) The average of net migration rateThe net migration rate is defined as net migration rate

= Mechanical increase Average population of this regiontimes 100 which was calculated based on Table 2 Net migra-tion rate2009 = 1121631860 times 104 = 0006030269 asymp 603Similarly the net migration rates for the years 2010 to 2014were calculated as follows net migration rate2010 = 556 netmigration rate2011 = 641 net migration rate2012 = 517net migration rate2013 = 519 and net migration rate2014 =347 The preceding net migration rates were averaged asfollows net migration ratemean value = 531permil = 000531

222 Existing Literature (M2) For some of the special modelparameters refer to the researched data such as for thecontribution rate of NOx (PMx) of the vehicle individualvehicle annualNOx (PMx) emissions dissipation and controlrate of NOx (PMx) and scrap rate According to Yang et al[20] and Zhu [21] (1) Per vehicle annual NOx emissions =002 tyearvehicle Per vehicle annual of PMx emissions =004tyearvehicle (2) Contribution rate of NOx from thevehicle = 05 Contribution rate of PMx from the vehicle =06 (3) Dissipation rate of NOx = 02 dissipation rate of PMx= 04 (4) Scrap rate = 0067 (5) Ratio of motor vehicle tripsasymp 055

223 Indirect Data Based on SD-GM Approach (M3) Thesystem dynamics and grey model theory refers to theapproach integrating system dynamics and grey model the-ory Incomplete data information or data stability poorly

Discrete Dynamics in Nature and Society 3

Amount of GDPGrowth of GDP

Growth rate of GDP

Amount ofpopulation

Growth ofpopulation

Predictive valueof birth rate Predictive value

of death rate

Net migration rate

Attraction degreeof city

Per capita annualincome

Populationreduction

Net migration

The average of netmigration rate

Impact factorof policy

Impact factor of thegrowth of GDP

Adjustment coefficientof birth rate

Adjustment coefficientof death rate

Graphical function ofthe growth of GDP

Amount of NOxgeneration (ANOG)NOx emissions

Per vehicle annual ofNOx emissions

Dissipation rate ofNOx

Pollution degreeof NOx

Air pollutioncontrol

Annual dissipationof NOx

Contribution rate ofNOx from vehicle

Degree of air pollution(DAP)

Weight ratio of NOx

Weight ratio ofPMx

Attraction degree of thegrowth of vehicles

Growth rate ofmotor vehicles

Growth rate of vehicleownership

Amount of motor vehicletrips (AMVT)

Ratio of motorvehicle trips

Amount of PMxgeneration (APMG)

PMx emissionsDissipation and control

rate of PMxAnnual dissipation of PMx

Contribution rate of PMx from vehicle

Per vehicle annualof PMx emissions

Pollution degreeof PMx

Amount of motorvehicles

Growthof motorvehicles

Annualscrapped

Scraprate

Air pollution chargingfee (APCF)

Attraction degree ofvehicle trips Cost of motor

vehicle trips

ltTimegt

Birth rateDeathrate

Figure 1 Stock-flow diagram of the motor vehicle pollution charging management model

Degree of airpollution

Amount of motorvehicles

NOx (PMx)emissions

+

Growth of motorvehicles

Attraction degree ofgrowth of vehicles

Cost of motorvehicle trips

Attraction degreeof vehicle trips

+

+

-

Air pollutioncontrol

+

+

B1

+

Amount of motorvehicle trips

+

+

(a)

Amount of motorvehicles

Growth rate ofmotor vehicles

Air pollutioncontrol

-

Amount of motorvehicle trips

NOx (PMx)emissions

Degree of airpollution

+

+ B2

Attraction degree ofgrowth of vehicles-

+

+

+

(b)

Figure 2 Major loops (a) Negative feedback loop of NOx (PMx) emissions (b) Negative feedback loop of AMVT

4 Discrete Dynamics in Nature and Society

Table 1 Historical values of the main status variables (data is from 2010-2015 Statistical Yearbook of Beijing)

Time 2009 2010 2011 2012 2013 2014Amount of motor vehicles 4019 4809 4983 5200 5437 5591(10000 vehicles)Amount of population 18600 19619 20186 20693 21148 21516(10000 persons)GDP gross 121530 141136 162519 178794 198008 213308(100 million yuan)

Table 2 Historical values of main correlated variables Unit person

Time 2009 2010 2011 2012 2013 2014Mechanical increase 112163 109091 129313 107072 109656 74654Inflows 189744 185101 211447 190510 198869 166600Outflows 77581 76010 82134 83438 89213 91946

Table 3 Predictive value of birth rate and its average

Time 2015 2016 2017 2018 2019 2020Predictive value 873permil 894permil 914permil 935permil 956permil 977permilAverage 925permil

Table 4 Predictive value of death rate and its average

Time 2015 2016 2017 2018 2019 2020Predictive value 473permil 483permil 464permil 504permil 515permil 525permilAverage 494permil

generated major errors in the mean-based forecast andestimation which failed to meet the laws of change anddata information development The data was first processedusing theoretical methods such as regression analysis andgrey prediction Valuable implicit rules were then gener-ated in accordance with the actual changes in the datatrends Finally a nonlinear relationship between variableswas characterized in accordance with the graphical functionlogical function etc Three methods are given in the follow-ing

(1) First Method The aim of this method is to determinea reasonable value to meet the actual situation of Beijingin recent years Statistical approaches (such as regressionanalysis) based on large sample data can be used because ofthe abundance of data on birth and death ratesThe value wasfirst predicted by regression analysis after which the meanvalue was calculated Finally the value was slightly adjustedby combining the actual change trends of the variables todetermine the birth rate and death rate

Tables 3 and 4 present the predicted data that wereobtained from the regression analysis on the historical birthrate and death rate values of the permanent resident pop-ulation in Beijing However the implementation of a pop-ulation policy specifically the ldquotwo-child policyrdquo generatedan increase in the birth rate And the death rate remainedat about 5 These results were consistent with the currentstatus of Beijing

(2) Second Method The goal of this method is to describethe dynamic trends between variables by using the graphicalfunction Especially grey prediction model can improvethe prediction accuracy by the use of accumulated gener-ating operator and buffer operator Predictions were firstconducted using the GM (11) model in the absence of anobvious relationship between the variables or in the presenceof imperfect data information Subsequently graphical orlogical functions were generated by combining the actualchange rules of the variables This method was used todetermine the growth rate of the gross domestic product(GDP) and vehicle ownership growth rate Taking the GDPgrowth rate in Beijing as an example the detailed calculationsare presented in the following

Definition 1 Assume that the original sequence is

119883(0) = (119909(0) (1) 119909(0) (2) 119909(0) (119899)) (1)

119883(1) is its accumulation generated sequence (1-AGO)

119883(1) = (119909(1) (1) 119909(1) (2) 119909(1) (119899)) (2)

wherein

119909(1) (119896) = 119896sum119894=1

119909(0) (119894) 119896 = 1 2 119899 (3)

Discrete Dynamics in Nature and Society 5

such that119889119909(1)119889119905 + 119886119909(1) = 119887 (4)

The preceding equation is the winterization equation of thegrey GM (11) prediction model [22]

If 119909(0)(119896) ge 0 119896 = 1 2 119899 then and119886 = (119886 119887)119879 is theparameter list and satisfies

and119886 = (119886 119887)119879 = (119861119879119861)minus1 119861119879119884 (5)

wherein

119861 =[[[[[[[[[[[[

minus119909(1) (1) + 119909(1) (2)2 1

minus119909(1) (2) + 119909(1) (3)2 1

minus119909(1) (119899 minus 1) + 119909(1) (119899)2 1

]]]]]]]]]]]]

119884 =[[[[[[[[

119909(0) (2)119909(0) (3)

119909(0) (119899)

]]]]]]]]

(6)

(i) Time response formula of the solution of the winterizationequation 119889119909(1)119889119905 + 119886119909(1) = 119887 is

119909(1) (119905) = (119909(1) (1) minus 119887119886) 119890minus119886119905 + 119887

119886 (7)

(ii) Time response formula of the GM(11) model 119909(0)(119896) + 119886 sdot(119909(1)(119896) + 119909(1)(119896 minus 1))2 = 119887 isand119909(1) (119896 + 1) = (119909(0) (1) minus 119887

119886) 119890minus119886119896 + 119887119886 119896 = 1 2 3 119899

(8)

(iii) Predicted value model of the original model is

and119884 (119896 + 1) = and119909(0) (119896 + 1) = and119909(1) (119896 + 1) minus and119909(1) (119896)= (1 minus 119890119886) (119909(0) (1) minus 119887

119886) 119890minus119886119896(9)

The following definitions are provided in Liu et al [23]

Definition 2 Assume that the images of zero starting point ofthese two sequences

119883119894 = (119909119894 (1) 119909119894 (2) 119909119894 (119899)) 119883119895 = (119909119895 (1) 119909119895 (2) 119909119895 (119899)) (10)

are

1198830119894 = (1199090119894 (1) 1199090119894 (2) 1199090119894 (119899)) 1198830119895 = (1199090119895 (1) 1199090119895 (2) 1199090119895 (119899)) (11)

such that

120585119894119895 = 1 + 10038161003816100381610038161199041198941003816100381610038161003816 + 10038161003816100381610038161003816119904119895100381610038161003816100381610038161 + 10038161003816100381610038161199041198941003816100381610038161003816 + 1003816100381610038161003816100381611990411989510038161003816100381610038161003816 + 10038161003816100381610038161003816119904119894 minus 11990411989510038161003816100381610038161003816 (12)

The presented equation is the absolute degree of grey inci-dence (GAID) of 119883119894 and 119883119895 Assume that 119883119894 and 119883119895 aresequences of the same length with nonzero initial values 1198831015840119894and 1198831015840119895 are the initial images of 119883119894 and 119883119895 respectively 11988310158400119894and11988310158400119895 are the images of the zero starting point of sequences1198831015840119894 and 1198831015840119895 respectively and the GAID of 1198831015840119894 and 1198831015840119895 is calledthe relative degree of grey incidence (GRID) of 119883119894 and 119883119895Based on these definitions the following equation is thendefined

119903119894119895 = 1 + 10038161003816100381610038161003816119904101584011989410038161003816100381610038161003816 + 100381610038161003816100381610038161199041015840119895100381610038161003816100381610038161 + 100381610038161003816100381611990410158401198941003816100381610038161003816 + 10038161003816100381610038161003816119904101584011989510038161003816100381610038161003816 + 100381610038161003816100381610038161199041015840119894 minus 119904101584011989510038161003816100381610038161003816 (13)

such that

120576119894119895 = 120579120585119894119895 + (1 minus 120579) 119903119894119895 (14)

is defined as the synthetic degree of grey incidence (GSID) of119883119894 and 119883119895 wherein 120579 isin [0 1]Definition 3 Assume that119883(0) is the original sequence and119883(0) isits simulative sequence and 120576 is the degree of grey incidencebetween 119883(0) and and119883(0) In the case of 120576 gt 1205760 for the given1205760 gt 0 this model is defined as the qualified verification ofthe degree of grey incidence See Table 5 for the accuracy testgrade

The requirement of this model for correlation 120576 is ldquothebigger the betterrdquo

Step 1 (data processing) First write the original data as theform of sequence

119883(0) = (119909(0) (1) 119909(0) (2) 119909(0) (10))= (81178 98468 111150 121530 141136 162519 178794 198008 213308 230146)

(15)

6 Discrete Dynamics in Nature and Society

Second introduce the second-order average weakeningoperator 1198632 as

119883(0)1198632 = (119909(0) (1) 1198892 119909(0) (2) 1198892 119909(0) (10) 1198892) (16)

wherein

119909(0) (119896) 1198892 = 110 minus 119896 + 1 [119909(0) (119896) 119889 + 119909(0) (119896 + 1) 119889

+ + 119909(0) (10) 119889] 119909(0) (119896) 119889 = 1

10 minus 119896 + 1 [119909(0) (119896) + 119909(0) (119896 + 1) + + 119909(0) (10)] 119896 = 1 2 3 10

(17)

Obtain

119883(0)1198632 = (191742 195978 200266 20465 209105 213463 21769 221898 225937 230146) ≜ 119883= (119909 (1) 119909 (2) 119909 (3) 119909 (10)) (18)

Step 2 Calculate the 1-AGO sequence of sequence 119883 andobtain sequence 119883(1)

119883(1) = (119909(1) (1) 119909(1) (2) 119909(1) (3) 119909(1) (10))= (191742 38772 587986 792636 1001741 1215204 1432894 1654792 1880729 2110875) (19)

Step 3 Calculate its simulative sequence based on the greyGM (11) prediction model

According to Definition 1 the grey GM (11) predictionmodel is used to obtain the time response formula as follows

and119909(1) (119896 + 1) = 9728182119890002119896 minus 953644and119884 (119896 + 1) = and119909(0) (119896 + 1) = and119909(1) (119896 + 1) minus and119909(1) (119896)

(20)

The simulative sequence can then be calculated as

and119883= (and119909 (1) and119909 (2) and119909 (10))= (191742 196536 2005157 204576 2087185 2129448 2172568 2216561 2261444 2307236)

(21)

Step 4 (accuracy test) According to Steps 1 and 3 the originalsequence and its simulative sequence were respectivelycalculated as follows

119883 =[[[[[[[[[[

119909 (1)119909 (2)119909 (3)

119909 (10)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[[[[[[[[[

191742195978200266204650209105213463217690221898225937230146

]]]]]]]]]]]]]]]]]]]]]]]

and119883 =

[[[[[[[[[[[[[

and119909 (1)and119909 (2)and119909 (3)

and119909 (10)

]]]]]]]]]]]]]

=

[[[[[[[[[[[[[[[[[[[[[[[

191742196536020051572045760208718521294482172568221656122614442307236

]]]]]]]]]]]]]]]]]]]]]]]

(22)

Therefore one can calculate

|119904| =10038161003816100381610038161003816100381610038161003816100381610038169sum119896=2

[119909 (119896) minus 119909 (1)] + 12 [119909 (10) minus 119909 (1)]

1003816100381610038161003816100381610038161003816100381610038161003816

Discrete Dynamics in Nature and Society 7

Table 5 Reference list of accuracy test grade

Accuracy grade Grade 1 Grade 2 Grade 3 Grade 4Degree of grey incidence 1205760 090 080 070 060

Table 6 Amount of GDP and its growth rate

Time Amount of GDP (t) Growth rate Time Amount of GDP (t) Growth rate2005 69695e+011 --- 2013 198008e+012 010752006 81178e+011 01648 2014 213308e+012 007732007 98468e+011 02130 2015 230146e+012 007892008 11115e+012 01288 2016 2353956e+012 0022812009 12153e+012 00934 2017 2401622e+012 0020302010 141136e+012 01613 2018 2450253e+012 0020252011 162519e+012 01515 2019 2499868e+012 0020242012 178794e+012 01001 2020 2550488e+012 0020249

= 1742531003816100381610038161003816100381610038161003816and1199041003816100381610038161003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816100381610038169sum119896=2

[and119909 (119896) minus and119909 (1)] + 12 [and119909 (10) minus and119909 (1)]

1003816100381610038161003816100381610038161003816100381610038161003816= 1739031

1003816100381610038161003816100381610038161003816and119904 minus1199041003816100381610038161003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816100381610038169sum119896=2

[119909 (119896) minus 119909 (1) minus (and119909 (119896) minus and119909 (1))]

+ 12 [119909 (10) minus 119909 (1) minus (and119909 (10) minus and119909 (1))]

1003816100381610038161003816100381610038161003816100381610038161003816 = 3499(23)

such that

120585 = 1 + |119904| + 1003816100381610038161003816100381610038161003816and1199041003816100381610038161003816100381610038161003816

1 + |119904| + 1003816100381610038161003816100381610038161003816and1199041003816100381610038161003816100381610038161003816 +

1003816100381610038161003816100381610038161003816and119904 minus1199041003816100381610038161003816100381610038161003816

asymp 09990 (24)

Similarly 119903 = 09993 when 120579 = 05 exist1205760 = 09 therebydefining

120576 = 120579120585 + (1 minus 120579) 119903 = 09991 gt 09 = 1205760 (25)

Therefore this model is defined as the qualified verificationof the degree of grey incidence

Step 5 (predict future data) According to

and119909(1) (119896 + 1) = 9728182119890002119896 minus 953644and119909(0) (119896 + 1) = and119909(1) (119896 + 1) minus and119909(1) (119896)

(26)

a prediction of the next five steps was calculated as follows

and119883=

[[[[[[[[[[[[[[

and119909(0) (11)and119909(0) (12)and119909(0) (13)and119909(0) (14)and119909(0) (15)

]]]]]]]]]]]]]]

=[[[[[[[[[

23539562401622245025324998682550488

]]]]]]]]]

(27)

Step 6 (establish the graphical function) The GDP gross andits growth rate (2005-2020) were calculated using the abovesteps See Table 6 for specific results

Therefore onemay establish the graphical function of thegrowth of GDP

Graphical function of the growth of GDP= WITHLOOKUP (Amount of GDP ([(8e+011 0)- (3e+012 03)](81178e+011 01648) (98468e+011 0213) (11115e+01201288) (12153e+012 00934) (141136e+012 01613)(162519e+012 01515) (178794e+012 01001) (198008e+012 01075) (213308e+012 00773) (230146e+012 00789)(235396e+012 002281) (240162e+012 00203) (245025e+012 002025) (249987e+012 002024) (255049e+0120020249)))

Similarly onemay establish the Graphical function aboutthe growth rate of vehicle ownership See Appendix B forspecific results

(3)ThirdMethodThe purpose of this method is to determinesome variables with nonlinear characteristics because theyare difficult to define directly such as degree of air pollutionand air pollution control In the actual situation estimationswere conducted by utilizing data from the official website(M1) and the first two prediction methods Main basisSlightly adjust the change trend of the variables to meetthe actual change rules that have been observed in Beijingin recent years As a result several variables have been

8 Discrete Dynamics in Nature and Society

Table 7 Estimated values of pollution degree of NOx and PMx in Beijing

Time Amount of motor vehicles (vehicle) ANOG (t) APMG (t) Actual pollution degree2014 5591e+006 11182e+005 22364e+005 Serious pollution2013 5437e+006 10874e+005 21748e+005 Serious pollution2012 5200e+006 10400e+005 20800e+005 Moderate pollution2011 4983e+006 9966e+004 19932e+005 Moderate pollution2010 4809e+006 9618e+004 19236e+005 Moderate pollution2009 4019e+006 8038e+004 16076e+005 Mild pollution2008 3504e+006 7008e+004 14016e+005 Mild pollution2007 3072e+006 6144e+004 12288e+005 Mild pollution2006 2754e+006 5508e+004 11016e+005 Mild pollution

confirmed including the attraction degree of the city netmigration rate degree of air pollution air pollution controlattraction degree of vehicle trips attraction degree of growthof the vehicles and growth rate ofmotor vehiclesThe presentstudy characterized the degree of air pollution as an example

(a) Estimation of Degree of Air Pollution The present studyestimated the degree of air pollution mainly based on theamount of NOx generation (ANOG) and amount of PMxgeneration (APMG) in accordance with historical data inStatistical Yearbook of Beijing from 2006 to 2014 In additionthe methods were also combined to estimate the ANOG andAPMG See Table 7 for detailed results

According to the actual situation of air pollution causedby motor vehicle exhaust emission in Beijing serious pol-lution was observed from 2013 to 2014 moderate pollutionwas generated between 2010 and 2012 and mild pollutionoccurred before 2009Therefore this paper defines the degreeof air pollution caused by ANOG as follows

(I)The degree of air pollution exhibited a value range thatis defined as (0 1) wherein a value of 08 and above indicatesserious pollution a value lower than 08 but higher than 05means moderate pollution and a value lower than 05 meansmild pollution

(II) From 2013 to 2014 Beijing exhibited a very seriousdegree of air pollution such that the estimated value ofNOx pollution was characterized between 08 and 1 at acorresponding ANOG of 108740 t to 111820 t From 2010 to2012 the degree of air pollution was moderate such that theestimated value of pollution NOx was within the interval of(05 08) at a corresponding ANOG of 96180 t to 104000 tFrom 2006 to 2009 the pollution degree was mild such thatthe estimated value of NOx pollution was lower than 05

According to the provisions above establish the logicalfunction of pollution degree of NOx

Pollution degree of NOx = IF THEN ELSE (Amount ofNOxgenerationgt= 11182e+005 09 IFTHENELSE (Amountof NOx generationgt= 10874e+005 08 IF THEN ELSE(Amount of NOx generationgt= 10400e+005 07 IF THENELSE (Amount of NOx generationgt= 9966e+004 06 IFTHENELSE (Amount of NOx generationgt= 9618e+004 05IF THEN ELSE (Amount of NOx generationgt= 8038e+00403 IF THEN ELSE (Amount of NOx generationgt=7008e+004 025 IF THEN ELSE (Amount of NOx

generationgt= 6144e+004 02 IF THEN ELSE (Amount ofNOx generationgt= 5508e+004 015 01 )))))))))

In the same way one can establish the logical function ofpollution degree of PMx

Pollution degree of PMx = IF THEN ELSE (Amountof PMx generationgt= 22364e+005 09 IF THEN ELSE(Amount of PMx generationgt= 21748e+005 08 IF THENELSE (Amount of PMx generationgt= 20800e+005 07 IFTHEN ELSE (Amount of PMx generationgt= 19932e+00506 IF THEN ELSE (Amount of PMx generationgt=19236e+005 05 IF THEN ELSE (Amount of PMxgenerationgt= 16076e+005 03 IF THEN ELSE (Amountof PMx generationgt= 14016e+005 025 IF THEN ELSE(Amount of PMx generationgt= 12288e+005 02 IF THENELSE (Amount of PMx generationgt= 11016e+005 015 01)))))))))

Therefore

119863119890119892119903119890119890 119900119891 119886119894119903 119901119900119897119897119906119905119894119900119899= 120573 lowast 119901119900119897119897119906119905119894119900119899 119889119890119892119903119890119890 119900119891 119873119874119909 + 120574

lowast 119901119900119897119897119906119905119894119900119899 119889119890119892119903119890119890 119900119891 119875119872119909(28)

wherein 120573 refers to the weight ratio of NOx 120574 refers to weightratio of PMx and 120573 + 120574 = 1(b) Estimation of Net Migration Rate According to Jia et al(2017) the attraction degree in Beijing was calculated to beabout 07056 [24]

According to Table 2 the permanent resident populationin Beijing exhibited a mechanical increase from 2009 to2014 respectively 112163 109091 129313 107072 109656and 74654 persons Therefore the net migration rates wererespectively calculated as 603 556 641 517 519and 347 A continuously decreasing trend was observeddue to registered residence migration and settlement policiesin Beijing In addition the net migration rate (mean value)of 531 must be adjusted given that it is obviously higherthan 347 and is inconsistent with the actual conditionsin Beijing Therefore the present study set the followingconditions

119873119890119905 119898119894119892119903119886119905119894119900119899 119903119886119905119890= 119899119890119905 119898119894119892119903119886119905119894119900119899 119903119886119905119890119898119890119886119899 V119886119897119906119890

Discrete Dynamics in Nature and Society 9

(a) APMG APCF=5(a) APMG APCF=100(a) APMG APCF=1000

100000

125000

150000

175000

200000

ton

2011 2013 2015 2017 20192009Time (year)

(a) APMG

(b) ANOG APCF=5(b) ANOG APCF=100(b) ANOG APCF=1000

2011 2013 2015 2017 20192009Time (year)

80000

110000

140000

170000

200000

ton

(b) ANOG

(c) AMVT APCF=5(c) AMVT APCF=100(c) AMVT APCF=1000

2011 2013 2015 2017 20192009Time (year)

2 M

25 M

3 M

35 M

4 M

vehi

cle

(c) AMVT

Figure 3 Extreme condition test (a) APMG (b) ANOG (c) AMVT

times 119886119905119905119903119886119888119905119894119900119899 119889119890119892119903119890119890 119900119891 119888119894119905119910120572(29)

where 120572 refers to the impact factor of policy Based on thiscalculation 120572 = 15 generates calculations that are close tothe actual value See the appendixes for descriptions of theother variables and main equations

3 Simulation and Result Analysis

31 Model Test

311 Extreme Condition Test The extreme condition testmainly aims to inspect the stability applicability in extremeconditions and accuracy of the equations in the test modelto represent the change trends of the realistic system and theintentions of the decision maker

According to Figure 3(a) the APMG exhibited a continu-ous decrease following an increase in the APCF In particularthe minimum value of APMG was obtained when the APCFwas at the limit value (1000 yuandaysdotvehicle) In additionwhen APCF was equal to 5 the maximum APMG value wasobtained which is consistent with the actual laws therebyconfirming the stability of the model in extreme conditions

A deeper analysis indicated a larger interval between curves1 and 2 and a shorter interval between curves 2 and curve3 thereby indicating that the APCF did not exceed 100yuandaysdotvehicle

The change rules presented in Figures 3(b) and 3(c) weresimilar to those in Figure 3(a)

312 Sensitivity Test The model behaviors exhibited dif-ferent and sensitive results at different parameter valuesSpecifically the behavior model changed following an appro-priate change of parameter In addition the policies generatedthrough the model analysis changed following a change inparameters

According to Figure 4(a) with time all the curves firstrose and then slowly descended Specifically in the earlyperiod of policy implementation (before 2014) the effect wasnot obvious because part-time drivers may not have had adeep understanding of the purpose of the implementationand the significance of the APCF policy thereby resultingin a continuous increase in AMVT due to sharp increasein motor vehicle ownership The AMVT growth rate wasmore effectively controlled following a longer period due tocontinuous policy implementation and fulfilment After 2016the growth rate continuously decreased thereby allowing

10 Discrete Dynamics in Nature and Society

(a) AMVT APCF=5(a) AMVT APCF=10(a) AMVT APCF=20(a) AMVT APCF=30(a) AMVT APCF=40(a) AMVT APCF=50(a) AMVT APCF=60(a) AMVT APCF=70(a) AMVT APCF=80(a) AMVT APCF=90(a) AMVT APCF=100

2 M

25 M

3 M

35 M

4 Mve

hicle

2011 2013 2015 2017 20192009Time (year)

(a) AMVT

(b) APMG APCF=5(b) APMG APCF=10(b) APMG APCF=20(b) APMG APCF=30(b) APMG APCF=40(b) APMG APCF=50(b) APMG APCF=60(b) APMG APCF=70(b) APMG APCF=80(b) APMG APCF=90(b) APMG APCF=100

100000

125000

150000

175000

200000

ton

2011 2013 2015 2017 20192009Time (year)

(b) APMG

(c) ANOG APCF=5(c) ANOG APCF=10(c) ANOG APCF=20(c) ANOG APCF=30(c) ANOG APCF=40(c) ANOG APCF=50(c) ANOG APCF=60(c) ANOG APCF=70(c) ANOG APCF=80(c) ANOG APCF=90(c) ANOG APCF=100

80000

110000

140000

170000

200000

ton

2011 2013 2015 2017 20192009Time (year)

(c) ANOG

Figure 4 Sensitivity test (a) AMVT (b) APMG (c) ANOG

the APCF policy to exhibit good effects based on long-termpractice improvement and fulfilment

Following further analysis the AMVT exhibited amarginal decreasing effect following an increase in APCFfrom curve 1 to curve 6 especially in curves 3ndash6 whichindicates that a larger APCF is not always better The analysisresults are presented in Figures 4(b) and 4(c)

In conclusion the APCF value range was observed withinthe interval of [30 50] based on the above analysis from the

perspective of AMVT reduction (alleviate traffic jam) as wellas APMG and ANOG emission reduction Table 8 presentsthe detailed analysis results

32 Analysis of Results The AMVT exhibited a continuousdecrease following an increase in APCF which indicates theability of this policy to restrict increases in AMVT Specif-ically obvious changes were in the intervals of [5 10] and[10 20] wherein theAMVTexhibited a decrease of 166649

Discrete Dynamics in Nature and Society 11

and 105055 respectively The AMVT exhibited a decreaseof 35103 24912 and 16793 in the intervals of [20 30][30 40] and [40 50] respectivelyHoweverminimal changeswere observed in the interval of 50 yuandaysdotvehicle aboveIn addition the APMG exhibited a decrease of 13967789137 28538 20987 and 14128 respectively in theabove intervals and exhibited very minimal changes in theinterval of 50 above The ANOG exhibited similar changerules

Therefore the interval [30 50] is deemed a reasonablevalue range based on the analysis on the degree of effect ofdifferent APCFs on the AMVT APMG and ANOG

In particular the change trends of AMVT APMG andANOG were generally consistent as presented in Figure 6specifically Figure 5(d) Figures 5(a)ndash5(c) exhibited obviousdecreasing trend rates that were continuously weakened inthe interval of [30 50] In addition the change was verylimited as the APCF exceeded 50 yuandaysdotvehicle

Therefore an effective APCF range of [30 50]was chosenbased on the development trends analysis of the change ratesof the main variables

33 Model Validation Historical data (2009-2015) on theamount of motor vehicles and population in Beijing arepresented in Table 9 wherein the conformance of theirrespective GSID was tested

331 Qualified Verification of the Degree of Grey Incidenceon the Population of Beijing The original sequence and itssimulation value sequence are respectively presented asfollows

1198830 =[[[[[[[[[[

1199090 (1)1199090 (2)1199090 (3)

1199090 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

18600119890 + 00719619119890 + 00720186119890 + 00720693119890 + 00721148119890 + 00721516119890 + 00721705119890 + 007

]]]]]]]]]]]]]]]

1198831 =[[[[[[[[[[

1199091 (1)1199091 (2)1199091 (3)

1199091 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

186000119890 + 007187390119890 + 007188790119890 + 007190200119890 + 007191621119890 + 007193053119890 + 007194495119890 + 007

]]]]]]]]]]]]]]]

(30)

The following was derived based on their calculations

100381610038161003816100381611990401003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

11990900 (119896) + 1211990900 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 117145

100381610038161003816100381611990411003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

11990901 (119896) + 1211990901 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 025295

10038161003816100381610038161199040 minus 11990411003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

(11990901 (119896) minus 11990900 (119896)) + 12 (11990901 (7) minus 11990900 (7))

1003816100381610038161003816100381610038161003816100381610038161003816= 09185

(31)

Therefore we are able to obtain the value of the GAID

12058501 = 1 + 100381610038161003816100381611990401003816100381610038161003816 + 1003816100381610038161003816119904110038161003816100381610038161 + 100381610038161003816100381611990401003816100381610038161003816 + 100381610038161003816100381611990411003816100381610038161003816 + 10038161003816100381610038161199040 minus 11990411003816100381610038161003816= 1 + 117145 + 025295

1 + 117145 + 025295 + 09185 asymp 07275(32)

In a similar way

100381610038161003816100381610038161199041015840010038161003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

119909101584000 (119896) + 12119909101584000 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 062985100381610038161003816100381610038161199041015840110038161003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

119909101584001 (119896) + 12119909101584001 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 0136051003816100381610038161003816100381611990410158400 minus 1199041015840110038161003816100381610038161003816

=10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

(119909101584001 (119896) minus 119909101584000 (119896)) + 12 (119909101584001 (7) minus 119909101584000 (7))

1003816100381610038161003816100381610038161003816100381610038161003816= 04938

(33)

Therefore GRID is

11990301 = 1 + 100381610038161003816100381610038161199041015840010038161003816100381610038161003816 + 1003816100381610038161003816100381611990410158401100381610038161003816100381610038161 + 1003816100381610038161003816119904101584001003816100381610038161003816 + 1003816100381610038161003816119904101584011003816100381610038161003816 + 100381610038161003816100381611990410158400 minus 119904101584011003816100381610038161003816= 1 + 062985 + 013605

1 + 062985 + 013605 + 04938 asymp 07815(34)

When 120579 = 05 and exist1205760 = 07 then12057601 = 12057912058501 + (1 minus 120579) 11990301 = 05 times 07275 + 05 times 07815

= 07545 gt 07 = 1205760 (35)

Therefore according to Table 5 the accuracy was determinedto be between grade 2 and grade 3

332 Qualified Verification of the Degree of Grey Incidenceon the Amount of Motor Vehicles in Beijing The original

12 Discrete Dynamics in Nature and Society

Table 8 The effects of different APCFs on AMVT APNG and ANOG

APCF AMVT Trend Variation APMG Trend Variation ANOG Trend Variation() () ()

5 345229e+006 -- -- 161737 -- -- 154899 -- --10 287697e+006 darr -166649 139146 darr -139677 137782 darr -11050420 257473e+006 darr -105055 126743 darr -89137 128122 darr -7011130 248435e+006 darr -35103 123126 darr -28538 125306 darr -2197940 242246e+006 darr -24912 120542 darr -20987 123272 darr -1623250 238178e+006 darr -16793 118839 darr -14128 121928 darr -1090360 235237e+006 darr -12348 117604 darr -10392 120952 darr -0800570 232979e+006 darr -09599 116655 darr -08069 120202 darr -0620180 231171e+006 darr -07760 115894 darr -06524 119599 darr -0501790 229680e+006 darr -06450 115265 darr -05427 119101 darr -04164100 228421e+006 darr -05482 114734 darr -04607 118680 darr -03535

Table 9 Historical data and their simulation values (2009-2015)

Time Amount of motor vehicles (vehicle) Amount of population (person)Actual value Simulation value Actual value Simulation value

2009 4019e+006 401900e+006 18600e+007 186000e+0072010 4809e+006 457571e+006 19619e+007 187390e+0072011 4983e+006 528216e+006 20186e+007 188790e+0072012 5200e+006 560956e+006 20693e+007 190200e+0072013 5437e+006 577509e+006 21148e+007 191621e+0072014 5591e+006 584424e+006 21516e+007 193053e+0072015 5619e+006 591422e+006 21705e+007 194495e+007

sequence and its simulation value sequence were respec-tively calculated as follows

119883119894 =[[[[[[[[[[

119909119894 (1)119909119894 (2)119909119894 (3)

119909119894 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

4019119890 + 0064809119890 + 0064983119890 + 0065200119890 + 0065437119890 + 0065591119890 + 0065619119890 + 006

]]]]]]]]]]]]]]]

119883119895 =[[[[[[[[[[

119909119895 (1)119909119895 (2)119909119895 (3)

119909119895 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

401900119890 + 006457571119890 + 006528216119890 + 006560956119890 + 006577509119890 + 006584424119890 + 006591422119890 + 006

]]]]]]]]]]]]]]]

(36)

TheGAID andGRIDwere respectively calculated as follows

120585119894119895 asymp 09235119903119894119895 asymp 09390 (37)

Hence when exist1205760 = 09 and 120579 = 05120576119894119895 = 120579120585119894119895 + (1 minus 120579) 119903119894119895 = 09313 gt 09 = 1205760 (38)

Therefore according to Definition 3 and Table 5 thismodel verified the degree of grey incidence and exhibited anaccuracy belonging to grade 1

34 Policy Simulation Analysis and Discussion

341 Horizontal Analysis According to the horizontal anal-ysis the curves exhibited different changes with time Thespecific analysis results are presented as follows

Following the adoption of the low charge policy egAPCF = 5 yuandaysdotvehicle the AMVT (curve 1) exhibiteda decrease since about 2014 as exhibited in Figure 6(a)Although the growth rates of ANOG and APMG exhibited adecrease the total emissions maintained an increasing trendthereby resulting in high DAP levels (curve 4) The analysisresults indicate the inability of the low charge policy toeffectively reduce the DAP

According to Figure 6(f) curve 1 first exhibited aslow rise (before 2013) and a subsequent sharp descentfollowing the adoption of the high charge policy (APCF= 50 yuandaylowastvehicle) As a result the AMVT valuesdescended until 2013 wherein its descending range continu-ously increased Curve 3 terminated its previously continuousrise and instead descended slowly Similarly the rising rate

Discrete Dynamics in Nature and Society 13

0

2

4

6

8

10

12

14

16

18A

MV

T (

)

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

(a) AMVT

0

2

4

6

8

10

12

14

APM

G (

)

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

(b) APMG

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

0

2

4

6

8

10

12

AN

OG

()

(c) ANOG

AMVT ()APMG ()ANOG ()

0

2

4

6

8

10

12

14

16

18

5 20 8010 50 60 7030 9040 100

(d) Trend comparison

Figure 5 Development trends of the change rates of the main variables (a) AMVT (b) APMG (c) ANOG (d) Trend comparison

Table 10 The comparison of different policies

Variable APCF (yuandaylowastvehicle) Trend Variation ()5 50

AMVT (vehicle) 345229e+006 238178e+006 darr -3101APMG (t) 161737e+005 118839e+005 darr -2652ANOG (t) 154899e+005 121928e+005 darr -2129DAP 06 0525 darr -1250

of curve 2 slowed down relatively These results indicatethe effective control on the increase of APMG and ANOGafter which the values began to descend slowly Curve 4exhibited three phases specifically a rapid rise between 2011and 2014 a slow rise in rate between 2014 and 2018 and a slowdescent after 2018These results indicate the presence of DAPimprovements which exhibited gradual descent after 2018

The analysis results in Figures 6(b)ndash6(e) were similar tothose presented above

342 Vertical Analysis According to Figures 6(a)ndash6(f) theAPCF exhibited a continuous increase thereby generating achange in the rules of all the curves as follows

(i) AMVT (curve 1)TheAMVT exhibited a continuousdecrease Within a certain range the increase inAPCF aided in the descent of the AMVT therebyfurther alleviating the traffic pressures

(ii) APMG (curve 3) and ANOG (curve 2) A charge ofmore than 30 (Figures 6(d)ndash6(f)) generated a slowdescent in APMGMeanwhile the increase in ANOGalso exhibited effective restraint

(iii) DAP (curve 4)TheDAP exhibited an overall declineespecially following the implementation of a highcharge policy (APCF isin [40 50]) A subsequentdescending trend was later observed in the period ofanalogue simulation as presented in Figures 6(e) and6(f)

343 Comparison of Policies According to Table 10 in thepresence of a low charge policy (APCF=5) the AMVTAPMG ANOG and DAP under a high charge pol-icy exhibited an obvious decrease which indicates thatthe implementation of a high charge policy effectivelyreduced motor vehicle exhaust emissions to restrain the

14 Discrete Dynamics in Nature and Society

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

083 M

10000004

2 M00

2011 2013 2015 2017 20192009Time (year)

AMVT APCF=5ANOG APCF=5APMG APCF=5DAP APCF=5

vehicletontonDmnl

(a)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=10ANOG APCF=10APMG APCF=10DAP APCF=10

vehicletontonDmnl

(b)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=20ANOG APCF=20APMG APCF=20DAP APCF=20

vehicletontonDmnl

(c)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=30ANOG APCF=30APMG APCF=30DAP APCF=30

vehicletontonDmnl

(d)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=40ANOG APCF=40APMG APCF=40DAP APCF=40

vehicletontonDmnl

(e)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=50ANOG APCF=50APMG APCF=50DAP APCF=50

vehicletontonDmnl

(f)

Figure 6 Policy simulation (a) APCF=5 (b) APCF=10 (c) APCF=20 (d) APCF=30 (e) APCF=40 (f) APCF=50

intensification of ldquohazerdquo pollution degree in Beijing Specif-ically the gap between curves 1 and 2 exhibited a continuouswidening as presented in Figure 7(a) After 2013 curve 2exhibited an obvious descent Therefore the APCF policyeffectively reduced the AMVT and enabled an about 3101decrease in 2020

The results in Figures 7(b)ndash7(d) were similarly analyzed

In conclusion the adoption of a low charge policygenerated increasing APMG and ANOG trends as presentedin Figures 6(a) and 6(b) thereby suggesting the inabilityof the low charge policy to effectively reduce the DAP Anincrease of the fee to a certain extent especially followingthe implementation of a high charge policy (Figures 6(e) and6(f)) not only reduced the AMVT and alleviated traffic jams

Discrete Dynamics in Nature and Society 15

APCF=5

APCF=50

x 106

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 20202009Time (year)

2

25

3

35ve

hicle

(a) AMVT

APCF=5

APCF=50

x 105

20182017 2019 20202015 2016201420122011 201320102009Time (year)

11

12

13

14

15

16

17

ton

(b) APMG

APCF=5

APCF=50

x 105

08

09

1

11

12

13

14

15

16

ton

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 20202009Time (year)

(c) ANOG

02

APCF=5

APCF=50

2009 2011 20122010 20142013 2016 2017 20182015 20202019Time (year)

025

03

035

04

045

05

055D

mnl

(d) DAP

Figure 7 Comparison of the policies (a) AVT (b) APMG (c) ANOG (d) DAP

in cities but also effectively reduced the APMG and ANOGthereby reducing the DAP

According to a comparison on the different schemes atthe end of the analogue simulation period the high chargepolicy functioned as follows in terms of the emission reduc-tion of the motor vehicle exhaust the APMG and ANOGexhibited reductions of 2652 and 2129 respectively interms of alleviating traffic jams the AMVT exhibited a 3101decrease and in terms of reducing the degree of air pollutionthe DAP exhibited a 1250 decrease

4 Conclusions

41 Main Conclusions To resolve the air pollution problemsgenerated by motor vehicle exhaust emission the presentstudy introduced the charging mechanism and built a motorvehicle exhaust emission reduction strategy managementmodel using economic means and the SD-GM approach to

generate the following conclusions based on tests validationof the models and the simulation analysis of policies

(1)Within a certain range the reduction effects of APMGandANOGexhibited continuous enhancements following anincrease in APCF However the APCF did not always followthe principle ldquobigger means betterrdquo because the emissionreduction effect which was generated by an increase inthe APCF exhibited a marginal decreasing effect Accord-ing to the sensitivity analysis a pollution charge of 30ndash50yuandaysdotvehicle for the motor vehicles in Beijing was withinthe relatively reasonable range

(2) Three high charge policy functions were generatedbased on a comparison of the simulation results of thedifferent charging schemes the implementation of highcharge policies not only reduced the AMVT and alleviatedtraffic jams (Figures 6(e) 6(f) and 7(a) Table 10) but alsoeffectively reduced the APMG andANOG (Figures 6(e) 6(f)7(b) and 7(c) Tables 5 and 10) thereby further reducing theDAP (Figures 6(e) 6(f) and 7(d) Table 10) According to the

16 Discrete Dynamics in Nature and Society

contrastive analysis the DAP exhibited a decrease of about1250

(3) However the following problems were encounteredfollowing the implementation of the APCF policy (a) Theimplementation of the APCF policy increased the cost ofmotor vehicle trips and urged part-time drivers to take publictransportation which increased the burden of public trans-portation The subsidy policy and other applicable policiesmust be introduced to improve the public transport supplylevel and service quality Otherwise the trip demands ofpassengers will be difficult to satisfy which will influencethe implementation of the APCF policy (b) In the earlyperiods of APCF policy implementation an increase in thecost of motor vehicle trips due to the insufficient publicunderstanding and utilization of the APCF policy loweredits public support rate The government must strengthenits public relations work especially regarding the purposeand significance of its implementation to improve publicawareness and acknowledgment (c) The purpose of thesepolicies must be supervised and managed to gather APCFincome and improve public transportation infrastructures

42 Deficiencies and Future Work The present study consid-ered NOx and PMx as the principal motor vehicle emissionpollutants Future research must fully consider other com-ponents such as SO2 airborne particles hydrocarbons COand CO2 Secondly the implementation of a single chargingmeasure can reduce the supply level of public transportationFuture research should consider a subsidy mechanism toimprove the service quality Thirdly the function and effectof a single policy are limited Future work must considerthe integration of multiple policies to improve the emissionreduction effect For example future work may focus priorityon public transportation improvement of fuel quality vigor-ous promotion of new energy vehicles and improvements inemission standards

Appendix

A

See Table 11

B

Summary of the major variables and equations(1) Cost of motor vehicle trips = Air pollution charging

feelowast (1+ Air pollution control)(2) Amount ofNOx generation = INTEG (NOx emissions

- Annual dissipation of NOx 80380)(3) NOx emissions = Per vehicle annual of NOx

emissionslowast Amount of motor vehicle tripslowast Contributionrate of NOx from vehicle

(4) Contribution rate of NOx from vehicle = 05(5) Dissipation rate of NOx = 02(6) Annual dissipation of NOx = Amount of NOx

generationlowast Dissipation rate of NOx(7) Per vehicle annual of NOx emissions = 002

(8) Amount of PMx generation = INTEG (PMxemissions- Annual dissipation of PMx 160760)

(9) PMx emissions = Amount of motor vehicle tripslowastContribution rate of PMx from vehiclelowast Per vehicle annualof PMx emissions

(10) Contribution rate of PMx from vehicle = 05(11) Per vehicle annual of PMx emissions = 004(12) Annual dissipation of PMx = Amount of PMx

generationlowast Dissipation and control rate of PMx(13) Dissipation and control rate of PMx = 05(14) Pollution degree of NOx = IF THEN ELSE (Amount

of NOx generationgt= 11182e+005 09 IF THEN ELSE(Amount of NOx generationgt= 10874e+005 08 IF THENELSE (Amount of NOx generationgt= 10400e+005 07 IFTHEN ELSE (Amount of NOx generationgt= 9966e+00406 IF THEN ELSE (Amount of NOx generationgt=9618e+004 05 IF THEN ELSE (Amount of NOxgenerationgt= 8038e+004 03 IF THEN ELSE (Amountof NOx generationgt= 7008e+004 025 IF THEN ELSE(Amount of NOx generationgt= 6144e+004 02 IF THENELSE (Amount of NOx generationgt= 5508e+004 015 01)))))))))

(15) Pollution degree of PMx = IF THEN ELSE (Amountof PMx generationgt= 22364e+005 09 IF THEN ELSE(Amount of PMx generationgt= 21748e+005 08 IF THENELSE (Amount of PMx generationgt= 20800e+005 07 IFTHEN ELSE (Amount of PMx generationgt= 19932e+00506 IF THEN ELSE (Amount of PMx generationgt=19236e+005 05 IF THEN ELSE (Amount of PMxgenerationgt= 16076e+005 03 IF THEN ELSE (Amountof PMx generationgt= 14016e+005 025 IF THEN ELSE(Amount of PMx generationgt= 12288e+005 02 IF THENELSE (Amount of PMx generationgt= 11016e+005 015 01)))))))))

(16) Ratio of motor vehicle trips = 055(17) Amount of motor vehicle trips = Amount of motor

vehicleslowast Ratio of motor vehicle trips(18) Degree of air pollution = Weight ratio of NOxlowast

Pollution degree of NOx+ Weight ratio of PMxlowast Pollutiondegree of PMx

(19) Weight ratio of PMx = 05(20) Weight ratio of NOx = 05(21) Air pollution control = IF THEN ELSE (Degree of air

pollutiongt= 07 1 IF THEN ELSE (Degree of air pollutiongt=06 08 IF THEN ELSE (Degree of air pollutiongt= 05 07IF THEN ELSE (Degree of air pollutiongt= 04 06 IF THENELSE (Degree of air pollutiongt= 03 05 IF THEN ELSE(Degree of air pollutiongt= 025 045 IF THENELSE (Degreeof air pollutiongt= 02 04 IF THEN ELSE (Degree of airpollutiongt= 015 035 03))))))))

(22) Attraction degree of the growth of vehicles= (1-Airpollution control)lowast 055+ Attraction degree of vehicle tripslowast045

(23) Per capita annual income = Amount of GDPAmount of population

(24) Amount of population = INTEG (Growth of popu-lation+ Net migration- Population reduction 186e+007)

(25) Birth rate = Adjustment coefficient of birth ratelowastPredictive value of birth rate

Discrete Dynamics in Nature and Society 17

Table 11 Description of main variables in stock flow diagram

Signicant variable Unit Variable type Data sourceAir pollution charging fee yuandaysdotvehicle ConstantAir pollution control Dmnl Auxiliary variable M1+M3Amount of GDP yuan Level M1Amount of motor vehicles vehicle Level M1Amount of motor vehicle trips vehicle Auxiliary variableAmount of NOx (PMx) generation ton Level M1Amount of population person Level M1Annual dissipation of NOx (PMx) tonyear FlowAnnual scrapped vehicleyear FlowAttraction degree of city Constant M2Attraction degree of the growth of vehicles Auxiliary variable M1+M3Attraction degree of vehicle trips Auxiliary variable M1+M3Birth rate 1year Constant M3Contribution rate of NOx (PMx) from vehicle Constant M2Cost of motor vehicle trips yuandaysdotvehicle Auxiliary variable M3Death rate 1year Constant M3Degree of air pollution Dmnl Auxiliary variable M3Dissipation and control rate of NOx (PMx) 1year Constant M2Graphical function of the growth of GDP Dmnl Auxiliary variable M3Growth of GDP yuanyear FlowGrowth rate of motor vehicles 1year Auxiliary variable M1+M3Growth of motor vehicles vehicleyear FlowGrowth of population personyear FlowGrowth rate of vehicle ownership Dmnl Auxiliary variable M1+M3Impact factor of policy Dmnl Constant M3Net migration personyear FlowNet migration rate 1year Constant M1+M3NOx (PMx) emissions tonyear FlowPer capita annual income yuanperson Auxiliary variablePer vehicle annual of NOx (PMx) emissions tonyearsdotvehicle Constant M2Pollution degree of NOx (PMx) Dmnl Auxiliary variable M1+M3Population reduction personyear FlowRatio of motor vehicle trips Constant M2Scrap rate 1year Constant M2The average of net migration rate 1year Constant M1Weight ratio of PMx (NOx) Auxiliary variable M3

(26) Predictive value of birth rate = 000925(27) Death rate = Adjustment coefficient of death ratelowast

Predictive value of death rate(28) Predictive value of death rate = 000494(29) Net migration = Amount of populationlowastNet migra-

tion rate(30) Net migration rate = The average of net migration

ratelowast Attraction degree of cityand(Impact factor of policy)(31) Impact factor of policy = 15(32) The average of net migration rate = 000531(33) Attraction degree of city = 07056(34) Amount of GDP = INTEG (Growth of GDP

12153e+012)

(35) Graphical function of the growth of GDP = WITHLOOKUP (Amount of GDP ([(8e+011 0)- (3e+ 012 03)](81178e+011 01648) (98468e+011 0213) (11115e+01201288) (12153e+012 00934) (141136e+012 01613)(162519e+012 01515) (178794e+012 01001) (198008e+01201075) (213308e+012 00773) (230146e+012 00789)(235396e+012 002281) (240162e+012 00203) (245025e+012 002025) (249987e+012 002024) (255049e+0120020249)))

(36) Growth rate of GDP = Graphical function of thegrowth of GDPlowast Impact factor of the growth of GDP

(37) Amount of motor vehicles = INTEG (Growth ofmotor vehicles- Annual scrapped 4019e+006)

18 Discrete Dynamics in Nature and Society

(38) Annual scrapped = Amount of motor vehicleslowastScrap rate

(39) Scrap rate = 0067

Conflicts of Interest

The author declares no conflicts of interest

Acknowledgments

This work has been partially supported by the NationalNatural Science Foundation of China (71571119) ShanghaiFirst-Class Academic Discipline Project (S1201YLXK) andChina Postdoctoral Science Foundation (2018M630404)Theauthor would like to thank LetPub (httpwwwletpubcom)for providing linguistic assistance during the preparation ofthis manuscript

References

[1] X Liu S Ma J Tian N Jia and G Li ldquoA system dynamicsapproach to scenario analysis for urban passenger transportenergy consumption and CO2 emissions A case study ofBeijingrdquo Energy Policy vol 85 pp 253ndash270 2015

[2] B Xu L Luo and B Lin ldquoA dynamic analysis of air pollutionemissions in China Evidence from nonparametric additiveregression modelsrdquo Ecological Indicators vol 63 pp 346ndash3582016

[3] S Leinert H Daly B Hyde and B O Gallachoir ldquoCo-benefitsNot always Quantifying the negative effect of a CO2-reducingcar taxation policy on NOx emissionsrdquo Energy Policy vol 63pp 1151ndash1159 2013

[4] Z Cheng L Li and J Liu ldquoIdentifying the spatial effects anddriving factors of urban PM25 pollution in Chinardquo EcologicalIndicators vol 82 pp 61ndash75 2017

[5] N Kaida and K Kaida ldquoSpillover effect of congestion chargingon pro-environmental behaviorrdquo Environment Developmentand Sustainability vol 17 no 3 pp 409ndash421 2015

[6] R Penabaena-Niebles V Cantillo and J L Moura ldquoImpactof transition between signal timing plans in social cost basedin delay fuel consumption and air emissionsrdquo TransportationResearch Part D Transport and Environment vol 41 pp 445ndash456 2015

[7] DDing andB Shuai ldquoA traffic restriction scheme for enhancingcarpoolingrdquoDiscreteDynamics inNature and Society Article ID9626938 9 pages 2017

[8] D Kong X Guo B Yang and D Wu ldquoAnalyzing the Impactof Trucks on Traffic Flow Based on an Improved CellularAutomaton Modelrdquo Discrete Dynamics in Nature and Societyvol 2016 pp 1ndash14 2016

[9] S Cakmak C Hebbern J D Cakmak and J Vanos ldquoThemodifying effect of socioeconomic status on the relationshipbetween traffic air pollution and respiratory health in elemen-tary schoolchildrenrdquo Journal of Environmental Managementvol 177 pp 1ndash8 2016

[10] L Song H Song J Lin et al ldquoPM25 emissions from differenttypes of heavy-duty truck a case study and meta-analysis ofthe Beijing-Tianjin-Hebei regionrdquo Environmental Science andPollution Research vol 24 no 12 pp 11206ndash11214 2017

[11] Z Hu S Kang C Li et al ldquoLight absorption of biomassburning and vehicle emission-sourced carbonaceous aerosolsof the Tibetan Plateaurdquo Environmental Science and PollutionResearch vol 24 no 18 pp 15369ndash15378 2017

[12] X Cen H K Lo and L Li ldquoA framework for estimating trafficemissions The development of Passenger Car Emission UnitrdquoTransportation Research Part D Transport and Environmentvol 44 pp 78ndash92 2016

[13] S Wang X Liu C Zhou J Hu and J Ou ldquoExamining theimpacts of socioeconomic factors urban form and transporta-tion networks on CO2 emissions in Chinarsquos megacitiesrdquoAppliedEnergy vol 185 pp 189ndash200 2017

[14] Q Wang K Hubacek K Feng Y-M Wei and Q-M LiangldquoDistributional effects of carbon taxationrdquo Applied Energy vol184 pp 1123ndash1131 2016

[15] C Johansson L Burman and B Forsberg ldquoThe effects ofcongestions tax on air quality and healthrdquo Atmospheric Envi-ronment vol 43 no 31 pp 4843ndash4854 2009

[16] A Rakowska K C Wong T Townsend et al ldquoImpact of trafficvolume and composition on the air quality and pedestrianexposure in urban street canyonrdquo Atmospheric Environmentvol 98 pp 260ndash270 2014

[17] S Batterman R Ganguly and P Harbin ldquoHigh resolutionspatial and temporal mapping of traffic-related air pollutantsrdquoInternational Journal of Environmental Research and PublicHealth vol 12 no 4 pp 3646ndash3666 2015

[18] J Eliasson M Borjesson D van Amelsfort K Brundell-Freijand L Engelson ldquoAccuracy of congestion pricing forecastsrdquoTransportation Research Part A Policy and Practice vol 52 pp34ndash46 2013

[19] J Eliasson ldquoThe role of attitude structures direct experienceand reframing for the success of congestion pricingrdquo Trans-portation Research Part A Policy and Practice vol 67 pp 81ndash952014

[20] H X Yang J D Li H Zhang and S Q Liu ldquoResearch on thegovernance of urban traffic jam based on system dynamicsrdquoSystems EngineeringTheory and Practice vol 34 no 8 pp 2135ndash2143 2014 (Chinese)

[21] M H Zhu Research on Socio-Economic Impact of UrbanTrafficCongestion [PhD thesis] Beijing JiaotongUniversity 2013(Chinese)

[22] B Zeng Research on Modeling Technologies of Grey Prediction[PhD thesis] Nanjing University of Aeronautics and Astronau-tics 2011 (Chinese)

[23] S F Liu Y J Yang and L F Wu Grey System Theory andApplication Science Press Beijing China 2017

[24] S W Jia K Yang J J Zhao and G L Yan ldquoThe traffic-congestion charging fee management model based on thesystem dynamics approachrdquo Mathematical Problems in Engi-neering vol 2017 Article ID 3024898 13 pages 2017

Discrete Dynamics in Nature and Society 3

Amount of GDPGrowth of GDP

Growth rate of GDP

Amount ofpopulation

Growth ofpopulation

Predictive valueof birth rate Predictive value

of death rate

Net migration rate

Attraction degreeof city

Per capita annualincome

Populationreduction

Net migration

The average of netmigration rate

Impact factorof policy

Impact factor of thegrowth of GDP

Adjustment coefficientof birth rate

Adjustment coefficientof death rate

Graphical function ofthe growth of GDP

Amount of NOxgeneration (ANOG)NOx emissions

Per vehicle annual ofNOx emissions

Dissipation rate ofNOx

Pollution degreeof NOx

Air pollutioncontrol

Annual dissipationof NOx

Contribution rate ofNOx from vehicle

Degree of air pollution(DAP)

Weight ratio of NOx

Weight ratio ofPMx

Attraction degree of thegrowth of vehicles

Growth rate ofmotor vehicles

Growth rate of vehicleownership

Amount of motor vehicletrips (AMVT)

Ratio of motorvehicle trips

Amount of PMxgeneration (APMG)

PMx emissionsDissipation and control

rate of PMxAnnual dissipation of PMx

Contribution rate of PMx from vehicle

Per vehicle annualof PMx emissions

Pollution degreeof PMx

Amount of motorvehicles

Growthof motorvehicles

Annualscrapped

Scraprate

Air pollution chargingfee (APCF)

Attraction degree ofvehicle trips Cost of motor

vehicle trips

ltTimegt

Birth rateDeathrate

Figure 1 Stock-flow diagram of the motor vehicle pollution charging management model

Degree of airpollution

Amount of motorvehicles

NOx (PMx)emissions

+

Growth of motorvehicles

Attraction degree ofgrowth of vehicles

Cost of motorvehicle trips

Attraction degreeof vehicle trips

+

+

-

Air pollutioncontrol

+

+

B1

+

Amount of motorvehicle trips

+

+

(a)

Amount of motorvehicles

Growth rate ofmotor vehicles

Air pollutioncontrol

-

Amount of motorvehicle trips

NOx (PMx)emissions

Degree of airpollution

+

+ B2

Attraction degree ofgrowth of vehicles-

+

+

+

(b)

Figure 2 Major loops (a) Negative feedback loop of NOx (PMx) emissions (b) Negative feedback loop of AMVT

4 Discrete Dynamics in Nature and Society

Table 1 Historical values of the main status variables (data is from 2010-2015 Statistical Yearbook of Beijing)

Time 2009 2010 2011 2012 2013 2014Amount of motor vehicles 4019 4809 4983 5200 5437 5591(10000 vehicles)Amount of population 18600 19619 20186 20693 21148 21516(10000 persons)GDP gross 121530 141136 162519 178794 198008 213308(100 million yuan)

Table 2 Historical values of main correlated variables Unit person

Time 2009 2010 2011 2012 2013 2014Mechanical increase 112163 109091 129313 107072 109656 74654Inflows 189744 185101 211447 190510 198869 166600Outflows 77581 76010 82134 83438 89213 91946

Table 3 Predictive value of birth rate and its average

Time 2015 2016 2017 2018 2019 2020Predictive value 873permil 894permil 914permil 935permil 956permil 977permilAverage 925permil

Table 4 Predictive value of death rate and its average

Time 2015 2016 2017 2018 2019 2020Predictive value 473permil 483permil 464permil 504permil 515permil 525permilAverage 494permil

generated major errors in the mean-based forecast andestimation which failed to meet the laws of change anddata information development The data was first processedusing theoretical methods such as regression analysis andgrey prediction Valuable implicit rules were then gener-ated in accordance with the actual changes in the datatrends Finally a nonlinear relationship between variableswas characterized in accordance with the graphical functionlogical function etc Three methods are given in the follow-ing

(1) First Method The aim of this method is to determinea reasonable value to meet the actual situation of Beijingin recent years Statistical approaches (such as regressionanalysis) based on large sample data can be used because ofthe abundance of data on birth and death ratesThe value wasfirst predicted by regression analysis after which the meanvalue was calculated Finally the value was slightly adjustedby combining the actual change trends of the variables todetermine the birth rate and death rate

Tables 3 and 4 present the predicted data that wereobtained from the regression analysis on the historical birthrate and death rate values of the permanent resident pop-ulation in Beijing However the implementation of a pop-ulation policy specifically the ldquotwo-child policyrdquo generatedan increase in the birth rate And the death rate remainedat about 5 These results were consistent with the currentstatus of Beijing

(2) Second Method The goal of this method is to describethe dynamic trends between variables by using the graphicalfunction Especially grey prediction model can improvethe prediction accuracy by the use of accumulated gener-ating operator and buffer operator Predictions were firstconducted using the GM (11) model in the absence of anobvious relationship between the variables or in the presenceof imperfect data information Subsequently graphical orlogical functions were generated by combining the actualchange rules of the variables This method was used todetermine the growth rate of the gross domestic product(GDP) and vehicle ownership growth rate Taking the GDPgrowth rate in Beijing as an example the detailed calculationsare presented in the following

Definition 1 Assume that the original sequence is

119883(0) = (119909(0) (1) 119909(0) (2) 119909(0) (119899)) (1)

119883(1) is its accumulation generated sequence (1-AGO)

119883(1) = (119909(1) (1) 119909(1) (2) 119909(1) (119899)) (2)

wherein

119909(1) (119896) = 119896sum119894=1

119909(0) (119894) 119896 = 1 2 119899 (3)

Discrete Dynamics in Nature and Society 5

such that119889119909(1)119889119905 + 119886119909(1) = 119887 (4)

The preceding equation is the winterization equation of thegrey GM (11) prediction model [22]

If 119909(0)(119896) ge 0 119896 = 1 2 119899 then and119886 = (119886 119887)119879 is theparameter list and satisfies

and119886 = (119886 119887)119879 = (119861119879119861)minus1 119861119879119884 (5)

wherein

119861 =[[[[[[[[[[[[

minus119909(1) (1) + 119909(1) (2)2 1

minus119909(1) (2) + 119909(1) (3)2 1

minus119909(1) (119899 minus 1) + 119909(1) (119899)2 1

]]]]]]]]]]]]

119884 =[[[[[[[[

119909(0) (2)119909(0) (3)

119909(0) (119899)

]]]]]]]]

(6)

(i) Time response formula of the solution of the winterizationequation 119889119909(1)119889119905 + 119886119909(1) = 119887 is

119909(1) (119905) = (119909(1) (1) minus 119887119886) 119890minus119886119905 + 119887

119886 (7)

(ii) Time response formula of the GM(11) model 119909(0)(119896) + 119886 sdot(119909(1)(119896) + 119909(1)(119896 minus 1))2 = 119887 isand119909(1) (119896 + 1) = (119909(0) (1) minus 119887

119886) 119890minus119886119896 + 119887119886 119896 = 1 2 3 119899

(8)

(iii) Predicted value model of the original model is

and119884 (119896 + 1) = and119909(0) (119896 + 1) = and119909(1) (119896 + 1) minus and119909(1) (119896)= (1 minus 119890119886) (119909(0) (1) minus 119887

119886) 119890minus119886119896(9)

The following definitions are provided in Liu et al [23]

Definition 2 Assume that the images of zero starting point ofthese two sequences

119883119894 = (119909119894 (1) 119909119894 (2) 119909119894 (119899)) 119883119895 = (119909119895 (1) 119909119895 (2) 119909119895 (119899)) (10)

are

1198830119894 = (1199090119894 (1) 1199090119894 (2) 1199090119894 (119899)) 1198830119895 = (1199090119895 (1) 1199090119895 (2) 1199090119895 (119899)) (11)

such that

120585119894119895 = 1 + 10038161003816100381610038161199041198941003816100381610038161003816 + 10038161003816100381610038161003816119904119895100381610038161003816100381610038161 + 10038161003816100381610038161199041198941003816100381610038161003816 + 1003816100381610038161003816100381611990411989510038161003816100381610038161003816 + 10038161003816100381610038161003816119904119894 minus 11990411989510038161003816100381610038161003816 (12)

The presented equation is the absolute degree of grey inci-dence (GAID) of 119883119894 and 119883119895 Assume that 119883119894 and 119883119895 aresequences of the same length with nonzero initial values 1198831015840119894and 1198831015840119895 are the initial images of 119883119894 and 119883119895 respectively 11988310158400119894and11988310158400119895 are the images of the zero starting point of sequences1198831015840119894 and 1198831015840119895 respectively and the GAID of 1198831015840119894 and 1198831015840119895 is calledthe relative degree of grey incidence (GRID) of 119883119894 and 119883119895Based on these definitions the following equation is thendefined

119903119894119895 = 1 + 10038161003816100381610038161003816119904101584011989410038161003816100381610038161003816 + 100381610038161003816100381610038161199041015840119895100381610038161003816100381610038161 + 100381610038161003816100381611990410158401198941003816100381610038161003816 + 10038161003816100381610038161003816119904101584011989510038161003816100381610038161003816 + 100381610038161003816100381610038161199041015840119894 minus 119904101584011989510038161003816100381610038161003816 (13)

such that

120576119894119895 = 120579120585119894119895 + (1 minus 120579) 119903119894119895 (14)

is defined as the synthetic degree of grey incidence (GSID) of119883119894 and 119883119895 wherein 120579 isin [0 1]Definition 3 Assume that119883(0) is the original sequence and119883(0) isits simulative sequence and 120576 is the degree of grey incidencebetween 119883(0) and and119883(0) In the case of 120576 gt 1205760 for the given1205760 gt 0 this model is defined as the qualified verification ofthe degree of grey incidence See Table 5 for the accuracy testgrade

The requirement of this model for correlation 120576 is ldquothebigger the betterrdquo

Step 1 (data processing) First write the original data as theform of sequence

119883(0) = (119909(0) (1) 119909(0) (2) 119909(0) (10))= (81178 98468 111150 121530 141136 162519 178794 198008 213308 230146)

(15)

6 Discrete Dynamics in Nature and Society

Second introduce the second-order average weakeningoperator 1198632 as

119883(0)1198632 = (119909(0) (1) 1198892 119909(0) (2) 1198892 119909(0) (10) 1198892) (16)

wherein

119909(0) (119896) 1198892 = 110 minus 119896 + 1 [119909(0) (119896) 119889 + 119909(0) (119896 + 1) 119889

+ + 119909(0) (10) 119889] 119909(0) (119896) 119889 = 1

10 minus 119896 + 1 [119909(0) (119896) + 119909(0) (119896 + 1) + + 119909(0) (10)] 119896 = 1 2 3 10

(17)

Obtain

119883(0)1198632 = (191742 195978 200266 20465 209105 213463 21769 221898 225937 230146) ≜ 119883= (119909 (1) 119909 (2) 119909 (3) 119909 (10)) (18)

Step 2 Calculate the 1-AGO sequence of sequence 119883 andobtain sequence 119883(1)

119883(1) = (119909(1) (1) 119909(1) (2) 119909(1) (3) 119909(1) (10))= (191742 38772 587986 792636 1001741 1215204 1432894 1654792 1880729 2110875) (19)

Step 3 Calculate its simulative sequence based on the greyGM (11) prediction model

According to Definition 1 the grey GM (11) predictionmodel is used to obtain the time response formula as follows

and119909(1) (119896 + 1) = 9728182119890002119896 minus 953644and119884 (119896 + 1) = and119909(0) (119896 + 1) = and119909(1) (119896 + 1) minus and119909(1) (119896)

(20)

The simulative sequence can then be calculated as

and119883= (and119909 (1) and119909 (2) and119909 (10))= (191742 196536 2005157 204576 2087185 2129448 2172568 2216561 2261444 2307236)

(21)

Step 4 (accuracy test) According to Steps 1 and 3 the originalsequence and its simulative sequence were respectivelycalculated as follows

119883 =[[[[[[[[[[

119909 (1)119909 (2)119909 (3)

119909 (10)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[[[[[[[[[

191742195978200266204650209105213463217690221898225937230146

]]]]]]]]]]]]]]]]]]]]]]]

and119883 =

[[[[[[[[[[[[[

and119909 (1)and119909 (2)and119909 (3)

and119909 (10)

]]]]]]]]]]]]]

=

[[[[[[[[[[[[[[[[[[[[[[[

191742196536020051572045760208718521294482172568221656122614442307236

]]]]]]]]]]]]]]]]]]]]]]]

(22)

Therefore one can calculate

|119904| =10038161003816100381610038161003816100381610038161003816100381610038169sum119896=2

[119909 (119896) minus 119909 (1)] + 12 [119909 (10) minus 119909 (1)]

1003816100381610038161003816100381610038161003816100381610038161003816

Discrete Dynamics in Nature and Society 7

Table 5 Reference list of accuracy test grade

Accuracy grade Grade 1 Grade 2 Grade 3 Grade 4Degree of grey incidence 1205760 090 080 070 060

Table 6 Amount of GDP and its growth rate

Time Amount of GDP (t) Growth rate Time Amount of GDP (t) Growth rate2005 69695e+011 --- 2013 198008e+012 010752006 81178e+011 01648 2014 213308e+012 007732007 98468e+011 02130 2015 230146e+012 007892008 11115e+012 01288 2016 2353956e+012 0022812009 12153e+012 00934 2017 2401622e+012 0020302010 141136e+012 01613 2018 2450253e+012 0020252011 162519e+012 01515 2019 2499868e+012 0020242012 178794e+012 01001 2020 2550488e+012 0020249

= 1742531003816100381610038161003816100381610038161003816and1199041003816100381610038161003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816100381610038169sum119896=2

[and119909 (119896) minus and119909 (1)] + 12 [and119909 (10) minus and119909 (1)]

1003816100381610038161003816100381610038161003816100381610038161003816= 1739031

1003816100381610038161003816100381610038161003816and119904 minus1199041003816100381610038161003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816100381610038169sum119896=2

[119909 (119896) minus 119909 (1) minus (and119909 (119896) minus and119909 (1))]

+ 12 [119909 (10) minus 119909 (1) minus (and119909 (10) minus and119909 (1))]

1003816100381610038161003816100381610038161003816100381610038161003816 = 3499(23)

such that

120585 = 1 + |119904| + 1003816100381610038161003816100381610038161003816and1199041003816100381610038161003816100381610038161003816

1 + |119904| + 1003816100381610038161003816100381610038161003816and1199041003816100381610038161003816100381610038161003816 +

1003816100381610038161003816100381610038161003816and119904 minus1199041003816100381610038161003816100381610038161003816

asymp 09990 (24)

Similarly 119903 = 09993 when 120579 = 05 exist1205760 = 09 therebydefining

120576 = 120579120585 + (1 minus 120579) 119903 = 09991 gt 09 = 1205760 (25)

Therefore this model is defined as the qualified verificationof the degree of grey incidence

Step 5 (predict future data) According to

and119909(1) (119896 + 1) = 9728182119890002119896 minus 953644and119909(0) (119896 + 1) = and119909(1) (119896 + 1) minus and119909(1) (119896)

(26)

a prediction of the next five steps was calculated as follows

and119883=

[[[[[[[[[[[[[[

and119909(0) (11)and119909(0) (12)and119909(0) (13)and119909(0) (14)and119909(0) (15)

]]]]]]]]]]]]]]

=[[[[[[[[[

23539562401622245025324998682550488

]]]]]]]]]

(27)

Step 6 (establish the graphical function) The GDP gross andits growth rate (2005-2020) were calculated using the abovesteps See Table 6 for specific results

Therefore onemay establish the graphical function of thegrowth of GDP

Graphical function of the growth of GDP= WITHLOOKUP (Amount of GDP ([(8e+011 0)- (3e+012 03)](81178e+011 01648) (98468e+011 0213) (11115e+01201288) (12153e+012 00934) (141136e+012 01613)(162519e+012 01515) (178794e+012 01001) (198008e+012 01075) (213308e+012 00773) (230146e+012 00789)(235396e+012 002281) (240162e+012 00203) (245025e+012 002025) (249987e+012 002024) (255049e+0120020249)))

Similarly onemay establish the Graphical function aboutthe growth rate of vehicle ownership See Appendix B forspecific results

(3)ThirdMethodThe purpose of this method is to determinesome variables with nonlinear characteristics because theyare difficult to define directly such as degree of air pollutionand air pollution control In the actual situation estimationswere conducted by utilizing data from the official website(M1) and the first two prediction methods Main basisSlightly adjust the change trend of the variables to meetthe actual change rules that have been observed in Beijingin recent years As a result several variables have been

8 Discrete Dynamics in Nature and Society

Table 7 Estimated values of pollution degree of NOx and PMx in Beijing

Time Amount of motor vehicles (vehicle) ANOG (t) APMG (t) Actual pollution degree2014 5591e+006 11182e+005 22364e+005 Serious pollution2013 5437e+006 10874e+005 21748e+005 Serious pollution2012 5200e+006 10400e+005 20800e+005 Moderate pollution2011 4983e+006 9966e+004 19932e+005 Moderate pollution2010 4809e+006 9618e+004 19236e+005 Moderate pollution2009 4019e+006 8038e+004 16076e+005 Mild pollution2008 3504e+006 7008e+004 14016e+005 Mild pollution2007 3072e+006 6144e+004 12288e+005 Mild pollution2006 2754e+006 5508e+004 11016e+005 Mild pollution

confirmed including the attraction degree of the city netmigration rate degree of air pollution air pollution controlattraction degree of vehicle trips attraction degree of growthof the vehicles and growth rate ofmotor vehiclesThe presentstudy characterized the degree of air pollution as an example

(a) Estimation of Degree of Air Pollution The present studyestimated the degree of air pollution mainly based on theamount of NOx generation (ANOG) and amount of PMxgeneration (APMG) in accordance with historical data inStatistical Yearbook of Beijing from 2006 to 2014 In additionthe methods were also combined to estimate the ANOG andAPMG See Table 7 for detailed results

According to the actual situation of air pollution causedby motor vehicle exhaust emission in Beijing serious pol-lution was observed from 2013 to 2014 moderate pollutionwas generated between 2010 and 2012 and mild pollutionoccurred before 2009Therefore this paper defines the degreeof air pollution caused by ANOG as follows

(I)The degree of air pollution exhibited a value range thatis defined as (0 1) wherein a value of 08 and above indicatesserious pollution a value lower than 08 but higher than 05means moderate pollution and a value lower than 05 meansmild pollution

(II) From 2013 to 2014 Beijing exhibited a very seriousdegree of air pollution such that the estimated value ofNOx pollution was characterized between 08 and 1 at acorresponding ANOG of 108740 t to 111820 t From 2010 to2012 the degree of air pollution was moderate such that theestimated value of pollution NOx was within the interval of(05 08) at a corresponding ANOG of 96180 t to 104000 tFrom 2006 to 2009 the pollution degree was mild such thatthe estimated value of NOx pollution was lower than 05

According to the provisions above establish the logicalfunction of pollution degree of NOx

Pollution degree of NOx = IF THEN ELSE (Amount ofNOxgenerationgt= 11182e+005 09 IFTHENELSE (Amountof NOx generationgt= 10874e+005 08 IF THEN ELSE(Amount of NOx generationgt= 10400e+005 07 IF THENELSE (Amount of NOx generationgt= 9966e+004 06 IFTHENELSE (Amount of NOx generationgt= 9618e+004 05IF THEN ELSE (Amount of NOx generationgt= 8038e+00403 IF THEN ELSE (Amount of NOx generationgt=7008e+004 025 IF THEN ELSE (Amount of NOx

generationgt= 6144e+004 02 IF THEN ELSE (Amount ofNOx generationgt= 5508e+004 015 01 )))))))))

In the same way one can establish the logical function ofpollution degree of PMx

Pollution degree of PMx = IF THEN ELSE (Amountof PMx generationgt= 22364e+005 09 IF THEN ELSE(Amount of PMx generationgt= 21748e+005 08 IF THENELSE (Amount of PMx generationgt= 20800e+005 07 IFTHEN ELSE (Amount of PMx generationgt= 19932e+00506 IF THEN ELSE (Amount of PMx generationgt=19236e+005 05 IF THEN ELSE (Amount of PMxgenerationgt= 16076e+005 03 IF THEN ELSE (Amountof PMx generationgt= 14016e+005 025 IF THEN ELSE(Amount of PMx generationgt= 12288e+005 02 IF THENELSE (Amount of PMx generationgt= 11016e+005 015 01)))))))))

Therefore

119863119890119892119903119890119890 119900119891 119886119894119903 119901119900119897119897119906119905119894119900119899= 120573 lowast 119901119900119897119897119906119905119894119900119899 119889119890119892119903119890119890 119900119891 119873119874119909 + 120574

lowast 119901119900119897119897119906119905119894119900119899 119889119890119892119903119890119890 119900119891 119875119872119909(28)

wherein 120573 refers to the weight ratio of NOx 120574 refers to weightratio of PMx and 120573 + 120574 = 1(b) Estimation of Net Migration Rate According to Jia et al(2017) the attraction degree in Beijing was calculated to beabout 07056 [24]

According to Table 2 the permanent resident populationin Beijing exhibited a mechanical increase from 2009 to2014 respectively 112163 109091 129313 107072 109656and 74654 persons Therefore the net migration rates wererespectively calculated as 603 556 641 517 519and 347 A continuously decreasing trend was observeddue to registered residence migration and settlement policiesin Beijing In addition the net migration rate (mean value)of 531 must be adjusted given that it is obviously higherthan 347 and is inconsistent with the actual conditionsin Beijing Therefore the present study set the followingconditions

119873119890119905 119898119894119892119903119886119905119894119900119899 119903119886119905119890= 119899119890119905 119898119894119892119903119886119905119894119900119899 119903119886119905119890119898119890119886119899 V119886119897119906119890

Discrete Dynamics in Nature and Society 9

(a) APMG APCF=5(a) APMG APCF=100(a) APMG APCF=1000

100000

125000

150000

175000

200000

ton

2011 2013 2015 2017 20192009Time (year)

(a) APMG

(b) ANOG APCF=5(b) ANOG APCF=100(b) ANOG APCF=1000

2011 2013 2015 2017 20192009Time (year)

80000

110000

140000

170000

200000

ton

(b) ANOG

(c) AMVT APCF=5(c) AMVT APCF=100(c) AMVT APCF=1000

2011 2013 2015 2017 20192009Time (year)

2 M

25 M

3 M

35 M

4 M

vehi

cle

(c) AMVT

Figure 3 Extreme condition test (a) APMG (b) ANOG (c) AMVT

times 119886119905119905119903119886119888119905119894119900119899 119889119890119892119903119890119890 119900119891 119888119894119905119910120572(29)

where 120572 refers to the impact factor of policy Based on thiscalculation 120572 = 15 generates calculations that are close tothe actual value See the appendixes for descriptions of theother variables and main equations

3 Simulation and Result Analysis

31 Model Test

311 Extreme Condition Test The extreme condition testmainly aims to inspect the stability applicability in extremeconditions and accuracy of the equations in the test modelto represent the change trends of the realistic system and theintentions of the decision maker

According to Figure 3(a) the APMG exhibited a continu-ous decrease following an increase in the APCF In particularthe minimum value of APMG was obtained when the APCFwas at the limit value (1000 yuandaysdotvehicle) In additionwhen APCF was equal to 5 the maximum APMG value wasobtained which is consistent with the actual laws therebyconfirming the stability of the model in extreme conditions

A deeper analysis indicated a larger interval between curves1 and 2 and a shorter interval between curves 2 and curve3 thereby indicating that the APCF did not exceed 100yuandaysdotvehicle

The change rules presented in Figures 3(b) and 3(c) weresimilar to those in Figure 3(a)

312 Sensitivity Test The model behaviors exhibited dif-ferent and sensitive results at different parameter valuesSpecifically the behavior model changed following an appro-priate change of parameter In addition the policies generatedthrough the model analysis changed following a change inparameters

According to Figure 4(a) with time all the curves firstrose and then slowly descended Specifically in the earlyperiod of policy implementation (before 2014) the effect wasnot obvious because part-time drivers may not have had adeep understanding of the purpose of the implementationand the significance of the APCF policy thereby resultingin a continuous increase in AMVT due to sharp increasein motor vehicle ownership The AMVT growth rate wasmore effectively controlled following a longer period due tocontinuous policy implementation and fulfilment After 2016the growth rate continuously decreased thereby allowing

10 Discrete Dynamics in Nature and Society

(a) AMVT APCF=5(a) AMVT APCF=10(a) AMVT APCF=20(a) AMVT APCF=30(a) AMVT APCF=40(a) AMVT APCF=50(a) AMVT APCF=60(a) AMVT APCF=70(a) AMVT APCF=80(a) AMVT APCF=90(a) AMVT APCF=100

2 M

25 M

3 M

35 M

4 Mve

hicle

2011 2013 2015 2017 20192009Time (year)

(a) AMVT

(b) APMG APCF=5(b) APMG APCF=10(b) APMG APCF=20(b) APMG APCF=30(b) APMG APCF=40(b) APMG APCF=50(b) APMG APCF=60(b) APMG APCF=70(b) APMG APCF=80(b) APMG APCF=90(b) APMG APCF=100

100000

125000

150000

175000

200000

ton

2011 2013 2015 2017 20192009Time (year)

(b) APMG

(c) ANOG APCF=5(c) ANOG APCF=10(c) ANOG APCF=20(c) ANOG APCF=30(c) ANOG APCF=40(c) ANOG APCF=50(c) ANOG APCF=60(c) ANOG APCF=70(c) ANOG APCF=80(c) ANOG APCF=90(c) ANOG APCF=100

80000

110000

140000

170000

200000

ton

2011 2013 2015 2017 20192009Time (year)

(c) ANOG

Figure 4 Sensitivity test (a) AMVT (b) APMG (c) ANOG

the APCF policy to exhibit good effects based on long-termpractice improvement and fulfilment

Following further analysis the AMVT exhibited amarginal decreasing effect following an increase in APCFfrom curve 1 to curve 6 especially in curves 3ndash6 whichindicates that a larger APCF is not always better The analysisresults are presented in Figures 4(b) and 4(c)

In conclusion the APCF value range was observed withinthe interval of [30 50] based on the above analysis from the

perspective of AMVT reduction (alleviate traffic jam) as wellas APMG and ANOG emission reduction Table 8 presentsthe detailed analysis results

32 Analysis of Results The AMVT exhibited a continuousdecrease following an increase in APCF which indicates theability of this policy to restrict increases in AMVT Specif-ically obvious changes were in the intervals of [5 10] and[10 20] wherein theAMVTexhibited a decrease of 166649

Discrete Dynamics in Nature and Society 11

and 105055 respectively The AMVT exhibited a decreaseof 35103 24912 and 16793 in the intervals of [20 30][30 40] and [40 50] respectivelyHoweverminimal changeswere observed in the interval of 50 yuandaysdotvehicle aboveIn addition the APMG exhibited a decrease of 13967789137 28538 20987 and 14128 respectively in theabove intervals and exhibited very minimal changes in theinterval of 50 above The ANOG exhibited similar changerules

Therefore the interval [30 50] is deemed a reasonablevalue range based on the analysis on the degree of effect ofdifferent APCFs on the AMVT APMG and ANOG

In particular the change trends of AMVT APMG andANOG were generally consistent as presented in Figure 6specifically Figure 5(d) Figures 5(a)ndash5(c) exhibited obviousdecreasing trend rates that were continuously weakened inthe interval of [30 50] In addition the change was verylimited as the APCF exceeded 50 yuandaysdotvehicle

Therefore an effective APCF range of [30 50]was chosenbased on the development trends analysis of the change ratesof the main variables

33 Model Validation Historical data (2009-2015) on theamount of motor vehicles and population in Beijing arepresented in Table 9 wherein the conformance of theirrespective GSID was tested

331 Qualified Verification of the Degree of Grey Incidenceon the Population of Beijing The original sequence and itssimulation value sequence are respectively presented asfollows

1198830 =[[[[[[[[[[

1199090 (1)1199090 (2)1199090 (3)

1199090 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

18600119890 + 00719619119890 + 00720186119890 + 00720693119890 + 00721148119890 + 00721516119890 + 00721705119890 + 007

]]]]]]]]]]]]]]]

1198831 =[[[[[[[[[[

1199091 (1)1199091 (2)1199091 (3)

1199091 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

186000119890 + 007187390119890 + 007188790119890 + 007190200119890 + 007191621119890 + 007193053119890 + 007194495119890 + 007

]]]]]]]]]]]]]]]

(30)

The following was derived based on their calculations

100381610038161003816100381611990401003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

11990900 (119896) + 1211990900 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 117145

100381610038161003816100381611990411003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

11990901 (119896) + 1211990901 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 025295

10038161003816100381610038161199040 minus 11990411003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

(11990901 (119896) minus 11990900 (119896)) + 12 (11990901 (7) minus 11990900 (7))

1003816100381610038161003816100381610038161003816100381610038161003816= 09185

(31)

Therefore we are able to obtain the value of the GAID

12058501 = 1 + 100381610038161003816100381611990401003816100381610038161003816 + 1003816100381610038161003816119904110038161003816100381610038161 + 100381610038161003816100381611990401003816100381610038161003816 + 100381610038161003816100381611990411003816100381610038161003816 + 10038161003816100381610038161199040 minus 11990411003816100381610038161003816= 1 + 117145 + 025295

1 + 117145 + 025295 + 09185 asymp 07275(32)

In a similar way

100381610038161003816100381610038161199041015840010038161003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

119909101584000 (119896) + 12119909101584000 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 062985100381610038161003816100381610038161199041015840110038161003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

119909101584001 (119896) + 12119909101584001 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 0136051003816100381610038161003816100381611990410158400 minus 1199041015840110038161003816100381610038161003816

=10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

(119909101584001 (119896) minus 119909101584000 (119896)) + 12 (119909101584001 (7) minus 119909101584000 (7))

1003816100381610038161003816100381610038161003816100381610038161003816= 04938

(33)

Therefore GRID is

11990301 = 1 + 100381610038161003816100381610038161199041015840010038161003816100381610038161003816 + 1003816100381610038161003816100381611990410158401100381610038161003816100381610038161 + 1003816100381610038161003816119904101584001003816100381610038161003816 + 1003816100381610038161003816119904101584011003816100381610038161003816 + 100381610038161003816100381611990410158400 minus 119904101584011003816100381610038161003816= 1 + 062985 + 013605

1 + 062985 + 013605 + 04938 asymp 07815(34)

When 120579 = 05 and exist1205760 = 07 then12057601 = 12057912058501 + (1 minus 120579) 11990301 = 05 times 07275 + 05 times 07815

= 07545 gt 07 = 1205760 (35)

Therefore according to Table 5 the accuracy was determinedto be between grade 2 and grade 3

332 Qualified Verification of the Degree of Grey Incidenceon the Amount of Motor Vehicles in Beijing The original

12 Discrete Dynamics in Nature and Society

Table 8 The effects of different APCFs on AMVT APNG and ANOG

APCF AMVT Trend Variation APMG Trend Variation ANOG Trend Variation() () ()

5 345229e+006 -- -- 161737 -- -- 154899 -- --10 287697e+006 darr -166649 139146 darr -139677 137782 darr -11050420 257473e+006 darr -105055 126743 darr -89137 128122 darr -7011130 248435e+006 darr -35103 123126 darr -28538 125306 darr -2197940 242246e+006 darr -24912 120542 darr -20987 123272 darr -1623250 238178e+006 darr -16793 118839 darr -14128 121928 darr -1090360 235237e+006 darr -12348 117604 darr -10392 120952 darr -0800570 232979e+006 darr -09599 116655 darr -08069 120202 darr -0620180 231171e+006 darr -07760 115894 darr -06524 119599 darr -0501790 229680e+006 darr -06450 115265 darr -05427 119101 darr -04164100 228421e+006 darr -05482 114734 darr -04607 118680 darr -03535

Table 9 Historical data and their simulation values (2009-2015)

Time Amount of motor vehicles (vehicle) Amount of population (person)Actual value Simulation value Actual value Simulation value

2009 4019e+006 401900e+006 18600e+007 186000e+0072010 4809e+006 457571e+006 19619e+007 187390e+0072011 4983e+006 528216e+006 20186e+007 188790e+0072012 5200e+006 560956e+006 20693e+007 190200e+0072013 5437e+006 577509e+006 21148e+007 191621e+0072014 5591e+006 584424e+006 21516e+007 193053e+0072015 5619e+006 591422e+006 21705e+007 194495e+007

sequence and its simulation value sequence were respec-tively calculated as follows

119883119894 =[[[[[[[[[[

119909119894 (1)119909119894 (2)119909119894 (3)

119909119894 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

4019119890 + 0064809119890 + 0064983119890 + 0065200119890 + 0065437119890 + 0065591119890 + 0065619119890 + 006

]]]]]]]]]]]]]]]

119883119895 =[[[[[[[[[[

119909119895 (1)119909119895 (2)119909119895 (3)

119909119895 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

401900119890 + 006457571119890 + 006528216119890 + 006560956119890 + 006577509119890 + 006584424119890 + 006591422119890 + 006

]]]]]]]]]]]]]]]

(36)

TheGAID andGRIDwere respectively calculated as follows

120585119894119895 asymp 09235119903119894119895 asymp 09390 (37)

Hence when exist1205760 = 09 and 120579 = 05120576119894119895 = 120579120585119894119895 + (1 minus 120579) 119903119894119895 = 09313 gt 09 = 1205760 (38)

Therefore according to Definition 3 and Table 5 thismodel verified the degree of grey incidence and exhibited anaccuracy belonging to grade 1

34 Policy Simulation Analysis and Discussion

341 Horizontal Analysis According to the horizontal anal-ysis the curves exhibited different changes with time Thespecific analysis results are presented as follows

Following the adoption of the low charge policy egAPCF = 5 yuandaysdotvehicle the AMVT (curve 1) exhibiteda decrease since about 2014 as exhibited in Figure 6(a)Although the growth rates of ANOG and APMG exhibited adecrease the total emissions maintained an increasing trendthereby resulting in high DAP levels (curve 4) The analysisresults indicate the inability of the low charge policy toeffectively reduce the DAP

According to Figure 6(f) curve 1 first exhibited aslow rise (before 2013) and a subsequent sharp descentfollowing the adoption of the high charge policy (APCF= 50 yuandaylowastvehicle) As a result the AMVT valuesdescended until 2013 wherein its descending range continu-ously increased Curve 3 terminated its previously continuousrise and instead descended slowly Similarly the rising rate

Discrete Dynamics in Nature and Society 13

0

2

4

6

8

10

12

14

16

18A

MV

T (

)

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

(a) AMVT

0

2

4

6

8

10

12

14

APM

G (

)

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

(b) APMG

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

0

2

4

6

8

10

12

AN

OG

()

(c) ANOG

AMVT ()APMG ()ANOG ()

0

2

4

6

8

10

12

14

16

18

5 20 8010 50 60 7030 9040 100

(d) Trend comparison

Figure 5 Development trends of the change rates of the main variables (a) AMVT (b) APMG (c) ANOG (d) Trend comparison

Table 10 The comparison of different policies

Variable APCF (yuandaylowastvehicle) Trend Variation ()5 50

AMVT (vehicle) 345229e+006 238178e+006 darr -3101APMG (t) 161737e+005 118839e+005 darr -2652ANOG (t) 154899e+005 121928e+005 darr -2129DAP 06 0525 darr -1250

of curve 2 slowed down relatively These results indicatethe effective control on the increase of APMG and ANOGafter which the values began to descend slowly Curve 4exhibited three phases specifically a rapid rise between 2011and 2014 a slow rise in rate between 2014 and 2018 and a slowdescent after 2018These results indicate the presence of DAPimprovements which exhibited gradual descent after 2018

The analysis results in Figures 6(b)ndash6(e) were similar tothose presented above

342 Vertical Analysis According to Figures 6(a)ndash6(f) theAPCF exhibited a continuous increase thereby generating achange in the rules of all the curves as follows

(i) AMVT (curve 1)TheAMVT exhibited a continuousdecrease Within a certain range the increase inAPCF aided in the descent of the AMVT therebyfurther alleviating the traffic pressures

(ii) APMG (curve 3) and ANOG (curve 2) A charge ofmore than 30 (Figures 6(d)ndash6(f)) generated a slowdescent in APMGMeanwhile the increase in ANOGalso exhibited effective restraint

(iii) DAP (curve 4)TheDAP exhibited an overall declineespecially following the implementation of a highcharge policy (APCF isin [40 50]) A subsequentdescending trend was later observed in the period ofanalogue simulation as presented in Figures 6(e) and6(f)

343 Comparison of Policies According to Table 10 in thepresence of a low charge policy (APCF=5) the AMVTAPMG ANOG and DAP under a high charge pol-icy exhibited an obvious decrease which indicates thatthe implementation of a high charge policy effectivelyreduced motor vehicle exhaust emissions to restrain the

14 Discrete Dynamics in Nature and Society

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

083 M

10000004

2 M00

2011 2013 2015 2017 20192009Time (year)

AMVT APCF=5ANOG APCF=5APMG APCF=5DAP APCF=5

vehicletontonDmnl

(a)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=10ANOG APCF=10APMG APCF=10DAP APCF=10

vehicletontonDmnl

(b)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=20ANOG APCF=20APMG APCF=20DAP APCF=20

vehicletontonDmnl

(c)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=30ANOG APCF=30APMG APCF=30DAP APCF=30

vehicletontonDmnl

(d)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=40ANOG APCF=40APMG APCF=40DAP APCF=40

vehicletontonDmnl

(e)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=50ANOG APCF=50APMG APCF=50DAP APCF=50

vehicletontonDmnl

(f)

Figure 6 Policy simulation (a) APCF=5 (b) APCF=10 (c) APCF=20 (d) APCF=30 (e) APCF=40 (f) APCF=50

intensification of ldquohazerdquo pollution degree in Beijing Specif-ically the gap between curves 1 and 2 exhibited a continuouswidening as presented in Figure 7(a) After 2013 curve 2exhibited an obvious descent Therefore the APCF policyeffectively reduced the AMVT and enabled an about 3101decrease in 2020

The results in Figures 7(b)ndash7(d) were similarly analyzed

In conclusion the adoption of a low charge policygenerated increasing APMG and ANOG trends as presentedin Figures 6(a) and 6(b) thereby suggesting the inabilityof the low charge policy to effectively reduce the DAP Anincrease of the fee to a certain extent especially followingthe implementation of a high charge policy (Figures 6(e) and6(f)) not only reduced the AMVT and alleviated traffic jams

Discrete Dynamics in Nature and Society 15

APCF=5

APCF=50

x 106

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 20202009Time (year)

2

25

3

35ve

hicle

(a) AMVT

APCF=5

APCF=50

x 105

20182017 2019 20202015 2016201420122011 201320102009Time (year)

11

12

13

14

15

16

17

ton

(b) APMG

APCF=5

APCF=50

x 105

08

09

1

11

12

13

14

15

16

ton

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 20202009Time (year)

(c) ANOG

02

APCF=5

APCF=50

2009 2011 20122010 20142013 2016 2017 20182015 20202019Time (year)

025

03

035

04

045

05

055D

mnl

(d) DAP

Figure 7 Comparison of the policies (a) AVT (b) APMG (c) ANOG (d) DAP

in cities but also effectively reduced the APMG and ANOGthereby reducing the DAP

According to a comparison on the different schemes atthe end of the analogue simulation period the high chargepolicy functioned as follows in terms of the emission reduc-tion of the motor vehicle exhaust the APMG and ANOGexhibited reductions of 2652 and 2129 respectively interms of alleviating traffic jams the AMVT exhibited a 3101decrease and in terms of reducing the degree of air pollutionthe DAP exhibited a 1250 decrease

4 Conclusions

41 Main Conclusions To resolve the air pollution problemsgenerated by motor vehicle exhaust emission the presentstudy introduced the charging mechanism and built a motorvehicle exhaust emission reduction strategy managementmodel using economic means and the SD-GM approach to

generate the following conclusions based on tests validationof the models and the simulation analysis of policies

(1)Within a certain range the reduction effects of APMGandANOGexhibited continuous enhancements following anincrease in APCF However the APCF did not always followthe principle ldquobigger means betterrdquo because the emissionreduction effect which was generated by an increase inthe APCF exhibited a marginal decreasing effect Accord-ing to the sensitivity analysis a pollution charge of 30ndash50yuandaysdotvehicle for the motor vehicles in Beijing was withinthe relatively reasonable range

(2) Three high charge policy functions were generatedbased on a comparison of the simulation results of thedifferent charging schemes the implementation of highcharge policies not only reduced the AMVT and alleviatedtraffic jams (Figures 6(e) 6(f) and 7(a) Table 10) but alsoeffectively reduced the APMG andANOG (Figures 6(e) 6(f)7(b) and 7(c) Tables 5 and 10) thereby further reducing theDAP (Figures 6(e) 6(f) and 7(d) Table 10) According to the

16 Discrete Dynamics in Nature and Society

contrastive analysis the DAP exhibited a decrease of about1250

(3) However the following problems were encounteredfollowing the implementation of the APCF policy (a) Theimplementation of the APCF policy increased the cost ofmotor vehicle trips and urged part-time drivers to take publictransportation which increased the burden of public trans-portation The subsidy policy and other applicable policiesmust be introduced to improve the public transport supplylevel and service quality Otherwise the trip demands ofpassengers will be difficult to satisfy which will influencethe implementation of the APCF policy (b) In the earlyperiods of APCF policy implementation an increase in thecost of motor vehicle trips due to the insufficient publicunderstanding and utilization of the APCF policy loweredits public support rate The government must strengthenits public relations work especially regarding the purposeand significance of its implementation to improve publicawareness and acknowledgment (c) The purpose of thesepolicies must be supervised and managed to gather APCFincome and improve public transportation infrastructures

42 Deficiencies and Future Work The present study consid-ered NOx and PMx as the principal motor vehicle emissionpollutants Future research must fully consider other com-ponents such as SO2 airborne particles hydrocarbons COand CO2 Secondly the implementation of a single chargingmeasure can reduce the supply level of public transportationFuture research should consider a subsidy mechanism toimprove the service quality Thirdly the function and effectof a single policy are limited Future work must considerthe integration of multiple policies to improve the emissionreduction effect For example future work may focus priorityon public transportation improvement of fuel quality vigor-ous promotion of new energy vehicles and improvements inemission standards

Appendix

A

See Table 11

B

Summary of the major variables and equations(1) Cost of motor vehicle trips = Air pollution charging

feelowast (1+ Air pollution control)(2) Amount ofNOx generation = INTEG (NOx emissions

- Annual dissipation of NOx 80380)(3) NOx emissions = Per vehicle annual of NOx

emissionslowast Amount of motor vehicle tripslowast Contributionrate of NOx from vehicle

(4) Contribution rate of NOx from vehicle = 05(5) Dissipation rate of NOx = 02(6) Annual dissipation of NOx = Amount of NOx

generationlowast Dissipation rate of NOx(7) Per vehicle annual of NOx emissions = 002

(8) Amount of PMx generation = INTEG (PMxemissions- Annual dissipation of PMx 160760)

(9) PMx emissions = Amount of motor vehicle tripslowastContribution rate of PMx from vehiclelowast Per vehicle annualof PMx emissions

(10) Contribution rate of PMx from vehicle = 05(11) Per vehicle annual of PMx emissions = 004(12) Annual dissipation of PMx = Amount of PMx

generationlowast Dissipation and control rate of PMx(13) Dissipation and control rate of PMx = 05(14) Pollution degree of NOx = IF THEN ELSE (Amount

of NOx generationgt= 11182e+005 09 IF THEN ELSE(Amount of NOx generationgt= 10874e+005 08 IF THENELSE (Amount of NOx generationgt= 10400e+005 07 IFTHEN ELSE (Amount of NOx generationgt= 9966e+00406 IF THEN ELSE (Amount of NOx generationgt=9618e+004 05 IF THEN ELSE (Amount of NOxgenerationgt= 8038e+004 03 IF THEN ELSE (Amountof NOx generationgt= 7008e+004 025 IF THEN ELSE(Amount of NOx generationgt= 6144e+004 02 IF THENELSE (Amount of NOx generationgt= 5508e+004 015 01)))))))))

(15) Pollution degree of PMx = IF THEN ELSE (Amountof PMx generationgt= 22364e+005 09 IF THEN ELSE(Amount of PMx generationgt= 21748e+005 08 IF THENELSE (Amount of PMx generationgt= 20800e+005 07 IFTHEN ELSE (Amount of PMx generationgt= 19932e+00506 IF THEN ELSE (Amount of PMx generationgt=19236e+005 05 IF THEN ELSE (Amount of PMxgenerationgt= 16076e+005 03 IF THEN ELSE (Amountof PMx generationgt= 14016e+005 025 IF THEN ELSE(Amount of PMx generationgt= 12288e+005 02 IF THENELSE (Amount of PMx generationgt= 11016e+005 015 01)))))))))

(16) Ratio of motor vehicle trips = 055(17) Amount of motor vehicle trips = Amount of motor

vehicleslowast Ratio of motor vehicle trips(18) Degree of air pollution = Weight ratio of NOxlowast

Pollution degree of NOx+ Weight ratio of PMxlowast Pollutiondegree of PMx

(19) Weight ratio of PMx = 05(20) Weight ratio of NOx = 05(21) Air pollution control = IF THEN ELSE (Degree of air

pollutiongt= 07 1 IF THEN ELSE (Degree of air pollutiongt=06 08 IF THEN ELSE (Degree of air pollutiongt= 05 07IF THEN ELSE (Degree of air pollutiongt= 04 06 IF THENELSE (Degree of air pollutiongt= 03 05 IF THEN ELSE(Degree of air pollutiongt= 025 045 IF THENELSE (Degreeof air pollutiongt= 02 04 IF THEN ELSE (Degree of airpollutiongt= 015 035 03))))))))

(22) Attraction degree of the growth of vehicles= (1-Airpollution control)lowast 055+ Attraction degree of vehicle tripslowast045

(23) Per capita annual income = Amount of GDPAmount of population

(24) Amount of population = INTEG (Growth of popu-lation+ Net migration- Population reduction 186e+007)

(25) Birth rate = Adjustment coefficient of birth ratelowastPredictive value of birth rate

Discrete Dynamics in Nature and Society 17

Table 11 Description of main variables in stock flow diagram

Signicant variable Unit Variable type Data sourceAir pollution charging fee yuandaysdotvehicle ConstantAir pollution control Dmnl Auxiliary variable M1+M3Amount of GDP yuan Level M1Amount of motor vehicles vehicle Level M1Amount of motor vehicle trips vehicle Auxiliary variableAmount of NOx (PMx) generation ton Level M1Amount of population person Level M1Annual dissipation of NOx (PMx) tonyear FlowAnnual scrapped vehicleyear FlowAttraction degree of city Constant M2Attraction degree of the growth of vehicles Auxiliary variable M1+M3Attraction degree of vehicle trips Auxiliary variable M1+M3Birth rate 1year Constant M3Contribution rate of NOx (PMx) from vehicle Constant M2Cost of motor vehicle trips yuandaysdotvehicle Auxiliary variable M3Death rate 1year Constant M3Degree of air pollution Dmnl Auxiliary variable M3Dissipation and control rate of NOx (PMx) 1year Constant M2Graphical function of the growth of GDP Dmnl Auxiliary variable M3Growth of GDP yuanyear FlowGrowth rate of motor vehicles 1year Auxiliary variable M1+M3Growth of motor vehicles vehicleyear FlowGrowth of population personyear FlowGrowth rate of vehicle ownership Dmnl Auxiliary variable M1+M3Impact factor of policy Dmnl Constant M3Net migration personyear FlowNet migration rate 1year Constant M1+M3NOx (PMx) emissions tonyear FlowPer capita annual income yuanperson Auxiliary variablePer vehicle annual of NOx (PMx) emissions tonyearsdotvehicle Constant M2Pollution degree of NOx (PMx) Dmnl Auxiliary variable M1+M3Population reduction personyear FlowRatio of motor vehicle trips Constant M2Scrap rate 1year Constant M2The average of net migration rate 1year Constant M1Weight ratio of PMx (NOx) Auxiliary variable M3

(26) Predictive value of birth rate = 000925(27) Death rate = Adjustment coefficient of death ratelowast

Predictive value of death rate(28) Predictive value of death rate = 000494(29) Net migration = Amount of populationlowastNet migra-

tion rate(30) Net migration rate = The average of net migration

ratelowast Attraction degree of cityand(Impact factor of policy)(31) Impact factor of policy = 15(32) The average of net migration rate = 000531(33) Attraction degree of city = 07056(34) Amount of GDP = INTEG (Growth of GDP

12153e+012)

(35) Graphical function of the growth of GDP = WITHLOOKUP (Amount of GDP ([(8e+011 0)- (3e+ 012 03)](81178e+011 01648) (98468e+011 0213) (11115e+01201288) (12153e+012 00934) (141136e+012 01613)(162519e+012 01515) (178794e+012 01001) (198008e+01201075) (213308e+012 00773) (230146e+012 00789)(235396e+012 002281) (240162e+012 00203) (245025e+012 002025) (249987e+012 002024) (255049e+0120020249)))

(36) Growth rate of GDP = Graphical function of thegrowth of GDPlowast Impact factor of the growth of GDP

(37) Amount of motor vehicles = INTEG (Growth ofmotor vehicles- Annual scrapped 4019e+006)

18 Discrete Dynamics in Nature and Society

(38) Annual scrapped = Amount of motor vehicleslowastScrap rate

(39) Scrap rate = 0067

Conflicts of Interest

The author declares no conflicts of interest

Acknowledgments

This work has been partially supported by the NationalNatural Science Foundation of China (71571119) ShanghaiFirst-Class Academic Discipline Project (S1201YLXK) andChina Postdoctoral Science Foundation (2018M630404)Theauthor would like to thank LetPub (httpwwwletpubcom)for providing linguistic assistance during the preparation ofthis manuscript

References

[1] X Liu S Ma J Tian N Jia and G Li ldquoA system dynamicsapproach to scenario analysis for urban passenger transportenergy consumption and CO2 emissions A case study ofBeijingrdquo Energy Policy vol 85 pp 253ndash270 2015

[2] B Xu L Luo and B Lin ldquoA dynamic analysis of air pollutionemissions in China Evidence from nonparametric additiveregression modelsrdquo Ecological Indicators vol 63 pp 346ndash3582016

[3] S Leinert H Daly B Hyde and B O Gallachoir ldquoCo-benefitsNot always Quantifying the negative effect of a CO2-reducingcar taxation policy on NOx emissionsrdquo Energy Policy vol 63pp 1151ndash1159 2013

[4] Z Cheng L Li and J Liu ldquoIdentifying the spatial effects anddriving factors of urban PM25 pollution in Chinardquo EcologicalIndicators vol 82 pp 61ndash75 2017

[5] N Kaida and K Kaida ldquoSpillover effect of congestion chargingon pro-environmental behaviorrdquo Environment Developmentand Sustainability vol 17 no 3 pp 409ndash421 2015

[6] R Penabaena-Niebles V Cantillo and J L Moura ldquoImpactof transition between signal timing plans in social cost basedin delay fuel consumption and air emissionsrdquo TransportationResearch Part D Transport and Environment vol 41 pp 445ndash456 2015

[7] DDing andB Shuai ldquoA traffic restriction scheme for enhancingcarpoolingrdquoDiscreteDynamics inNature and Society Article ID9626938 9 pages 2017

[8] D Kong X Guo B Yang and D Wu ldquoAnalyzing the Impactof Trucks on Traffic Flow Based on an Improved CellularAutomaton Modelrdquo Discrete Dynamics in Nature and Societyvol 2016 pp 1ndash14 2016

[9] S Cakmak C Hebbern J D Cakmak and J Vanos ldquoThemodifying effect of socioeconomic status on the relationshipbetween traffic air pollution and respiratory health in elemen-tary schoolchildrenrdquo Journal of Environmental Managementvol 177 pp 1ndash8 2016

[10] L Song H Song J Lin et al ldquoPM25 emissions from differenttypes of heavy-duty truck a case study and meta-analysis ofthe Beijing-Tianjin-Hebei regionrdquo Environmental Science andPollution Research vol 24 no 12 pp 11206ndash11214 2017

[11] Z Hu S Kang C Li et al ldquoLight absorption of biomassburning and vehicle emission-sourced carbonaceous aerosolsof the Tibetan Plateaurdquo Environmental Science and PollutionResearch vol 24 no 18 pp 15369ndash15378 2017

[12] X Cen H K Lo and L Li ldquoA framework for estimating trafficemissions The development of Passenger Car Emission UnitrdquoTransportation Research Part D Transport and Environmentvol 44 pp 78ndash92 2016

[13] S Wang X Liu C Zhou J Hu and J Ou ldquoExamining theimpacts of socioeconomic factors urban form and transporta-tion networks on CO2 emissions in Chinarsquos megacitiesrdquoAppliedEnergy vol 185 pp 189ndash200 2017

[14] Q Wang K Hubacek K Feng Y-M Wei and Q-M LiangldquoDistributional effects of carbon taxationrdquo Applied Energy vol184 pp 1123ndash1131 2016

[15] C Johansson L Burman and B Forsberg ldquoThe effects ofcongestions tax on air quality and healthrdquo Atmospheric Envi-ronment vol 43 no 31 pp 4843ndash4854 2009

[16] A Rakowska K C Wong T Townsend et al ldquoImpact of trafficvolume and composition on the air quality and pedestrianexposure in urban street canyonrdquo Atmospheric Environmentvol 98 pp 260ndash270 2014

[17] S Batterman R Ganguly and P Harbin ldquoHigh resolutionspatial and temporal mapping of traffic-related air pollutantsrdquoInternational Journal of Environmental Research and PublicHealth vol 12 no 4 pp 3646ndash3666 2015

[18] J Eliasson M Borjesson D van Amelsfort K Brundell-Freijand L Engelson ldquoAccuracy of congestion pricing forecastsrdquoTransportation Research Part A Policy and Practice vol 52 pp34ndash46 2013

[19] J Eliasson ldquoThe role of attitude structures direct experienceand reframing for the success of congestion pricingrdquo Trans-portation Research Part A Policy and Practice vol 67 pp 81ndash952014

[20] H X Yang J D Li H Zhang and S Q Liu ldquoResearch on thegovernance of urban traffic jam based on system dynamicsrdquoSystems EngineeringTheory and Practice vol 34 no 8 pp 2135ndash2143 2014 (Chinese)

[21] M H Zhu Research on Socio-Economic Impact of UrbanTrafficCongestion [PhD thesis] Beijing JiaotongUniversity 2013(Chinese)

[22] B Zeng Research on Modeling Technologies of Grey Prediction[PhD thesis] Nanjing University of Aeronautics and Astronau-tics 2011 (Chinese)

[23] S F Liu Y J Yang and L F Wu Grey System Theory andApplication Science Press Beijing China 2017

[24] S W Jia K Yang J J Zhao and G L Yan ldquoThe traffic-congestion charging fee management model based on thesystem dynamics approachrdquo Mathematical Problems in Engi-neering vol 2017 Article ID 3024898 13 pages 2017

4 Discrete Dynamics in Nature and Society

Table 1 Historical values of the main status variables (data is from 2010-2015 Statistical Yearbook of Beijing)

Time 2009 2010 2011 2012 2013 2014Amount of motor vehicles 4019 4809 4983 5200 5437 5591(10000 vehicles)Amount of population 18600 19619 20186 20693 21148 21516(10000 persons)GDP gross 121530 141136 162519 178794 198008 213308(100 million yuan)

Table 2 Historical values of main correlated variables Unit person

Time 2009 2010 2011 2012 2013 2014Mechanical increase 112163 109091 129313 107072 109656 74654Inflows 189744 185101 211447 190510 198869 166600Outflows 77581 76010 82134 83438 89213 91946

Table 3 Predictive value of birth rate and its average

Time 2015 2016 2017 2018 2019 2020Predictive value 873permil 894permil 914permil 935permil 956permil 977permilAverage 925permil

Table 4 Predictive value of death rate and its average

Time 2015 2016 2017 2018 2019 2020Predictive value 473permil 483permil 464permil 504permil 515permil 525permilAverage 494permil

generated major errors in the mean-based forecast andestimation which failed to meet the laws of change anddata information development The data was first processedusing theoretical methods such as regression analysis andgrey prediction Valuable implicit rules were then gener-ated in accordance with the actual changes in the datatrends Finally a nonlinear relationship between variableswas characterized in accordance with the graphical functionlogical function etc Three methods are given in the follow-ing

(1) First Method The aim of this method is to determinea reasonable value to meet the actual situation of Beijingin recent years Statistical approaches (such as regressionanalysis) based on large sample data can be used because ofthe abundance of data on birth and death ratesThe value wasfirst predicted by regression analysis after which the meanvalue was calculated Finally the value was slightly adjustedby combining the actual change trends of the variables todetermine the birth rate and death rate

Tables 3 and 4 present the predicted data that wereobtained from the regression analysis on the historical birthrate and death rate values of the permanent resident pop-ulation in Beijing However the implementation of a pop-ulation policy specifically the ldquotwo-child policyrdquo generatedan increase in the birth rate And the death rate remainedat about 5 These results were consistent with the currentstatus of Beijing

(2) Second Method The goal of this method is to describethe dynamic trends between variables by using the graphicalfunction Especially grey prediction model can improvethe prediction accuracy by the use of accumulated gener-ating operator and buffer operator Predictions were firstconducted using the GM (11) model in the absence of anobvious relationship between the variables or in the presenceof imperfect data information Subsequently graphical orlogical functions were generated by combining the actualchange rules of the variables This method was used todetermine the growth rate of the gross domestic product(GDP) and vehicle ownership growth rate Taking the GDPgrowth rate in Beijing as an example the detailed calculationsare presented in the following

Definition 1 Assume that the original sequence is

119883(0) = (119909(0) (1) 119909(0) (2) 119909(0) (119899)) (1)

119883(1) is its accumulation generated sequence (1-AGO)

119883(1) = (119909(1) (1) 119909(1) (2) 119909(1) (119899)) (2)

wherein

119909(1) (119896) = 119896sum119894=1

119909(0) (119894) 119896 = 1 2 119899 (3)

Discrete Dynamics in Nature and Society 5

such that119889119909(1)119889119905 + 119886119909(1) = 119887 (4)

The preceding equation is the winterization equation of thegrey GM (11) prediction model [22]

If 119909(0)(119896) ge 0 119896 = 1 2 119899 then and119886 = (119886 119887)119879 is theparameter list and satisfies

and119886 = (119886 119887)119879 = (119861119879119861)minus1 119861119879119884 (5)

wherein

119861 =[[[[[[[[[[[[

minus119909(1) (1) + 119909(1) (2)2 1

minus119909(1) (2) + 119909(1) (3)2 1

minus119909(1) (119899 minus 1) + 119909(1) (119899)2 1

]]]]]]]]]]]]

119884 =[[[[[[[[

119909(0) (2)119909(0) (3)

119909(0) (119899)

]]]]]]]]

(6)

(i) Time response formula of the solution of the winterizationequation 119889119909(1)119889119905 + 119886119909(1) = 119887 is

119909(1) (119905) = (119909(1) (1) minus 119887119886) 119890minus119886119905 + 119887

119886 (7)

(ii) Time response formula of the GM(11) model 119909(0)(119896) + 119886 sdot(119909(1)(119896) + 119909(1)(119896 minus 1))2 = 119887 isand119909(1) (119896 + 1) = (119909(0) (1) minus 119887

119886) 119890minus119886119896 + 119887119886 119896 = 1 2 3 119899

(8)

(iii) Predicted value model of the original model is

and119884 (119896 + 1) = and119909(0) (119896 + 1) = and119909(1) (119896 + 1) minus and119909(1) (119896)= (1 minus 119890119886) (119909(0) (1) minus 119887

119886) 119890minus119886119896(9)

The following definitions are provided in Liu et al [23]

Definition 2 Assume that the images of zero starting point ofthese two sequences

119883119894 = (119909119894 (1) 119909119894 (2) 119909119894 (119899)) 119883119895 = (119909119895 (1) 119909119895 (2) 119909119895 (119899)) (10)

are

1198830119894 = (1199090119894 (1) 1199090119894 (2) 1199090119894 (119899)) 1198830119895 = (1199090119895 (1) 1199090119895 (2) 1199090119895 (119899)) (11)

such that

120585119894119895 = 1 + 10038161003816100381610038161199041198941003816100381610038161003816 + 10038161003816100381610038161003816119904119895100381610038161003816100381610038161 + 10038161003816100381610038161199041198941003816100381610038161003816 + 1003816100381610038161003816100381611990411989510038161003816100381610038161003816 + 10038161003816100381610038161003816119904119894 minus 11990411989510038161003816100381610038161003816 (12)

The presented equation is the absolute degree of grey inci-dence (GAID) of 119883119894 and 119883119895 Assume that 119883119894 and 119883119895 aresequences of the same length with nonzero initial values 1198831015840119894and 1198831015840119895 are the initial images of 119883119894 and 119883119895 respectively 11988310158400119894and11988310158400119895 are the images of the zero starting point of sequences1198831015840119894 and 1198831015840119895 respectively and the GAID of 1198831015840119894 and 1198831015840119895 is calledthe relative degree of grey incidence (GRID) of 119883119894 and 119883119895Based on these definitions the following equation is thendefined

119903119894119895 = 1 + 10038161003816100381610038161003816119904101584011989410038161003816100381610038161003816 + 100381610038161003816100381610038161199041015840119895100381610038161003816100381610038161 + 100381610038161003816100381611990410158401198941003816100381610038161003816 + 10038161003816100381610038161003816119904101584011989510038161003816100381610038161003816 + 100381610038161003816100381610038161199041015840119894 minus 119904101584011989510038161003816100381610038161003816 (13)

such that

120576119894119895 = 120579120585119894119895 + (1 minus 120579) 119903119894119895 (14)

is defined as the synthetic degree of grey incidence (GSID) of119883119894 and 119883119895 wherein 120579 isin [0 1]Definition 3 Assume that119883(0) is the original sequence and119883(0) isits simulative sequence and 120576 is the degree of grey incidencebetween 119883(0) and and119883(0) In the case of 120576 gt 1205760 for the given1205760 gt 0 this model is defined as the qualified verification ofthe degree of grey incidence See Table 5 for the accuracy testgrade

The requirement of this model for correlation 120576 is ldquothebigger the betterrdquo

Step 1 (data processing) First write the original data as theform of sequence

119883(0) = (119909(0) (1) 119909(0) (2) 119909(0) (10))= (81178 98468 111150 121530 141136 162519 178794 198008 213308 230146)

(15)

6 Discrete Dynamics in Nature and Society

Second introduce the second-order average weakeningoperator 1198632 as

119883(0)1198632 = (119909(0) (1) 1198892 119909(0) (2) 1198892 119909(0) (10) 1198892) (16)

wherein

119909(0) (119896) 1198892 = 110 minus 119896 + 1 [119909(0) (119896) 119889 + 119909(0) (119896 + 1) 119889

+ + 119909(0) (10) 119889] 119909(0) (119896) 119889 = 1

10 minus 119896 + 1 [119909(0) (119896) + 119909(0) (119896 + 1) + + 119909(0) (10)] 119896 = 1 2 3 10

(17)

Obtain

119883(0)1198632 = (191742 195978 200266 20465 209105 213463 21769 221898 225937 230146) ≜ 119883= (119909 (1) 119909 (2) 119909 (3) 119909 (10)) (18)

Step 2 Calculate the 1-AGO sequence of sequence 119883 andobtain sequence 119883(1)

119883(1) = (119909(1) (1) 119909(1) (2) 119909(1) (3) 119909(1) (10))= (191742 38772 587986 792636 1001741 1215204 1432894 1654792 1880729 2110875) (19)

Step 3 Calculate its simulative sequence based on the greyGM (11) prediction model

According to Definition 1 the grey GM (11) predictionmodel is used to obtain the time response formula as follows

and119909(1) (119896 + 1) = 9728182119890002119896 minus 953644and119884 (119896 + 1) = and119909(0) (119896 + 1) = and119909(1) (119896 + 1) minus and119909(1) (119896)

(20)

The simulative sequence can then be calculated as

and119883= (and119909 (1) and119909 (2) and119909 (10))= (191742 196536 2005157 204576 2087185 2129448 2172568 2216561 2261444 2307236)

(21)

Step 4 (accuracy test) According to Steps 1 and 3 the originalsequence and its simulative sequence were respectivelycalculated as follows

119883 =[[[[[[[[[[

119909 (1)119909 (2)119909 (3)

119909 (10)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[[[[[[[[[

191742195978200266204650209105213463217690221898225937230146

]]]]]]]]]]]]]]]]]]]]]]]

and119883 =

[[[[[[[[[[[[[

and119909 (1)and119909 (2)and119909 (3)

and119909 (10)

]]]]]]]]]]]]]

=

[[[[[[[[[[[[[[[[[[[[[[[

191742196536020051572045760208718521294482172568221656122614442307236

]]]]]]]]]]]]]]]]]]]]]]]

(22)

Therefore one can calculate

|119904| =10038161003816100381610038161003816100381610038161003816100381610038169sum119896=2

[119909 (119896) minus 119909 (1)] + 12 [119909 (10) minus 119909 (1)]

1003816100381610038161003816100381610038161003816100381610038161003816

Discrete Dynamics in Nature and Society 7

Table 5 Reference list of accuracy test grade

Accuracy grade Grade 1 Grade 2 Grade 3 Grade 4Degree of grey incidence 1205760 090 080 070 060

Table 6 Amount of GDP and its growth rate

Time Amount of GDP (t) Growth rate Time Amount of GDP (t) Growth rate2005 69695e+011 --- 2013 198008e+012 010752006 81178e+011 01648 2014 213308e+012 007732007 98468e+011 02130 2015 230146e+012 007892008 11115e+012 01288 2016 2353956e+012 0022812009 12153e+012 00934 2017 2401622e+012 0020302010 141136e+012 01613 2018 2450253e+012 0020252011 162519e+012 01515 2019 2499868e+012 0020242012 178794e+012 01001 2020 2550488e+012 0020249

= 1742531003816100381610038161003816100381610038161003816and1199041003816100381610038161003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816100381610038169sum119896=2

[and119909 (119896) minus and119909 (1)] + 12 [and119909 (10) minus and119909 (1)]

1003816100381610038161003816100381610038161003816100381610038161003816= 1739031

1003816100381610038161003816100381610038161003816and119904 minus1199041003816100381610038161003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816100381610038169sum119896=2

[119909 (119896) minus 119909 (1) minus (and119909 (119896) minus and119909 (1))]

+ 12 [119909 (10) minus 119909 (1) minus (and119909 (10) minus and119909 (1))]

1003816100381610038161003816100381610038161003816100381610038161003816 = 3499(23)

such that

120585 = 1 + |119904| + 1003816100381610038161003816100381610038161003816and1199041003816100381610038161003816100381610038161003816

1 + |119904| + 1003816100381610038161003816100381610038161003816and1199041003816100381610038161003816100381610038161003816 +

1003816100381610038161003816100381610038161003816and119904 minus1199041003816100381610038161003816100381610038161003816

asymp 09990 (24)

Similarly 119903 = 09993 when 120579 = 05 exist1205760 = 09 therebydefining

120576 = 120579120585 + (1 minus 120579) 119903 = 09991 gt 09 = 1205760 (25)

Therefore this model is defined as the qualified verificationof the degree of grey incidence

Step 5 (predict future data) According to

and119909(1) (119896 + 1) = 9728182119890002119896 minus 953644and119909(0) (119896 + 1) = and119909(1) (119896 + 1) minus and119909(1) (119896)

(26)

a prediction of the next five steps was calculated as follows

and119883=

[[[[[[[[[[[[[[

and119909(0) (11)and119909(0) (12)and119909(0) (13)and119909(0) (14)and119909(0) (15)

]]]]]]]]]]]]]]

=[[[[[[[[[

23539562401622245025324998682550488

]]]]]]]]]

(27)

Step 6 (establish the graphical function) The GDP gross andits growth rate (2005-2020) were calculated using the abovesteps See Table 6 for specific results

Therefore onemay establish the graphical function of thegrowth of GDP

Graphical function of the growth of GDP= WITHLOOKUP (Amount of GDP ([(8e+011 0)- (3e+012 03)](81178e+011 01648) (98468e+011 0213) (11115e+01201288) (12153e+012 00934) (141136e+012 01613)(162519e+012 01515) (178794e+012 01001) (198008e+012 01075) (213308e+012 00773) (230146e+012 00789)(235396e+012 002281) (240162e+012 00203) (245025e+012 002025) (249987e+012 002024) (255049e+0120020249)))

Similarly onemay establish the Graphical function aboutthe growth rate of vehicle ownership See Appendix B forspecific results

(3)ThirdMethodThe purpose of this method is to determinesome variables with nonlinear characteristics because theyare difficult to define directly such as degree of air pollutionand air pollution control In the actual situation estimationswere conducted by utilizing data from the official website(M1) and the first two prediction methods Main basisSlightly adjust the change trend of the variables to meetthe actual change rules that have been observed in Beijingin recent years As a result several variables have been

8 Discrete Dynamics in Nature and Society

Table 7 Estimated values of pollution degree of NOx and PMx in Beijing

Time Amount of motor vehicles (vehicle) ANOG (t) APMG (t) Actual pollution degree2014 5591e+006 11182e+005 22364e+005 Serious pollution2013 5437e+006 10874e+005 21748e+005 Serious pollution2012 5200e+006 10400e+005 20800e+005 Moderate pollution2011 4983e+006 9966e+004 19932e+005 Moderate pollution2010 4809e+006 9618e+004 19236e+005 Moderate pollution2009 4019e+006 8038e+004 16076e+005 Mild pollution2008 3504e+006 7008e+004 14016e+005 Mild pollution2007 3072e+006 6144e+004 12288e+005 Mild pollution2006 2754e+006 5508e+004 11016e+005 Mild pollution

confirmed including the attraction degree of the city netmigration rate degree of air pollution air pollution controlattraction degree of vehicle trips attraction degree of growthof the vehicles and growth rate ofmotor vehiclesThe presentstudy characterized the degree of air pollution as an example

(a) Estimation of Degree of Air Pollution The present studyestimated the degree of air pollution mainly based on theamount of NOx generation (ANOG) and amount of PMxgeneration (APMG) in accordance with historical data inStatistical Yearbook of Beijing from 2006 to 2014 In additionthe methods were also combined to estimate the ANOG andAPMG See Table 7 for detailed results

According to the actual situation of air pollution causedby motor vehicle exhaust emission in Beijing serious pol-lution was observed from 2013 to 2014 moderate pollutionwas generated between 2010 and 2012 and mild pollutionoccurred before 2009Therefore this paper defines the degreeof air pollution caused by ANOG as follows

(I)The degree of air pollution exhibited a value range thatis defined as (0 1) wherein a value of 08 and above indicatesserious pollution a value lower than 08 but higher than 05means moderate pollution and a value lower than 05 meansmild pollution

(II) From 2013 to 2014 Beijing exhibited a very seriousdegree of air pollution such that the estimated value ofNOx pollution was characterized between 08 and 1 at acorresponding ANOG of 108740 t to 111820 t From 2010 to2012 the degree of air pollution was moderate such that theestimated value of pollution NOx was within the interval of(05 08) at a corresponding ANOG of 96180 t to 104000 tFrom 2006 to 2009 the pollution degree was mild such thatthe estimated value of NOx pollution was lower than 05

According to the provisions above establish the logicalfunction of pollution degree of NOx

Pollution degree of NOx = IF THEN ELSE (Amount ofNOxgenerationgt= 11182e+005 09 IFTHENELSE (Amountof NOx generationgt= 10874e+005 08 IF THEN ELSE(Amount of NOx generationgt= 10400e+005 07 IF THENELSE (Amount of NOx generationgt= 9966e+004 06 IFTHENELSE (Amount of NOx generationgt= 9618e+004 05IF THEN ELSE (Amount of NOx generationgt= 8038e+00403 IF THEN ELSE (Amount of NOx generationgt=7008e+004 025 IF THEN ELSE (Amount of NOx

generationgt= 6144e+004 02 IF THEN ELSE (Amount ofNOx generationgt= 5508e+004 015 01 )))))))))

In the same way one can establish the logical function ofpollution degree of PMx

Pollution degree of PMx = IF THEN ELSE (Amountof PMx generationgt= 22364e+005 09 IF THEN ELSE(Amount of PMx generationgt= 21748e+005 08 IF THENELSE (Amount of PMx generationgt= 20800e+005 07 IFTHEN ELSE (Amount of PMx generationgt= 19932e+00506 IF THEN ELSE (Amount of PMx generationgt=19236e+005 05 IF THEN ELSE (Amount of PMxgenerationgt= 16076e+005 03 IF THEN ELSE (Amountof PMx generationgt= 14016e+005 025 IF THEN ELSE(Amount of PMx generationgt= 12288e+005 02 IF THENELSE (Amount of PMx generationgt= 11016e+005 015 01)))))))))

Therefore

119863119890119892119903119890119890 119900119891 119886119894119903 119901119900119897119897119906119905119894119900119899= 120573 lowast 119901119900119897119897119906119905119894119900119899 119889119890119892119903119890119890 119900119891 119873119874119909 + 120574

lowast 119901119900119897119897119906119905119894119900119899 119889119890119892119903119890119890 119900119891 119875119872119909(28)

wherein 120573 refers to the weight ratio of NOx 120574 refers to weightratio of PMx and 120573 + 120574 = 1(b) Estimation of Net Migration Rate According to Jia et al(2017) the attraction degree in Beijing was calculated to beabout 07056 [24]

According to Table 2 the permanent resident populationin Beijing exhibited a mechanical increase from 2009 to2014 respectively 112163 109091 129313 107072 109656and 74654 persons Therefore the net migration rates wererespectively calculated as 603 556 641 517 519and 347 A continuously decreasing trend was observeddue to registered residence migration and settlement policiesin Beijing In addition the net migration rate (mean value)of 531 must be adjusted given that it is obviously higherthan 347 and is inconsistent with the actual conditionsin Beijing Therefore the present study set the followingconditions

119873119890119905 119898119894119892119903119886119905119894119900119899 119903119886119905119890= 119899119890119905 119898119894119892119903119886119905119894119900119899 119903119886119905119890119898119890119886119899 V119886119897119906119890

Discrete Dynamics in Nature and Society 9

(a) APMG APCF=5(a) APMG APCF=100(a) APMG APCF=1000

100000

125000

150000

175000

200000

ton

2011 2013 2015 2017 20192009Time (year)

(a) APMG

(b) ANOG APCF=5(b) ANOG APCF=100(b) ANOG APCF=1000

2011 2013 2015 2017 20192009Time (year)

80000

110000

140000

170000

200000

ton

(b) ANOG

(c) AMVT APCF=5(c) AMVT APCF=100(c) AMVT APCF=1000

2011 2013 2015 2017 20192009Time (year)

2 M

25 M

3 M

35 M

4 M

vehi

cle

(c) AMVT

Figure 3 Extreme condition test (a) APMG (b) ANOG (c) AMVT

times 119886119905119905119903119886119888119905119894119900119899 119889119890119892119903119890119890 119900119891 119888119894119905119910120572(29)

where 120572 refers to the impact factor of policy Based on thiscalculation 120572 = 15 generates calculations that are close tothe actual value See the appendixes for descriptions of theother variables and main equations

3 Simulation and Result Analysis

31 Model Test

311 Extreme Condition Test The extreme condition testmainly aims to inspect the stability applicability in extremeconditions and accuracy of the equations in the test modelto represent the change trends of the realistic system and theintentions of the decision maker

According to Figure 3(a) the APMG exhibited a continu-ous decrease following an increase in the APCF In particularthe minimum value of APMG was obtained when the APCFwas at the limit value (1000 yuandaysdotvehicle) In additionwhen APCF was equal to 5 the maximum APMG value wasobtained which is consistent with the actual laws therebyconfirming the stability of the model in extreme conditions

A deeper analysis indicated a larger interval between curves1 and 2 and a shorter interval between curves 2 and curve3 thereby indicating that the APCF did not exceed 100yuandaysdotvehicle

The change rules presented in Figures 3(b) and 3(c) weresimilar to those in Figure 3(a)

312 Sensitivity Test The model behaviors exhibited dif-ferent and sensitive results at different parameter valuesSpecifically the behavior model changed following an appro-priate change of parameter In addition the policies generatedthrough the model analysis changed following a change inparameters

According to Figure 4(a) with time all the curves firstrose and then slowly descended Specifically in the earlyperiod of policy implementation (before 2014) the effect wasnot obvious because part-time drivers may not have had adeep understanding of the purpose of the implementationand the significance of the APCF policy thereby resultingin a continuous increase in AMVT due to sharp increasein motor vehicle ownership The AMVT growth rate wasmore effectively controlled following a longer period due tocontinuous policy implementation and fulfilment After 2016the growth rate continuously decreased thereby allowing

10 Discrete Dynamics in Nature and Society

(a) AMVT APCF=5(a) AMVT APCF=10(a) AMVT APCF=20(a) AMVT APCF=30(a) AMVT APCF=40(a) AMVT APCF=50(a) AMVT APCF=60(a) AMVT APCF=70(a) AMVT APCF=80(a) AMVT APCF=90(a) AMVT APCF=100

2 M

25 M

3 M

35 M

4 Mve

hicle

2011 2013 2015 2017 20192009Time (year)

(a) AMVT

(b) APMG APCF=5(b) APMG APCF=10(b) APMG APCF=20(b) APMG APCF=30(b) APMG APCF=40(b) APMG APCF=50(b) APMG APCF=60(b) APMG APCF=70(b) APMG APCF=80(b) APMG APCF=90(b) APMG APCF=100

100000

125000

150000

175000

200000

ton

2011 2013 2015 2017 20192009Time (year)

(b) APMG

(c) ANOG APCF=5(c) ANOG APCF=10(c) ANOG APCF=20(c) ANOG APCF=30(c) ANOG APCF=40(c) ANOG APCF=50(c) ANOG APCF=60(c) ANOG APCF=70(c) ANOG APCF=80(c) ANOG APCF=90(c) ANOG APCF=100

80000

110000

140000

170000

200000

ton

2011 2013 2015 2017 20192009Time (year)

(c) ANOG

Figure 4 Sensitivity test (a) AMVT (b) APMG (c) ANOG

the APCF policy to exhibit good effects based on long-termpractice improvement and fulfilment

Following further analysis the AMVT exhibited amarginal decreasing effect following an increase in APCFfrom curve 1 to curve 6 especially in curves 3ndash6 whichindicates that a larger APCF is not always better The analysisresults are presented in Figures 4(b) and 4(c)

In conclusion the APCF value range was observed withinthe interval of [30 50] based on the above analysis from the

perspective of AMVT reduction (alleviate traffic jam) as wellas APMG and ANOG emission reduction Table 8 presentsthe detailed analysis results

32 Analysis of Results The AMVT exhibited a continuousdecrease following an increase in APCF which indicates theability of this policy to restrict increases in AMVT Specif-ically obvious changes were in the intervals of [5 10] and[10 20] wherein theAMVTexhibited a decrease of 166649

Discrete Dynamics in Nature and Society 11

and 105055 respectively The AMVT exhibited a decreaseof 35103 24912 and 16793 in the intervals of [20 30][30 40] and [40 50] respectivelyHoweverminimal changeswere observed in the interval of 50 yuandaysdotvehicle aboveIn addition the APMG exhibited a decrease of 13967789137 28538 20987 and 14128 respectively in theabove intervals and exhibited very minimal changes in theinterval of 50 above The ANOG exhibited similar changerules

Therefore the interval [30 50] is deemed a reasonablevalue range based on the analysis on the degree of effect ofdifferent APCFs on the AMVT APMG and ANOG

In particular the change trends of AMVT APMG andANOG were generally consistent as presented in Figure 6specifically Figure 5(d) Figures 5(a)ndash5(c) exhibited obviousdecreasing trend rates that were continuously weakened inthe interval of [30 50] In addition the change was verylimited as the APCF exceeded 50 yuandaysdotvehicle

Therefore an effective APCF range of [30 50]was chosenbased on the development trends analysis of the change ratesof the main variables

33 Model Validation Historical data (2009-2015) on theamount of motor vehicles and population in Beijing arepresented in Table 9 wherein the conformance of theirrespective GSID was tested

331 Qualified Verification of the Degree of Grey Incidenceon the Population of Beijing The original sequence and itssimulation value sequence are respectively presented asfollows

1198830 =[[[[[[[[[[

1199090 (1)1199090 (2)1199090 (3)

1199090 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

18600119890 + 00719619119890 + 00720186119890 + 00720693119890 + 00721148119890 + 00721516119890 + 00721705119890 + 007

]]]]]]]]]]]]]]]

1198831 =[[[[[[[[[[

1199091 (1)1199091 (2)1199091 (3)

1199091 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

186000119890 + 007187390119890 + 007188790119890 + 007190200119890 + 007191621119890 + 007193053119890 + 007194495119890 + 007

]]]]]]]]]]]]]]]

(30)

The following was derived based on their calculations

100381610038161003816100381611990401003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

11990900 (119896) + 1211990900 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 117145

100381610038161003816100381611990411003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

11990901 (119896) + 1211990901 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 025295

10038161003816100381610038161199040 minus 11990411003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

(11990901 (119896) minus 11990900 (119896)) + 12 (11990901 (7) minus 11990900 (7))

1003816100381610038161003816100381610038161003816100381610038161003816= 09185

(31)

Therefore we are able to obtain the value of the GAID

12058501 = 1 + 100381610038161003816100381611990401003816100381610038161003816 + 1003816100381610038161003816119904110038161003816100381610038161 + 100381610038161003816100381611990401003816100381610038161003816 + 100381610038161003816100381611990411003816100381610038161003816 + 10038161003816100381610038161199040 minus 11990411003816100381610038161003816= 1 + 117145 + 025295

1 + 117145 + 025295 + 09185 asymp 07275(32)

In a similar way

100381610038161003816100381610038161199041015840010038161003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

119909101584000 (119896) + 12119909101584000 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 062985100381610038161003816100381610038161199041015840110038161003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

119909101584001 (119896) + 12119909101584001 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 0136051003816100381610038161003816100381611990410158400 minus 1199041015840110038161003816100381610038161003816

=10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

(119909101584001 (119896) minus 119909101584000 (119896)) + 12 (119909101584001 (7) minus 119909101584000 (7))

1003816100381610038161003816100381610038161003816100381610038161003816= 04938

(33)

Therefore GRID is

11990301 = 1 + 100381610038161003816100381610038161199041015840010038161003816100381610038161003816 + 1003816100381610038161003816100381611990410158401100381610038161003816100381610038161 + 1003816100381610038161003816119904101584001003816100381610038161003816 + 1003816100381610038161003816119904101584011003816100381610038161003816 + 100381610038161003816100381611990410158400 minus 119904101584011003816100381610038161003816= 1 + 062985 + 013605

1 + 062985 + 013605 + 04938 asymp 07815(34)

When 120579 = 05 and exist1205760 = 07 then12057601 = 12057912058501 + (1 minus 120579) 11990301 = 05 times 07275 + 05 times 07815

= 07545 gt 07 = 1205760 (35)

Therefore according to Table 5 the accuracy was determinedto be between grade 2 and grade 3

332 Qualified Verification of the Degree of Grey Incidenceon the Amount of Motor Vehicles in Beijing The original

12 Discrete Dynamics in Nature and Society

Table 8 The effects of different APCFs on AMVT APNG and ANOG

APCF AMVT Trend Variation APMG Trend Variation ANOG Trend Variation() () ()

5 345229e+006 -- -- 161737 -- -- 154899 -- --10 287697e+006 darr -166649 139146 darr -139677 137782 darr -11050420 257473e+006 darr -105055 126743 darr -89137 128122 darr -7011130 248435e+006 darr -35103 123126 darr -28538 125306 darr -2197940 242246e+006 darr -24912 120542 darr -20987 123272 darr -1623250 238178e+006 darr -16793 118839 darr -14128 121928 darr -1090360 235237e+006 darr -12348 117604 darr -10392 120952 darr -0800570 232979e+006 darr -09599 116655 darr -08069 120202 darr -0620180 231171e+006 darr -07760 115894 darr -06524 119599 darr -0501790 229680e+006 darr -06450 115265 darr -05427 119101 darr -04164100 228421e+006 darr -05482 114734 darr -04607 118680 darr -03535

Table 9 Historical data and their simulation values (2009-2015)

Time Amount of motor vehicles (vehicle) Amount of population (person)Actual value Simulation value Actual value Simulation value

2009 4019e+006 401900e+006 18600e+007 186000e+0072010 4809e+006 457571e+006 19619e+007 187390e+0072011 4983e+006 528216e+006 20186e+007 188790e+0072012 5200e+006 560956e+006 20693e+007 190200e+0072013 5437e+006 577509e+006 21148e+007 191621e+0072014 5591e+006 584424e+006 21516e+007 193053e+0072015 5619e+006 591422e+006 21705e+007 194495e+007

sequence and its simulation value sequence were respec-tively calculated as follows

119883119894 =[[[[[[[[[[

119909119894 (1)119909119894 (2)119909119894 (3)

119909119894 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

4019119890 + 0064809119890 + 0064983119890 + 0065200119890 + 0065437119890 + 0065591119890 + 0065619119890 + 006

]]]]]]]]]]]]]]]

119883119895 =[[[[[[[[[[

119909119895 (1)119909119895 (2)119909119895 (3)

119909119895 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

401900119890 + 006457571119890 + 006528216119890 + 006560956119890 + 006577509119890 + 006584424119890 + 006591422119890 + 006

]]]]]]]]]]]]]]]

(36)

TheGAID andGRIDwere respectively calculated as follows

120585119894119895 asymp 09235119903119894119895 asymp 09390 (37)

Hence when exist1205760 = 09 and 120579 = 05120576119894119895 = 120579120585119894119895 + (1 minus 120579) 119903119894119895 = 09313 gt 09 = 1205760 (38)

Therefore according to Definition 3 and Table 5 thismodel verified the degree of grey incidence and exhibited anaccuracy belonging to grade 1

34 Policy Simulation Analysis and Discussion

341 Horizontal Analysis According to the horizontal anal-ysis the curves exhibited different changes with time Thespecific analysis results are presented as follows

Following the adoption of the low charge policy egAPCF = 5 yuandaysdotvehicle the AMVT (curve 1) exhibiteda decrease since about 2014 as exhibited in Figure 6(a)Although the growth rates of ANOG and APMG exhibited adecrease the total emissions maintained an increasing trendthereby resulting in high DAP levels (curve 4) The analysisresults indicate the inability of the low charge policy toeffectively reduce the DAP

According to Figure 6(f) curve 1 first exhibited aslow rise (before 2013) and a subsequent sharp descentfollowing the adoption of the high charge policy (APCF= 50 yuandaylowastvehicle) As a result the AMVT valuesdescended until 2013 wherein its descending range continu-ously increased Curve 3 terminated its previously continuousrise and instead descended slowly Similarly the rising rate

Discrete Dynamics in Nature and Society 13

0

2

4

6

8

10

12

14

16

18A

MV

T (

)

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

(a) AMVT

0

2

4

6

8

10

12

14

APM

G (

)

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

(b) APMG

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

0

2

4

6

8

10

12

AN

OG

()

(c) ANOG

AMVT ()APMG ()ANOG ()

0

2

4

6

8

10

12

14

16

18

5 20 8010 50 60 7030 9040 100

(d) Trend comparison

Figure 5 Development trends of the change rates of the main variables (a) AMVT (b) APMG (c) ANOG (d) Trend comparison

Table 10 The comparison of different policies

Variable APCF (yuandaylowastvehicle) Trend Variation ()5 50

AMVT (vehicle) 345229e+006 238178e+006 darr -3101APMG (t) 161737e+005 118839e+005 darr -2652ANOG (t) 154899e+005 121928e+005 darr -2129DAP 06 0525 darr -1250

of curve 2 slowed down relatively These results indicatethe effective control on the increase of APMG and ANOGafter which the values began to descend slowly Curve 4exhibited three phases specifically a rapid rise between 2011and 2014 a slow rise in rate between 2014 and 2018 and a slowdescent after 2018These results indicate the presence of DAPimprovements which exhibited gradual descent after 2018

The analysis results in Figures 6(b)ndash6(e) were similar tothose presented above

342 Vertical Analysis According to Figures 6(a)ndash6(f) theAPCF exhibited a continuous increase thereby generating achange in the rules of all the curves as follows

(i) AMVT (curve 1)TheAMVT exhibited a continuousdecrease Within a certain range the increase inAPCF aided in the descent of the AMVT therebyfurther alleviating the traffic pressures

(ii) APMG (curve 3) and ANOG (curve 2) A charge ofmore than 30 (Figures 6(d)ndash6(f)) generated a slowdescent in APMGMeanwhile the increase in ANOGalso exhibited effective restraint

(iii) DAP (curve 4)TheDAP exhibited an overall declineespecially following the implementation of a highcharge policy (APCF isin [40 50]) A subsequentdescending trend was later observed in the period ofanalogue simulation as presented in Figures 6(e) and6(f)

343 Comparison of Policies According to Table 10 in thepresence of a low charge policy (APCF=5) the AMVTAPMG ANOG and DAP under a high charge pol-icy exhibited an obvious decrease which indicates thatthe implementation of a high charge policy effectivelyreduced motor vehicle exhaust emissions to restrain the

14 Discrete Dynamics in Nature and Society

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

083 M

10000004

2 M00

2011 2013 2015 2017 20192009Time (year)

AMVT APCF=5ANOG APCF=5APMG APCF=5DAP APCF=5

vehicletontonDmnl

(a)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=10ANOG APCF=10APMG APCF=10DAP APCF=10

vehicletontonDmnl

(b)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=20ANOG APCF=20APMG APCF=20DAP APCF=20

vehicletontonDmnl

(c)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=30ANOG APCF=30APMG APCF=30DAP APCF=30

vehicletontonDmnl

(d)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=40ANOG APCF=40APMG APCF=40DAP APCF=40

vehicletontonDmnl

(e)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=50ANOG APCF=50APMG APCF=50DAP APCF=50

vehicletontonDmnl

(f)

Figure 6 Policy simulation (a) APCF=5 (b) APCF=10 (c) APCF=20 (d) APCF=30 (e) APCF=40 (f) APCF=50

intensification of ldquohazerdquo pollution degree in Beijing Specif-ically the gap between curves 1 and 2 exhibited a continuouswidening as presented in Figure 7(a) After 2013 curve 2exhibited an obvious descent Therefore the APCF policyeffectively reduced the AMVT and enabled an about 3101decrease in 2020

The results in Figures 7(b)ndash7(d) were similarly analyzed

In conclusion the adoption of a low charge policygenerated increasing APMG and ANOG trends as presentedin Figures 6(a) and 6(b) thereby suggesting the inabilityof the low charge policy to effectively reduce the DAP Anincrease of the fee to a certain extent especially followingthe implementation of a high charge policy (Figures 6(e) and6(f)) not only reduced the AMVT and alleviated traffic jams

Discrete Dynamics in Nature and Society 15

APCF=5

APCF=50

x 106

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 20202009Time (year)

2

25

3

35ve

hicle

(a) AMVT

APCF=5

APCF=50

x 105

20182017 2019 20202015 2016201420122011 201320102009Time (year)

11

12

13

14

15

16

17

ton

(b) APMG

APCF=5

APCF=50

x 105

08

09

1

11

12

13

14

15

16

ton

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 20202009Time (year)

(c) ANOG

02

APCF=5

APCF=50

2009 2011 20122010 20142013 2016 2017 20182015 20202019Time (year)

025

03

035

04

045

05

055D

mnl

(d) DAP

Figure 7 Comparison of the policies (a) AVT (b) APMG (c) ANOG (d) DAP

in cities but also effectively reduced the APMG and ANOGthereby reducing the DAP

According to a comparison on the different schemes atthe end of the analogue simulation period the high chargepolicy functioned as follows in terms of the emission reduc-tion of the motor vehicle exhaust the APMG and ANOGexhibited reductions of 2652 and 2129 respectively interms of alleviating traffic jams the AMVT exhibited a 3101decrease and in terms of reducing the degree of air pollutionthe DAP exhibited a 1250 decrease

4 Conclusions

41 Main Conclusions To resolve the air pollution problemsgenerated by motor vehicle exhaust emission the presentstudy introduced the charging mechanism and built a motorvehicle exhaust emission reduction strategy managementmodel using economic means and the SD-GM approach to

generate the following conclusions based on tests validationof the models and the simulation analysis of policies

(1)Within a certain range the reduction effects of APMGandANOGexhibited continuous enhancements following anincrease in APCF However the APCF did not always followthe principle ldquobigger means betterrdquo because the emissionreduction effect which was generated by an increase inthe APCF exhibited a marginal decreasing effect Accord-ing to the sensitivity analysis a pollution charge of 30ndash50yuandaysdotvehicle for the motor vehicles in Beijing was withinthe relatively reasonable range

(2) Three high charge policy functions were generatedbased on a comparison of the simulation results of thedifferent charging schemes the implementation of highcharge policies not only reduced the AMVT and alleviatedtraffic jams (Figures 6(e) 6(f) and 7(a) Table 10) but alsoeffectively reduced the APMG andANOG (Figures 6(e) 6(f)7(b) and 7(c) Tables 5 and 10) thereby further reducing theDAP (Figures 6(e) 6(f) and 7(d) Table 10) According to the

16 Discrete Dynamics in Nature and Society

contrastive analysis the DAP exhibited a decrease of about1250

(3) However the following problems were encounteredfollowing the implementation of the APCF policy (a) Theimplementation of the APCF policy increased the cost ofmotor vehicle trips and urged part-time drivers to take publictransportation which increased the burden of public trans-portation The subsidy policy and other applicable policiesmust be introduced to improve the public transport supplylevel and service quality Otherwise the trip demands ofpassengers will be difficult to satisfy which will influencethe implementation of the APCF policy (b) In the earlyperiods of APCF policy implementation an increase in thecost of motor vehicle trips due to the insufficient publicunderstanding and utilization of the APCF policy loweredits public support rate The government must strengthenits public relations work especially regarding the purposeand significance of its implementation to improve publicawareness and acknowledgment (c) The purpose of thesepolicies must be supervised and managed to gather APCFincome and improve public transportation infrastructures

42 Deficiencies and Future Work The present study consid-ered NOx and PMx as the principal motor vehicle emissionpollutants Future research must fully consider other com-ponents such as SO2 airborne particles hydrocarbons COand CO2 Secondly the implementation of a single chargingmeasure can reduce the supply level of public transportationFuture research should consider a subsidy mechanism toimprove the service quality Thirdly the function and effectof a single policy are limited Future work must considerthe integration of multiple policies to improve the emissionreduction effect For example future work may focus priorityon public transportation improvement of fuel quality vigor-ous promotion of new energy vehicles and improvements inemission standards

Appendix

A

See Table 11

B

Summary of the major variables and equations(1) Cost of motor vehicle trips = Air pollution charging

feelowast (1+ Air pollution control)(2) Amount ofNOx generation = INTEG (NOx emissions

- Annual dissipation of NOx 80380)(3) NOx emissions = Per vehicle annual of NOx

emissionslowast Amount of motor vehicle tripslowast Contributionrate of NOx from vehicle

(4) Contribution rate of NOx from vehicle = 05(5) Dissipation rate of NOx = 02(6) Annual dissipation of NOx = Amount of NOx

generationlowast Dissipation rate of NOx(7) Per vehicle annual of NOx emissions = 002

(8) Amount of PMx generation = INTEG (PMxemissions- Annual dissipation of PMx 160760)

(9) PMx emissions = Amount of motor vehicle tripslowastContribution rate of PMx from vehiclelowast Per vehicle annualof PMx emissions

(10) Contribution rate of PMx from vehicle = 05(11) Per vehicle annual of PMx emissions = 004(12) Annual dissipation of PMx = Amount of PMx

generationlowast Dissipation and control rate of PMx(13) Dissipation and control rate of PMx = 05(14) Pollution degree of NOx = IF THEN ELSE (Amount

of NOx generationgt= 11182e+005 09 IF THEN ELSE(Amount of NOx generationgt= 10874e+005 08 IF THENELSE (Amount of NOx generationgt= 10400e+005 07 IFTHEN ELSE (Amount of NOx generationgt= 9966e+00406 IF THEN ELSE (Amount of NOx generationgt=9618e+004 05 IF THEN ELSE (Amount of NOxgenerationgt= 8038e+004 03 IF THEN ELSE (Amountof NOx generationgt= 7008e+004 025 IF THEN ELSE(Amount of NOx generationgt= 6144e+004 02 IF THENELSE (Amount of NOx generationgt= 5508e+004 015 01)))))))))

(15) Pollution degree of PMx = IF THEN ELSE (Amountof PMx generationgt= 22364e+005 09 IF THEN ELSE(Amount of PMx generationgt= 21748e+005 08 IF THENELSE (Amount of PMx generationgt= 20800e+005 07 IFTHEN ELSE (Amount of PMx generationgt= 19932e+00506 IF THEN ELSE (Amount of PMx generationgt=19236e+005 05 IF THEN ELSE (Amount of PMxgenerationgt= 16076e+005 03 IF THEN ELSE (Amountof PMx generationgt= 14016e+005 025 IF THEN ELSE(Amount of PMx generationgt= 12288e+005 02 IF THENELSE (Amount of PMx generationgt= 11016e+005 015 01)))))))))

(16) Ratio of motor vehicle trips = 055(17) Amount of motor vehicle trips = Amount of motor

vehicleslowast Ratio of motor vehicle trips(18) Degree of air pollution = Weight ratio of NOxlowast

Pollution degree of NOx+ Weight ratio of PMxlowast Pollutiondegree of PMx

(19) Weight ratio of PMx = 05(20) Weight ratio of NOx = 05(21) Air pollution control = IF THEN ELSE (Degree of air

pollutiongt= 07 1 IF THEN ELSE (Degree of air pollutiongt=06 08 IF THEN ELSE (Degree of air pollutiongt= 05 07IF THEN ELSE (Degree of air pollutiongt= 04 06 IF THENELSE (Degree of air pollutiongt= 03 05 IF THEN ELSE(Degree of air pollutiongt= 025 045 IF THENELSE (Degreeof air pollutiongt= 02 04 IF THEN ELSE (Degree of airpollutiongt= 015 035 03))))))))

(22) Attraction degree of the growth of vehicles= (1-Airpollution control)lowast 055+ Attraction degree of vehicle tripslowast045

(23) Per capita annual income = Amount of GDPAmount of population

(24) Amount of population = INTEG (Growth of popu-lation+ Net migration- Population reduction 186e+007)

(25) Birth rate = Adjustment coefficient of birth ratelowastPredictive value of birth rate

Discrete Dynamics in Nature and Society 17

Table 11 Description of main variables in stock flow diagram

Signicant variable Unit Variable type Data sourceAir pollution charging fee yuandaysdotvehicle ConstantAir pollution control Dmnl Auxiliary variable M1+M3Amount of GDP yuan Level M1Amount of motor vehicles vehicle Level M1Amount of motor vehicle trips vehicle Auxiliary variableAmount of NOx (PMx) generation ton Level M1Amount of population person Level M1Annual dissipation of NOx (PMx) tonyear FlowAnnual scrapped vehicleyear FlowAttraction degree of city Constant M2Attraction degree of the growth of vehicles Auxiliary variable M1+M3Attraction degree of vehicle trips Auxiliary variable M1+M3Birth rate 1year Constant M3Contribution rate of NOx (PMx) from vehicle Constant M2Cost of motor vehicle trips yuandaysdotvehicle Auxiliary variable M3Death rate 1year Constant M3Degree of air pollution Dmnl Auxiliary variable M3Dissipation and control rate of NOx (PMx) 1year Constant M2Graphical function of the growth of GDP Dmnl Auxiliary variable M3Growth of GDP yuanyear FlowGrowth rate of motor vehicles 1year Auxiliary variable M1+M3Growth of motor vehicles vehicleyear FlowGrowth of population personyear FlowGrowth rate of vehicle ownership Dmnl Auxiliary variable M1+M3Impact factor of policy Dmnl Constant M3Net migration personyear FlowNet migration rate 1year Constant M1+M3NOx (PMx) emissions tonyear FlowPer capita annual income yuanperson Auxiliary variablePer vehicle annual of NOx (PMx) emissions tonyearsdotvehicle Constant M2Pollution degree of NOx (PMx) Dmnl Auxiliary variable M1+M3Population reduction personyear FlowRatio of motor vehicle trips Constant M2Scrap rate 1year Constant M2The average of net migration rate 1year Constant M1Weight ratio of PMx (NOx) Auxiliary variable M3

(26) Predictive value of birth rate = 000925(27) Death rate = Adjustment coefficient of death ratelowast

Predictive value of death rate(28) Predictive value of death rate = 000494(29) Net migration = Amount of populationlowastNet migra-

tion rate(30) Net migration rate = The average of net migration

ratelowast Attraction degree of cityand(Impact factor of policy)(31) Impact factor of policy = 15(32) The average of net migration rate = 000531(33) Attraction degree of city = 07056(34) Amount of GDP = INTEG (Growth of GDP

12153e+012)

(35) Graphical function of the growth of GDP = WITHLOOKUP (Amount of GDP ([(8e+011 0)- (3e+ 012 03)](81178e+011 01648) (98468e+011 0213) (11115e+01201288) (12153e+012 00934) (141136e+012 01613)(162519e+012 01515) (178794e+012 01001) (198008e+01201075) (213308e+012 00773) (230146e+012 00789)(235396e+012 002281) (240162e+012 00203) (245025e+012 002025) (249987e+012 002024) (255049e+0120020249)))

(36) Growth rate of GDP = Graphical function of thegrowth of GDPlowast Impact factor of the growth of GDP

(37) Amount of motor vehicles = INTEG (Growth ofmotor vehicles- Annual scrapped 4019e+006)

18 Discrete Dynamics in Nature and Society

(38) Annual scrapped = Amount of motor vehicleslowastScrap rate

(39) Scrap rate = 0067

Conflicts of Interest

The author declares no conflicts of interest

Acknowledgments

This work has been partially supported by the NationalNatural Science Foundation of China (71571119) ShanghaiFirst-Class Academic Discipline Project (S1201YLXK) andChina Postdoctoral Science Foundation (2018M630404)Theauthor would like to thank LetPub (httpwwwletpubcom)for providing linguistic assistance during the preparation ofthis manuscript

References

[1] X Liu S Ma J Tian N Jia and G Li ldquoA system dynamicsapproach to scenario analysis for urban passenger transportenergy consumption and CO2 emissions A case study ofBeijingrdquo Energy Policy vol 85 pp 253ndash270 2015

[2] B Xu L Luo and B Lin ldquoA dynamic analysis of air pollutionemissions in China Evidence from nonparametric additiveregression modelsrdquo Ecological Indicators vol 63 pp 346ndash3582016

[3] S Leinert H Daly B Hyde and B O Gallachoir ldquoCo-benefitsNot always Quantifying the negative effect of a CO2-reducingcar taxation policy on NOx emissionsrdquo Energy Policy vol 63pp 1151ndash1159 2013

[4] Z Cheng L Li and J Liu ldquoIdentifying the spatial effects anddriving factors of urban PM25 pollution in Chinardquo EcologicalIndicators vol 82 pp 61ndash75 2017

[5] N Kaida and K Kaida ldquoSpillover effect of congestion chargingon pro-environmental behaviorrdquo Environment Developmentand Sustainability vol 17 no 3 pp 409ndash421 2015

[6] R Penabaena-Niebles V Cantillo and J L Moura ldquoImpactof transition between signal timing plans in social cost basedin delay fuel consumption and air emissionsrdquo TransportationResearch Part D Transport and Environment vol 41 pp 445ndash456 2015

[7] DDing andB Shuai ldquoA traffic restriction scheme for enhancingcarpoolingrdquoDiscreteDynamics inNature and Society Article ID9626938 9 pages 2017

[8] D Kong X Guo B Yang and D Wu ldquoAnalyzing the Impactof Trucks on Traffic Flow Based on an Improved CellularAutomaton Modelrdquo Discrete Dynamics in Nature and Societyvol 2016 pp 1ndash14 2016

[9] S Cakmak C Hebbern J D Cakmak and J Vanos ldquoThemodifying effect of socioeconomic status on the relationshipbetween traffic air pollution and respiratory health in elemen-tary schoolchildrenrdquo Journal of Environmental Managementvol 177 pp 1ndash8 2016

[10] L Song H Song J Lin et al ldquoPM25 emissions from differenttypes of heavy-duty truck a case study and meta-analysis ofthe Beijing-Tianjin-Hebei regionrdquo Environmental Science andPollution Research vol 24 no 12 pp 11206ndash11214 2017

[11] Z Hu S Kang C Li et al ldquoLight absorption of biomassburning and vehicle emission-sourced carbonaceous aerosolsof the Tibetan Plateaurdquo Environmental Science and PollutionResearch vol 24 no 18 pp 15369ndash15378 2017

[12] X Cen H K Lo and L Li ldquoA framework for estimating trafficemissions The development of Passenger Car Emission UnitrdquoTransportation Research Part D Transport and Environmentvol 44 pp 78ndash92 2016

[13] S Wang X Liu C Zhou J Hu and J Ou ldquoExamining theimpacts of socioeconomic factors urban form and transporta-tion networks on CO2 emissions in Chinarsquos megacitiesrdquoAppliedEnergy vol 185 pp 189ndash200 2017

[14] Q Wang K Hubacek K Feng Y-M Wei and Q-M LiangldquoDistributional effects of carbon taxationrdquo Applied Energy vol184 pp 1123ndash1131 2016

[15] C Johansson L Burman and B Forsberg ldquoThe effects ofcongestions tax on air quality and healthrdquo Atmospheric Envi-ronment vol 43 no 31 pp 4843ndash4854 2009

[16] A Rakowska K C Wong T Townsend et al ldquoImpact of trafficvolume and composition on the air quality and pedestrianexposure in urban street canyonrdquo Atmospheric Environmentvol 98 pp 260ndash270 2014

[17] S Batterman R Ganguly and P Harbin ldquoHigh resolutionspatial and temporal mapping of traffic-related air pollutantsrdquoInternational Journal of Environmental Research and PublicHealth vol 12 no 4 pp 3646ndash3666 2015

[18] J Eliasson M Borjesson D van Amelsfort K Brundell-Freijand L Engelson ldquoAccuracy of congestion pricing forecastsrdquoTransportation Research Part A Policy and Practice vol 52 pp34ndash46 2013

[19] J Eliasson ldquoThe role of attitude structures direct experienceand reframing for the success of congestion pricingrdquo Trans-portation Research Part A Policy and Practice vol 67 pp 81ndash952014

[20] H X Yang J D Li H Zhang and S Q Liu ldquoResearch on thegovernance of urban traffic jam based on system dynamicsrdquoSystems EngineeringTheory and Practice vol 34 no 8 pp 2135ndash2143 2014 (Chinese)

[21] M H Zhu Research on Socio-Economic Impact of UrbanTrafficCongestion [PhD thesis] Beijing JiaotongUniversity 2013(Chinese)

[22] B Zeng Research on Modeling Technologies of Grey Prediction[PhD thesis] Nanjing University of Aeronautics and Astronau-tics 2011 (Chinese)

[23] S F Liu Y J Yang and L F Wu Grey System Theory andApplication Science Press Beijing China 2017

[24] S W Jia K Yang J J Zhao and G L Yan ldquoThe traffic-congestion charging fee management model based on thesystem dynamics approachrdquo Mathematical Problems in Engi-neering vol 2017 Article ID 3024898 13 pages 2017

Discrete Dynamics in Nature and Society 5

such that119889119909(1)119889119905 + 119886119909(1) = 119887 (4)

The preceding equation is the winterization equation of thegrey GM (11) prediction model [22]

If 119909(0)(119896) ge 0 119896 = 1 2 119899 then and119886 = (119886 119887)119879 is theparameter list and satisfies

and119886 = (119886 119887)119879 = (119861119879119861)minus1 119861119879119884 (5)

wherein

119861 =[[[[[[[[[[[[

minus119909(1) (1) + 119909(1) (2)2 1

minus119909(1) (2) + 119909(1) (3)2 1

minus119909(1) (119899 minus 1) + 119909(1) (119899)2 1

]]]]]]]]]]]]

119884 =[[[[[[[[

119909(0) (2)119909(0) (3)

119909(0) (119899)

]]]]]]]]

(6)

(i) Time response formula of the solution of the winterizationequation 119889119909(1)119889119905 + 119886119909(1) = 119887 is

119909(1) (119905) = (119909(1) (1) minus 119887119886) 119890minus119886119905 + 119887

119886 (7)

(ii) Time response formula of the GM(11) model 119909(0)(119896) + 119886 sdot(119909(1)(119896) + 119909(1)(119896 minus 1))2 = 119887 isand119909(1) (119896 + 1) = (119909(0) (1) minus 119887

119886) 119890minus119886119896 + 119887119886 119896 = 1 2 3 119899

(8)

(iii) Predicted value model of the original model is

and119884 (119896 + 1) = and119909(0) (119896 + 1) = and119909(1) (119896 + 1) minus and119909(1) (119896)= (1 minus 119890119886) (119909(0) (1) minus 119887

119886) 119890minus119886119896(9)

The following definitions are provided in Liu et al [23]

Definition 2 Assume that the images of zero starting point ofthese two sequences

119883119894 = (119909119894 (1) 119909119894 (2) 119909119894 (119899)) 119883119895 = (119909119895 (1) 119909119895 (2) 119909119895 (119899)) (10)

are

1198830119894 = (1199090119894 (1) 1199090119894 (2) 1199090119894 (119899)) 1198830119895 = (1199090119895 (1) 1199090119895 (2) 1199090119895 (119899)) (11)

such that

120585119894119895 = 1 + 10038161003816100381610038161199041198941003816100381610038161003816 + 10038161003816100381610038161003816119904119895100381610038161003816100381610038161 + 10038161003816100381610038161199041198941003816100381610038161003816 + 1003816100381610038161003816100381611990411989510038161003816100381610038161003816 + 10038161003816100381610038161003816119904119894 minus 11990411989510038161003816100381610038161003816 (12)

The presented equation is the absolute degree of grey inci-dence (GAID) of 119883119894 and 119883119895 Assume that 119883119894 and 119883119895 aresequences of the same length with nonzero initial values 1198831015840119894and 1198831015840119895 are the initial images of 119883119894 and 119883119895 respectively 11988310158400119894and11988310158400119895 are the images of the zero starting point of sequences1198831015840119894 and 1198831015840119895 respectively and the GAID of 1198831015840119894 and 1198831015840119895 is calledthe relative degree of grey incidence (GRID) of 119883119894 and 119883119895Based on these definitions the following equation is thendefined

119903119894119895 = 1 + 10038161003816100381610038161003816119904101584011989410038161003816100381610038161003816 + 100381610038161003816100381610038161199041015840119895100381610038161003816100381610038161 + 100381610038161003816100381611990410158401198941003816100381610038161003816 + 10038161003816100381610038161003816119904101584011989510038161003816100381610038161003816 + 100381610038161003816100381610038161199041015840119894 minus 119904101584011989510038161003816100381610038161003816 (13)

such that

120576119894119895 = 120579120585119894119895 + (1 minus 120579) 119903119894119895 (14)

is defined as the synthetic degree of grey incidence (GSID) of119883119894 and 119883119895 wherein 120579 isin [0 1]Definition 3 Assume that119883(0) is the original sequence and119883(0) isits simulative sequence and 120576 is the degree of grey incidencebetween 119883(0) and and119883(0) In the case of 120576 gt 1205760 for the given1205760 gt 0 this model is defined as the qualified verification ofthe degree of grey incidence See Table 5 for the accuracy testgrade

The requirement of this model for correlation 120576 is ldquothebigger the betterrdquo

Step 1 (data processing) First write the original data as theform of sequence

119883(0) = (119909(0) (1) 119909(0) (2) 119909(0) (10))= (81178 98468 111150 121530 141136 162519 178794 198008 213308 230146)

(15)

6 Discrete Dynamics in Nature and Society

Second introduce the second-order average weakeningoperator 1198632 as

119883(0)1198632 = (119909(0) (1) 1198892 119909(0) (2) 1198892 119909(0) (10) 1198892) (16)

wherein

119909(0) (119896) 1198892 = 110 minus 119896 + 1 [119909(0) (119896) 119889 + 119909(0) (119896 + 1) 119889

+ + 119909(0) (10) 119889] 119909(0) (119896) 119889 = 1

10 minus 119896 + 1 [119909(0) (119896) + 119909(0) (119896 + 1) + + 119909(0) (10)] 119896 = 1 2 3 10

(17)

Obtain

119883(0)1198632 = (191742 195978 200266 20465 209105 213463 21769 221898 225937 230146) ≜ 119883= (119909 (1) 119909 (2) 119909 (3) 119909 (10)) (18)

Step 2 Calculate the 1-AGO sequence of sequence 119883 andobtain sequence 119883(1)

119883(1) = (119909(1) (1) 119909(1) (2) 119909(1) (3) 119909(1) (10))= (191742 38772 587986 792636 1001741 1215204 1432894 1654792 1880729 2110875) (19)

Step 3 Calculate its simulative sequence based on the greyGM (11) prediction model

According to Definition 1 the grey GM (11) predictionmodel is used to obtain the time response formula as follows

and119909(1) (119896 + 1) = 9728182119890002119896 minus 953644and119884 (119896 + 1) = and119909(0) (119896 + 1) = and119909(1) (119896 + 1) minus and119909(1) (119896)

(20)

The simulative sequence can then be calculated as

and119883= (and119909 (1) and119909 (2) and119909 (10))= (191742 196536 2005157 204576 2087185 2129448 2172568 2216561 2261444 2307236)

(21)

Step 4 (accuracy test) According to Steps 1 and 3 the originalsequence and its simulative sequence were respectivelycalculated as follows

119883 =[[[[[[[[[[

119909 (1)119909 (2)119909 (3)

119909 (10)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[[[[[[[[[

191742195978200266204650209105213463217690221898225937230146

]]]]]]]]]]]]]]]]]]]]]]]

and119883 =

[[[[[[[[[[[[[

and119909 (1)and119909 (2)and119909 (3)

and119909 (10)

]]]]]]]]]]]]]

=

[[[[[[[[[[[[[[[[[[[[[[[

191742196536020051572045760208718521294482172568221656122614442307236

]]]]]]]]]]]]]]]]]]]]]]]

(22)

Therefore one can calculate

|119904| =10038161003816100381610038161003816100381610038161003816100381610038169sum119896=2

[119909 (119896) minus 119909 (1)] + 12 [119909 (10) minus 119909 (1)]

1003816100381610038161003816100381610038161003816100381610038161003816

Discrete Dynamics in Nature and Society 7

Table 5 Reference list of accuracy test grade

Accuracy grade Grade 1 Grade 2 Grade 3 Grade 4Degree of grey incidence 1205760 090 080 070 060

Table 6 Amount of GDP and its growth rate

Time Amount of GDP (t) Growth rate Time Amount of GDP (t) Growth rate2005 69695e+011 --- 2013 198008e+012 010752006 81178e+011 01648 2014 213308e+012 007732007 98468e+011 02130 2015 230146e+012 007892008 11115e+012 01288 2016 2353956e+012 0022812009 12153e+012 00934 2017 2401622e+012 0020302010 141136e+012 01613 2018 2450253e+012 0020252011 162519e+012 01515 2019 2499868e+012 0020242012 178794e+012 01001 2020 2550488e+012 0020249

= 1742531003816100381610038161003816100381610038161003816and1199041003816100381610038161003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816100381610038169sum119896=2

[and119909 (119896) minus and119909 (1)] + 12 [and119909 (10) minus and119909 (1)]

1003816100381610038161003816100381610038161003816100381610038161003816= 1739031

1003816100381610038161003816100381610038161003816and119904 minus1199041003816100381610038161003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816100381610038169sum119896=2

[119909 (119896) minus 119909 (1) minus (and119909 (119896) minus and119909 (1))]

+ 12 [119909 (10) minus 119909 (1) minus (and119909 (10) minus and119909 (1))]

1003816100381610038161003816100381610038161003816100381610038161003816 = 3499(23)

such that

120585 = 1 + |119904| + 1003816100381610038161003816100381610038161003816and1199041003816100381610038161003816100381610038161003816

1 + |119904| + 1003816100381610038161003816100381610038161003816and1199041003816100381610038161003816100381610038161003816 +

1003816100381610038161003816100381610038161003816and119904 minus1199041003816100381610038161003816100381610038161003816

asymp 09990 (24)

Similarly 119903 = 09993 when 120579 = 05 exist1205760 = 09 therebydefining

120576 = 120579120585 + (1 minus 120579) 119903 = 09991 gt 09 = 1205760 (25)

Therefore this model is defined as the qualified verificationof the degree of grey incidence

Step 5 (predict future data) According to

and119909(1) (119896 + 1) = 9728182119890002119896 minus 953644and119909(0) (119896 + 1) = and119909(1) (119896 + 1) minus and119909(1) (119896)

(26)

a prediction of the next five steps was calculated as follows

and119883=

[[[[[[[[[[[[[[

and119909(0) (11)and119909(0) (12)and119909(0) (13)and119909(0) (14)and119909(0) (15)

]]]]]]]]]]]]]]

=[[[[[[[[[

23539562401622245025324998682550488

]]]]]]]]]

(27)

Step 6 (establish the graphical function) The GDP gross andits growth rate (2005-2020) were calculated using the abovesteps See Table 6 for specific results

Therefore onemay establish the graphical function of thegrowth of GDP

Graphical function of the growth of GDP= WITHLOOKUP (Amount of GDP ([(8e+011 0)- (3e+012 03)](81178e+011 01648) (98468e+011 0213) (11115e+01201288) (12153e+012 00934) (141136e+012 01613)(162519e+012 01515) (178794e+012 01001) (198008e+012 01075) (213308e+012 00773) (230146e+012 00789)(235396e+012 002281) (240162e+012 00203) (245025e+012 002025) (249987e+012 002024) (255049e+0120020249)))

Similarly onemay establish the Graphical function aboutthe growth rate of vehicle ownership See Appendix B forspecific results

(3)ThirdMethodThe purpose of this method is to determinesome variables with nonlinear characteristics because theyare difficult to define directly such as degree of air pollutionand air pollution control In the actual situation estimationswere conducted by utilizing data from the official website(M1) and the first two prediction methods Main basisSlightly adjust the change trend of the variables to meetthe actual change rules that have been observed in Beijingin recent years As a result several variables have been

8 Discrete Dynamics in Nature and Society

Table 7 Estimated values of pollution degree of NOx and PMx in Beijing

Time Amount of motor vehicles (vehicle) ANOG (t) APMG (t) Actual pollution degree2014 5591e+006 11182e+005 22364e+005 Serious pollution2013 5437e+006 10874e+005 21748e+005 Serious pollution2012 5200e+006 10400e+005 20800e+005 Moderate pollution2011 4983e+006 9966e+004 19932e+005 Moderate pollution2010 4809e+006 9618e+004 19236e+005 Moderate pollution2009 4019e+006 8038e+004 16076e+005 Mild pollution2008 3504e+006 7008e+004 14016e+005 Mild pollution2007 3072e+006 6144e+004 12288e+005 Mild pollution2006 2754e+006 5508e+004 11016e+005 Mild pollution

confirmed including the attraction degree of the city netmigration rate degree of air pollution air pollution controlattraction degree of vehicle trips attraction degree of growthof the vehicles and growth rate ofmotor vehiclesThe presentstudy characterized the degree of air pollution as an example

(a) Estimation of Degree of Air Pollution The present studyestimated the degree of air pollution mainly based on theamount of NOx generation (ANOG) and amount of PMxgeneration (APMG) in accordance with historical data inStatistical Yearbook of Beijing from 2006 to 2014 In additionthe methods were also combined to estimate the ANOG andAPMG See Table 7 for detailed results

According to the actual situation of air pollution causedby motor vehicle exhaust emission in Beijing serious pol-lution was observed from 2013 to 2014 moderate pollutionwas generated between 2010 and 2012 and mild pollutionoccurred before 2009Therefore this paper defines the degreeof air pollution caused by ANOG as follows

(I)The degree of air pollution exhibited a value range thatis defined as (0 1) wherein a value of 08 and above indicatesserious pollution a value lower than 08 but higher than 05means moderate pollution and a value lower than 05 meansmild pollution

(II) From 2013 to 2014 Beijing exhibited a very seriousdegree of air pollution such that the estimated value ofNOx pollution was characterized between 08 and 1 at acorresponding ANOG of 108740 t to 111820 t From 2010 to2012 the degree of air pollution was moderate such that theestimated value of pollution NOx was within the interval of(05 08) at a corresponding ANOG of 96180 t to 104000 tFrom 2006 to 2009 the pollution degree was mild such thatthe estimated value of NOx pollution was lower than 05

According to the provisions above establish the logicalfunction of pollution degree of NOx

Pollution degree of NOx = IF THEN ELSE (Amount ofNOxgenerationgt= 11182e+005 09 IFTHENELSE (Amountof NOx generationgt= 10874e+005 08 IF THEN ELSE(Amount of NOx generationgt= 10400e+005 07 IF THENELSE (Amount of NOx generationgt= 9966e+004 06 IFTHENELSE (Amount of NOx generationgt= 9618e+004 05IF THEN ELSE (Amount of NOx generationgt= 8038e+00403 IF THEN ELSE (Amount of NOx generationgt=7008e+004 025 IF THEN ELSE (Amount of NOx

generationgt= 6144e+004 02 IF THEN ELSE (Amount ofNOx generationgt= 5508e+004 015 01 )))))))))

In the same way one can establish the logical function ofpollution degree of PMx

Pollution degree of PMx = IF THEN ELSE (Amountof PMx generationgt= 22364e+005 09 IF THEN ELSE(Amount of PMx generationgt= 21748e+005 08 IF THENELSE (Amount of PMx generationgt= 20800e+005 07 IFTHEN ELSE (Amount of PMx generationgt= 19932e+00506 IF THEN ELSE (Amount of PMx generationgt=19236e+005 05 IF THEN ELSE (Amount of PMxgenerationgt= 16076e+005 03 IF THEN ELSE (Amountof PMx generationgt= 14016e+005 025 IF THEN ELSE(Amount of PMx generationgt= 12288e+005 02 IF THENELSE (Amount of PMx generationgt= 11016e+005 015 01)))))))))

Therefore

119863119890119892119903119890119890 119900119891 119886119894119903 119901119900119897119897119906119905119894119900119899= 120573 lowast 119901119900119897119897119906119905119894119900119899 119889119890119892119903119890119890 119900119891 119873119874119909 + 120574

lowast 119901119900119897119897119906119905119894119900119899 119889119890119892119903119890119890 119900119891 119875119872119909(28)

wherein 120573 refers to the weight ratio of NOx 120574 refers to weightratio of PMx and 120573 + 120574 = 1(b) Estimation of Net Migration Rate According to Jia et al(2017) the attraction degree in Beijing was calculated to beabout 07056 [24]

According to Table 2 the permanent resident populationin Beijing exhibited a mechanical increase from 2009 to2014 respectively 112163 109091 129313 107072 109656and 74654 persons Therefore the net migration rates wererespectively calculated as 603 556 641 517 519and 347 A continuously decreasing trend was observeddue to registered residence migration and settlement policiesin Beijing In addition the net migration rate (mean value)of 531 must be adjusted given that it is obviously higherthan 347 and is inconsistent with the actual conditionsin Beijing Therefore the present study set the followingconditions

119873119890119905 119898119894119892119903119886119905119894119900119899 119903119886119905119890= 119899119890119905 119898119894119892119903119886119905119894119900119899 119903119886119905119890119898119890119886119899 V119886119897119906119890

Discrete Dynamics in Nature and Society 9

(a) APMG APCF=5(a) APMG APCF=100(a) APMG APCF=1000

100000

125000

150000

175000

200000

ton

2011 2013 2015 2017 20192009Time (year)

(a) APMG

(b) ANOG APCF=5(b) ANOG APCF=100(b) ANOG APCF=1000

2011 2013 2015 2017 20192009Time (year)

80000

110000

140000

170000

200000

ton

(b) ANOG

(c) AMVT APCF=5(c) AMVT APCF=100(c) AMVT APCF=1000

2011 2013 2015 2017 20192009Time (year)

2 M

25 M

3 M

35 M

4 M

vehi

cle

(c) AMVT

Figure 3 Extreme condition test (a) APMG (b) ANOG (c) AMVT

times 119886119905119905119903119886119888119905119894119900119899 119889119890119892119903119890119890 119900119891 119888119894119905119910120572(29)

where 120572 refers to the impact factor of policy Based on thiscalculation 120572 = 15 generates calculations that are close tothe actual value See the appendixes for descriptions of theother variables and main equations

3 Simulation and Result Analysis

31 Model Test

311 Extreme Condition Test The extreme condition testmainly aims to inspect the stability applicability in extremeconditions and accuracy of the equations in the test modelto represent the change trends of the realistic system and theintentions of the decision maker

According to Figure 3(a) the APMG exhibited a continu-ous decrease following an increase in the APCF In particularthe minimum value of APMG was obtained when the APCFwas at the limit value (1000 yuandaysdotvehicle) In additionwhen APCF was equal to 5 the maximum APMG value wasobtained which is consistent with the actual laws therebyconfirming the stability of the model in extreme conditions

A deeper analysis indicated a larger interval between curves1 and 2 and a shorter interval between curves 2 and curve3 thereby indicating that the APCF did not exceed 100yuandaysdotvehicle

The change rules presented in Figures 3(b) and 3(c) weresimilar to those in Figure 3(a)

312 Sensitivity Test The model behaviors exhibited dif-ferent and sensitive results at different parameter valuesSpecifically the behavior model changed following an appro-priate change of parameter In addition the policies generatedthrough the model analysis changed following a change inparameters

According to Figure 4(a) with time all the curves firstrose and then slowly descended Specifically in the earlyperiod of policy implementation (before 2014) the effect wasnot obvious because part-time drivers may not have had adeep understanding of the purpose of the implementationand the significance of the APCF policy thereby resultingin a continuous increase in AMVT due to sharp increasein motor vehicle ownership The AMVT growth rate wasmore effectively controlled following a longer period due tocontinuous policy implementation and fulfilment After 2016the growth rate continuously decreased thereby allowing

10 Discrete Dynamics in Nature and Society

(a) AMVT APCF=5(a) AMVT APCF=10(a) AMVT APCF=20(a) AMVT APCF=30(a) AMVT APCF=40(a) AMVT APCF=50(a) AMVT APCF=60(a) AMVT APCF=70(a) AMVT APCF=80(a) AMVT APCF=90(a) AMVT APCF=100

2 M

25 M

3 M

35 M

4 Mve

hicle

2011 2013 2015 2017 20192009Time (year)

(a) AMVT

(b) APMG APCF=5(b) APMG APCF=10(b) APMG APCF=20(b) APMG APCF=30(b) APMG APCF=40(b) APMG APCF=50(b) APMG APCF=60(b) APMG APCF=70(b) APMG APCF=80(b) APMG APCF=90(b) APMG APCF=100

100000

125000

150000

175000

200000

ton

2011 2013 2015 2017 20192009Time (year)

(b) APMG

(c) ANOG APCF=5(c) ANOG APCF=10(c) ANOG APCF=20(c) ANOG APCF=30(c) ANOG APCF=40(c) ANOG APCF=50(c) ANOG APCF=60(c) ANOG APCF=70(c) ANOG APCF=80(c) ANOG APCF=90(c) ANOG APCF=100

80000

110000

140000

170000

200000

ton

2011 2013 2015 2017 20192009Time (year)

(c) ANOG

Figure 4 Sensitivity test (a) AMVT (b) APMG (c) ANOG

the APCF policy to exhibit good effects based on long-termpractice improvement and fulfilment

Following further analysis the AMVT exhibited amarginal decreasing effect following an increase in APCFfrom curve 1 to curve 6 especially in curves 3ndash6 whichindicates that a larger APCF is not always better The analysisresults are presented in Figures 4(b) and 4(c)

In conclusion the APCF value range was observed withinthe interval of [30 50] based on the above analysis from the

perspective of AMVT reduction (alleviate traffic jam) as wellas APMG and ANOG emission reduction Table 8 presentsthe detailed analysis results

32 Analysis of Results The AMVT exhibited a continuousdecrease following an increase in APCF which indicates theability of this policy to restrict increases in AMVT Specif-ically obvious changes were in the intervals of [5 10] and[10 20] wherein theAMVTexhibited a decrease of 166649

Discrete Dynamics in Nature and Society 11

and 105055 respectively The AMVT exhibited a decreaseof 35103 24912 and 16793 in the intervals of [20 30][30 40] and [40 50] respectivelyHoweverminimal changeswere observed in the interval of 50 yuandaysdotvehicle aboveIn addition the APMG exhibited a decrease of 13967789137 28538 20987 and 14128 respectively in theabove intervals and exhibited very minimal changes in theinterval of 50 above The ANOG exhibited similar changerules

Therefore the interval [30 50] is deemed a reasonablevalue range based on the analysis on the degree of effect ofdifferent APCFs on the AMVT APMG and ANOG

In particular the change trends of AMVT APMG andANOG were generally consistent as presented in Figure 6specifically Figure 5(d) Figures 5(a)ndash5(c) exhibited obviousdecreasing trend rates that were continuously weakened inthe interval of [30 50] In addition the change was verylimited as the APCF exceeded 50 yuandaysdotvehicle

Therefore an effective APCF range of [30 50]was chosenbased on the development trends analysis of the change ratesof the main variables

33 Model Validation Historical data (2009-2015) on theamount of motor vehicles and population in Beijing arepresented in Table 9 wherein the conformance of theirrespective GSID was tested

331 Qualified Verification of the Degree of Grey Incidenceon the Population of Beijing The original sequence and itssimulation value sequence are respectively presented asfollows

1198830 =[[[[[[[[[[

1199090 (1)1199090 (2)1199090 (3)

1199090 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

18600119890 + 00719619119890 + 00720186119890 + 00720693119890 + 00721148119890 + 00721516119890 + 00721705119890 + 007

]]]]]]]]]]]]]]]

1198831 =[[[[[[[[[[

1199091 (1)1199091 (2)1199091 (3)

1199091 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

186000119890 + 007187390119890 + 007188790119890 + 007190200119890 + 007191621119890 + 007193053119890 + 007194495119890 + 007

]]]]]]]]]]]]]]]

(30)

The following was derived based on their calculations

100381610038161003816100381611990401003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

11990900 (119896) + 1211990900 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 117145

100381610038161003816100381611990411003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

11990901 (119896) + 1211990901 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 025295

10038161003816100381610038161199040 minus 11990411003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

(11990901 (119896) minus 11990900 (119896)) + 12 (11990901 (7) minus 11990900 (7))

1003816100381610038161003816100381610038161003816100381610038161003816= 09185

(31)

Therefore we are able to obtain the value of the GAID

12058501 = 1 + 100381610038161003816100381611990401003816100381610038161003816 + 1003816100381610038161003816119904110038161003816100381610038161 + 100381610038161003816100381611990401003816100381610038161003816 + 100381610038161003816100381611990411003816100381610038161003816 + 10038161003816100381610038161199040 minus 11990411003816100381610038161003816= 1 + 117145 + 025295

1 + 117145 + 025295 + 09185 asymp 07275(32)

In a similar way

100381610038161003816100381610038161199041015840010038161003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

119909101584000 (119896) + 12119909101584000 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 062985100381610038161003816100381610038161199041015840110038161003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

119909101584001 (119896) + 12119909101584001 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 0136051003816100381610038161003816100381611990410158400 minus 1199041015840110038161003816100381610038161003816

=10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

(119909101584001 (119896) minus 119909101584000 (119896)) + 12 (119909101584001 (7) minus 119909101584000 (7))

1003816100381610038161003816100381610038161003816100381610038161003816= 04938

(33)

Therefore GRID is

11990301 = 1 + 100381610038161003816100381610038161199041015840010038161003816100381610038161003816 + 1003816100381610038161003816100381611990410158401100381610038161003816100381610038161 + 1003816100381610038161003816119904101584001003816100381610038161003816 + 1003816100381610038161003816119904101584011003816100381610038161003816 + 100381610038161003816100381611990410158400 minus 119904101584011003816100381610038161003816= 1 + 062985 + 013605

1 + 062985 + 013605 + 04938 asymp 07815(34)

When 120579 = 05 and exist1205760 = 07 then12057601 = 12057912058501 + (1 minus 120579) 11990301 = 05 times 07275 + 05 times 07815

= 07545 gt 07 = 1205760 (35)

Therefore according to Table 5 the accuracy was determinedto be between grade 2 and grade 3

332 Qualified Verification of the Degree of Grey Incidenceon the Amount of Motor Vehicles in Beijing The original

12 Discrete Dynamics in Nature and Society

Table 8 The effects of different APCFs on AMVT APNG and ANOG

APCF AMVT Trend Variation APMG Trend Variation ANOG Trend Variation() () ()

5 345229e+006 -- -- 161737 -- -- 154899 -- --10 287697e+006 darr -166649 139146 darr -139677 137782 darr -11050420 257473e+006 darr -105055 126743 darr -89137 128122 darr -7011130 248435e+006 darr -35103 123126 darr -28538 125306 darr -2197940 242246e+006 darr -24912 120542 darr -20987 123272 darr -1623250 238178e+006 darr -16793 118839 darr -14128 121928 darr -1090360 235237e+006 darr -12348 117604 darr -10392 120952 darr -0800570 232979e+006 darr -09599 116655 darr -08069 120202 darr -0620180 231171e+006 darr -07760 115894 darr -06524 119599 darr -0501790 229680e+006 darr -06450 115265 darr -05427 119101 darr -04164100 228421e+006 darr -05482 114734 darr -04607 118680 darr -03535

Table 9 Historical data and their simulation values (2009-2015)

Time Amount of motor vehicles (vehicle) Amount of population (person)Actual value Simulation value Actual value Simulation value

2009 4019e+006 401900e+006 18600e+007 186000e+0072010 4809e+006 457571e+006 19619e+007 187390e+0072011 4983e+006 528216e+006 20186e+007 188790e+0072012 5200e+006 560956e+006 20693e+007 190200e+0072013 5437e+006 577509e+006 21148e+007 191621e+0072014 5591e+006 584424e+006 21516e+007 193053e+0072015 5619e+006 591422e+006 21705e+007 194495e+007

sequence and its simulation value sequence were respec-tively calculated as follows

119883119894 =[[[[[[[[[[

119909119894 (1)119909119894 (2)119909119894 (3)

119909119894 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

4019119890 + 0064809119890 + 0064983119890 + 0065200119890 + 0065437119890 + 0065591119890 + 0065619119890 + 006

]]]]]]]]]]]]]]]

119883119895 =[[[[[[[[[[

119909119895 (1)119909119895 (2)119909119895 (3)

119909119895 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

401900119890 + 006457571119890 + 006528216119890 + 006560956119890 + 006577509119890 + 006584424119890 + 006591422119890 + 006

]]]]]]]]]]]]]]]

(36)

TheGAID andGRIDwere respectively calculated as follows

120585119894119895 asymp 09235119903119894119895 asymp 09390 (37)

Hence when exist1205760 = 09 and 120579 = 05120576119894119895 = 120579120585119894119895 + (1 minus 120579) 119903119894119895 = 09313 gt 09 = 1205760 (38)

Therefore according to Definition 3 and Table 5 thismodel verified the degree of grey incidence and exhibited anaccuracy belonging to grade 1

34 Policy Simulation Analysis and Discussion

341 Horizontal Analysis According to the horizontal anal-ysis the curves exhibited different changes with time Thespecific analysis results are presented as follows

Following the adoption of the low charge policy egAPCF = 5 yuandaysdotvehicle the AMVT (curve 1) exhibiteda decrease since about 2014 as exhibited in Figure 6(a)Although the growth rates of ANOG and APMG exhibited adecrease the total emissions maintained an increasing trendthereby resulting in high DAP levels (curve 4) The analysisresults indicate the inability of the low charge policy toeffectively reduce the DAP

According to Figure 6(f) curve 1 first exhibited aslow rise (before 2013) and a subsequent sharp descentfollowing the adoption of the high charge policy (APCF= 50 yuandaylowastvehicle) As a result the AMVT valuesdescended until 2013 wherein its descending range continu-ously increased Curve 3 terminated its previously continuousrise and instead descended slowly Similarly the rising rate

Discrete Dynamics in Nature and Society 13

0

2

4

6

8

10

12

14

16

18A

MV

T (

)

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

(a) AMVT

0

2

4

6

8

10

12

14

APM

G (

)

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

(b) APMG

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

0

2

4

6

8

10

12

AN

OG

()

(c) ANOG

AMVT ()APMG ()ANOG ()

0

2

4

6

8

10

12

14

16

18

5 20 8010 50 60 7030 9040 100

(d) Trend comparison

Figure 5 Development trends of the change rates of the main variables (a) AMVT (b) APMG (c) ANOG (d) Trend comparison

Table 10 The comparison of different policies

Variable APCF (yuandaylowastvehicle) Trend Variation ()5 50

AMVT (vehicle) 345229e+006 238178e+006 darr -3101APMG (t) 161737e+005 118839e+005 darr -2652ANOG (t) 154899e+005 121928e+005 darr -2129DAP 06 0525 darr -1250

of curve 2 slowed down relatively These results indicatethe effective control on the increase of APMG and ANOGafter which the values began to descend slowly Curve 4exhibited three phases specifically a rapid rise between 2011and 2014 a slow rise in rate between 2014 and 2018 and a slowdescent after 2018These results indicate the presence of DAPimprovements which exhibited gradual descent after 2018

The analysis results in Figures 6(b)ndash6(e) were similar tothose presented above

342 Vertical Analysis According to Figures 6(a)ndash6(f) theAPCF exhibited a continuous increase thereby generating achange in the rules of all the curves as follows

(i) AMVT (curve 1)TheAMVT exhibited a continuousdecrease Within a certain range the increase inAPCF aided in the descent of the AMVT therebyfurther alleviating the traffic pressures

(ii) APMG (curve 3) and ANOG (curve 2) A charge ofmore than 30 (Figures 6(d)ndash6(f)) generated a slowdescent in APMGMeanwhile the increase in ANOGalso exhibited effective restraint

(iii) DAP (curve 4)TheDAP exhibited an overall declineespecially following the implementation of a highcharge policy (APCF isin [40 50]) A subsequentdescending trend was later observed in the period ofanalogue simulation as presented in Figures 6(e) and6(f)

343 Comparison of Policies According to Table 10 in thepresence of a low charge policy (APCF=5) the AMVTAPMG ANOG and DAP under a high charge pol-icy exhibited an obvious decrease which indicates thatthe implementation of a high charge policy effectivelyreduced motor vehicle exhaust emissions to restrain the

14 Discrete Dynamics in Nature and Society

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

083 M

10000004

2 M00

2011 2013 2015 2017 20192009Time (year)

AMVT APCF=5ANOG APCF=5APMG APCF=5DAP APCF=5

vehicletontonDmnl

(a)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=10ANOG APCF=10APMG APCF=10DAP APCF=10

vehicletontonDmnl

(b)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=20ANOG APCF=20APMG APCF=20DAP APCF=20

vehicletontonDmnl

(c)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=30ANOG APCF=30APMG APCF=30DAP APCF=30

vehicletontonDmnl

(d)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=40ANOG APCF=40APMG APCF=40DAP APCF=40

vehicletontonDmnl

(e)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=50ANOG APCF=50APMG APCF=50DAP APCF=50

vehicletontonDmnl

(f)

Figure 6 Policy simulation (a) APCF=5 (b) APCF=10 (c) APCF=20 (d) APCF=30 (e) APCF=40 (f) APCF=50

intensification of ldquohazerdquo pollution degree in Beijing Specif-ically the gap between curves 1 and 2 exhibited a continuouswidening as presented in Figure 7(a) After 2013 curve 2exhibited an obvious descent Therefore the APCF policyeffectively reduced the AMVT and enabled an about 3101decrease in 2020

The results in Figures 7(b)ndash7(d) were similarly analyzed

In conclusion the adoption of a low charge policygenerated increasing APMG and ANOG trends as presentedin Figures 6(a) and 6(b) thereby suggesting the inabilityof the low charge policy to effectively reduce the DAP Anincrease of the fee to a certain extent especially followingthe implementation of a high charge policy (Figures 6(e) and6(f)) not only reduced the AMVT and alleviated traffic jams

Discrete Dynamics in Nature and Society 15

APCF=5

APCF=50

x 106

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 20202009Time (year)

2

25

3

35ve

hicle

(a) AMVT

APCF=5

APCF=50

x 105

20182017 2019 20202015 2016201420122011 201320102009Time (year)

11

12

13

14

15

16

17

ton

(b) APMG

APCF=5

APCF=50

x 105

08

09

1

11

12

13

14

15

16

ton

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 20202009Time (year)

(c) ANOG

02

APCF=5

APCF=50

2009 2011 20122010 20142013 2016 2017 20182015 20202019Time (year)

025

03

035

04

045

05

055D

mnl

(d) DAP

Figure 7 Comparison of the policies (a) AVT (b) APMG (c) ANOG (d) DAP

in cities but also effectively reduced the APMG and ANOGthereby reducing the DAP

According to a comparison on the different schemes atthe end of the analogue simulation period the high chargepolicy functioned as follows in terms of the emission reduc-tion of the motor vehicle exhaust the APMG and ANOGexhibited reductions of 2652 and 2129 respectively interms of alleviating traffic jams the AMVT exhibited a 3101decrease and in terms of reducing the degree of air pollutionthe DAP exhibited a 1250 decrease

4 Conclusions

41 Main Conclusions To resolve the air pollution problemsgenerated by motor vehicle exhaust emission the presentstudy introduced the charging mechanism and built a motorvehicle exhaust emission reduction strategy managementmodel using economic means and the SD-GM approach to

generate the following conclusions based on tests validationof the models and the simulation analysis of policies

(1)Within a certain range the reduction effects of APMGandANOGexhibited continuous enhancements following anincrease in APCF However the APCF did not always followthe principle ldquobigger means betterrdquo because the emissionreduction effect which was generated by an increase inthe APCF exhibited a marginal decreasing effect Accord-ing to the sensitivity analysis a pollution charge of 30ndash50yuandaysdotvehicle for the motor vehicles in Beijing was withinthe relatively reasonable range

(2) Three high charge policy functions were generatedbased on a comparison of the simulation results of thedifferent charging schemes the implementation of highcharge policies not only reduced the AMVT and alleviatedtraffic jams (Figures 6(e) 6(f) and 7(a) Table 10) but alsoeffectively reduced the APMG andANOG (Figures 6(e) 6(f)7(b) and 7(c) Tables 5 and 10) thereby further reducing theDAP (Figures 6(e) 6(f) and 7(d) Table 10) According to the

16 Discrete Dynamics in Nature and Society

contrastive analysis the DAP exhibited a decrease of about1250

(3) However the following problems were encounteredfollowing the implementation of the APCF policy (a) Theimplementation of the APCF policy increased the cost ofmotor vehicle trips and urged part-time drivers to take publictransportation which increased the burden of public trans-portation The subsidy policy and other applicable policiesmust be introduced to improve the public transport supplylevel and service quality Otherwise the trip demands ofpassengers will be difficult to satisfy which will influencethe implementation of the APCF policy (b) In the earlyperiods of APCF policy implementation an increase in thecost of motor vehicle trips due to the insufficient publicunderstanding and utilization of the APCF policy loweredits public support rate The government must strengthenits public relations work especially regarding the purposeand significance of its implementation to improve publicawareness and acknowledgment (c) The purpose of thesepolicies must be supervised and managed to gather APCFincome and improve public transportation infrastructures

42 Deficiencies and Future Work The present study consid-ered NOx and PMx as the principal motor vehicle emissionpollutants Future research must fully consider other com-ponents such as SO2 airborne particles hydrocarbons COand CO2 Secondly the implementation of a single chargingmeasure can reduce the supply level of public transportationFuture research should consider a subsidy mechanism toimprove the service quality Thirdly the function and effectof a single policy are limited Future work must considerthe integration of multiple policies to improve the emissionreduction effect For example future work may focus priorityon public transportation improvement of fuel quality vigor-ous promotion of new energy vehicles and improvements inemission standards

Appendix

A

See Table 11

B

Summary of the major variables and equations(1) Cost of motor vehicle trips = Air pollution charging

feelowast (1+ Air pollution control)(2) Amount ofNOx generation = INTEG (NOx emissions

- Annual dissipation of NOx 80380)(3) NOx emissions = Per vehicle annual of NOx

emissionslowast Amount of motor vehicle tripslowast Contributionrate of NOx from vehicle

(4) Contribution rate of NOx from vehicle = 05(5) Dissipation rate of NOx = 02(6) Annual dissipation of NOx = Amount of NOx

generationlowast Dissipation rate of NOx(7) Per vehicle annual of NOx emissions = 002

(8) Amount of PMx generation = INTEG (PMxemissions- Annual dissipation of PMx 160760)

(9) PMx emissions = Amount of motor vehicle tripslowastContribution rate of PMx from vehiclelowast Per vehicle annualof PMx emissions

(10) Contribution rate of PMx from vehicle = 05(11) Per vehicle annual of PMx emissions = 004(12) Annual dissipation of PMx = Amount of PMx

generationlowast Dissipation and control rate of PMx(13) Dissipation and control rate of PMx = 05(14) Pollution degree of NOx = IF THEN ELSE (Amount

of NOx generationgt= 11182e+005 09 IF THEN ELSE(Amount of NOx generationgt= 10874e+005 08 IF THENELSE (Amount of NOx generationgt= 10400e+005 07 IFTHEN ELSE (Amount of NOx generationgt= 9966e+00406 IF THEN ELSE (Amount of NOx generationgt=9618e+004 05 IF THEN ELSE (Amount of NOxgenerationgt= 8038e+004 03 IF THEN ELSE (Amountof NOx generationgt= 7008e+004 025 IF THEN ELSE(Amount of NOx generationgt= 6144e+004 02 IF THENELSE (Amount of NOx generationgt= 5508e+004 015 01)))))))))

(15) Pollution degree of PMx = IF THEN ELSE (Amountof PMx generationgt= 22364e+005 09 IF THEN ELSE(Amount of PMx generationgt= 21748e+005 08 IF THENELSE (Amount of PMx generationgt= 20800e+005 07 IFTHEN ELSE (Amount of PMx generationgt= 19932e+00506 IF THEN ELSE (Amount of PMx generationgt=19236e+005 05 IF THEN ELSE (Amount of PMxgenerationgt= 16076e+005 03 IF THEN ELSE (Amountof PMx generationgt= 14016e+005 025 IF THEN ELSE(Amount of PMx generationgt= 12288e+005 02 IF THENELSE (Amount of PMx generationgt= 11016e+005 015 01)))))))))

(16) Ratio of motor vehicle trips = 055(17) Amount of motor vehicle trips = Amount of motor

vehicleslowast Ratio of motor vehicle trips(18) Degree of air pollution = Weight ratio of NOxlowast

Pollution degree of NOx+ Weight ratio of PMxlowast Pollutiondegree of PMx

(19) Weight ratio of PMx = 05(20) Weight ratio of NOx = 05(21) Air pollution control = IF THEN ELSE (Degree of air

pollutiongt= 07 1 IF THEN ELSE (Degree of air pollutiongt=06 08 IF THEN ELSE (Degree of air pollutiongt= 05 07IF THEN ELSE (Degree of air pollutiongt= 04 06 IF THENELSE (Degree of air pollutiongt= 03 05 IF THEN ELSE(Degree of air pollutiongt= 025 045 IF THENELSE (Degreeof air pollutiongt= 02 04 IF THEN ELSE (Degree of airpollutiongt= 015 035 03))))))))

(22) Attraction degree of the growth of vehicles= (1-Airpollution control)lowast 055+ Attraction degree of vehicle tripslowast045

(23) Per capita annual income = Amount of GDPAmount of population

(24) Amount of population = INTEG (Growth of popu-lation+ Net migration- Population reduction 186e+007)

(25) Birth rate = Adjustment coefficient of birth ratelowastPredictive value of birth rate

Discrete Dynamics in Nature and Society 17

Table 11 Description of main variables in stock flow diagram

Signicant variable Unit Variable type Data sourceAir pollution charging fee yuandaysdotvehicle ConstantAir pollution control Dmnl Auxiliary variable M1+M3Amount of GDP yuan Level M1Amount of motor vehicles vehicle Level M1Amount of motor vehicle trips vehicle Auxiliary variableAmount of NOx (PMx) generation ton Level M1Amount of population person Level M1Annual dissipation of NOx (PMx) tonyear FlowAnnual scrapped vehicleyear FlowAttraction degree of city Constant M2Attraction degree of the growth of vehicles Auxiliary variable M1+M3Attraction degree of vehicle trips Auxiliary variable M1+M3Birth rate 1year Constant M3Contribution rate of NOx (PMx) from vehicle Constant M2Cost of motor vehicle trips yuandaysdotvehicle Auxiliary variable M3Death rate 1year Constant M3Degree of air pollution Dmnl Auxiliary variable M3Dissipation and control rate of NOx (PMx) 1year Constant M2Graphical function of the growth of GDP Dmnl Auxiliary variable M3Growth of GDP yuanyear FlowGrowth rate of motor vehicles 1year Auxiliary variable M1+M3Growth of motor vehicles vehicleyear FlowGrowth of population personyear FlowGrowth rate of vehicle ownership Dmnl Auxiliary variable M1+M3Impact factor of policy Dmnl Constant M3Net migration personyear FlowNet migration rate 1year Constant M1+M3NOx (PMx) emissions tonyear FlowPer capita annual income yuanperson Auxiliary variablePer vehicle annual of NOx (PMx) emissions tonyearsdotvehicle Constant M2Pollution degree of NOx (PMx) Dmnl Auxiliary variable M1+M3Population reduction personyear FlowRatio of motor vehicle trips Constant M2Scrap rate 1year Constant M2The average of net migration rate 1year Constant M1Weight ratio of PMx (NOx) Auxiliary variable M3

(26) Predictive value of birth rate = 000925(27) Death rate = Adjustment coefficient of death ratelowast

Predictive value of death rate(28) Predictive value of death rate = 000494(29) Net migration = Amount of populationlowastNet migra-

tion rate(30) Net migration rate = The average of net migration

ratelowast Attraction degree of cityand(Impact factor of policy)(31) Impact factor of policy = 15(32) The average of net migration rate = 000531(33) Attraction degree of city = 07056(34) Amount of GDP = INTEG (Growth of GDP

12153e+012)

(35) Graphical function of the growth of GDP = WITHLOOKUP (Amount of GDP ([(8e+011 0)- (3e+ 012 03)](81178e+011 01648) (98468e+011 0213) (11115e+01201288) (12153e+012 00934) (141136e+012 01613)(162519e+012 01515) (178794e+012 01001) (198008e+01201075) (213308e+012 00773) (230146e+012 00789)(235396e+012 002281) (240162e+012 00203) (245025e+012 002025) (249987e+012 002024) (255049e+0120020249)))

(36) Growth rate of GDP = Graphical function of thegrowth of GDPlowast Impact factor of the growth of GDP

(37) Amount of motor vehicles = INTEG (Growth ofmotor vehicles- Annual scrapped 4019e+006)

18 Discrete Dynamics in Nature and Society

(38) Annual scrapped = Amount of motor vehicleslowastScrap rate

(39) Scrap rate = 0067

Conflicts of Interest

The author declares no conflicts of interest

Acknowledgments

This work has been partially supported by the NationalNatural Science Foundation of China (71571119) ShanghaiFirst-Class Academic Discipline Project (S1201YLXK) andChina Postdoctoral Science Foundation (2018M630404)Theauthor would like to thank LetPub (httpwwwletpubcom)for providing linguistic assistance during the preparation ofthis manuscript

References

[1] X Liu S Ma J Tian N Jia and G Li ldquoA system dynamicsapproach to scenario analysis for urban passenger transportenergy consumption and CO2 emissions A case study ofBeijingrdquo Energy Policy vol 85 pp 253ndash270 2015

[2] B Xu L Luo and B Lin ldquoA dynamic analysis of air pollutionemissions in China Evidence from nonparametric additiveregression modelsrdquo Ecological Indicators vol 63 pp 346ndash3582016

[3] S Leinert H Daly B Hyde and B O Gallachoir ldquoCo-benefitsNot always Quantifying the negative effect of a CO2-reducingcar taxation policy on NOx emissionsrdquo Energy Policy vol 63pp 1151ndash1159 2013

[4] Z Cheng L Li and J Liu ldquoIdentifying the spatial effects anddriving factors of urban PM25 pollution in Chinardquo EcologicalIndicators vol 82 pp 61ndash75 2017

[5] N Kaida and K Kaida ldquoSpillover effect of congestion chargingon pro-environmental behaviorrdquo Environment Developmentand Sustainability vol 17 no 3 pp 409ndash421 2015

[6] R Penabaena-Niebles V Cantillo and J L Moura ldquoImpactof transition between signal timing plans in social cost basedin delay fuel consumption and air emissionsrdquo TransportationResearch Part D Transport and Environment vol 41 pp 445ndash456 2015

[7] DDing andB Shuai ldquoA traffic restriction scheme for enhancingcarpoolingrdquoDiscreteDynamics inNature and Society Article ID9626938 9 pages 2017

[8] D Kong X Guo B Yang and D Wu ldquoAnalyzing the Impactof Trucks on Traffic Flow Based on an Improved CellularAutomaton Modelrdquo Discrete Dynamics in Nature and Societyvol 2016 pp 1ndash14 2016

[9] S Cakmak C Hebbern J D Cakmak and J Vanos ldquoThemodifying effect of socioeconomic status on the relationshipbetween traffic air pollution and respiratory health in elemen-tary schoolchildrenrdquo Journal of Environmental Managementvol 177 pp 1ndash8 2016

[10] L Song H Song J Lin et al ldquoPM25 emissions from differenttypes of heavy-duty truck a case study and meta-analysis ofthe Beijing-Tianjin-Hebei regionrdquo Environmental Science andPollution Research vol 24 no 12 pp 11206ndash11214 2017

[11] Z Hu S Kang C Li et al ldquoLight absorption of biomassburning and vehicle emission-sourced carbonaceous aerosolsof the Tibetan Plateaurdquo Environmental Science and PollutionResearch vol 24 no 18 pp 15369ndash15378 2017

[12] X Cen H K Lo and L Li ldquoA framework for estimating trafficemissions The development of Passenger Car Emission UnitrdquoTransportation Research Part D Transport and Environmentvol 44 pp 78ndash92 2016

[13] S Wang X Liu C Zhou J Hu and J Ou ldquoExamining theimpacts of socioeconomic factors urban form and transporta-tion networks on CO2 emissions in Chinarsquos megacitiesrdquoAppliedEnergy vol 185 pp 189ndash200 2017

[14] Q Wang K Hubacek K Feng Y-M Wei and Q-M LiangldquoDistributional effects of carbon taxationrdquo Applied Energy vol184 pp 1123ndash1131 2016

[15] C Johansson L Burman and B Forsberg ldquoThe effects ofcongestions tax on air quality and healthrdquo Atmospheric Envi-ronment vol 43 no 31 pp 4843ndash4854 2009

[16] A Rakowska K C Wong T Townsend et al ldquoImpact of trafficvolume and composition on the air quality and pedestrianexposure in urban street canyonrdquo Atmospheric Environmentvol 98 pp 260ndash270 2014

[17] S Batterman R Ganguly and P Harbin ldquoHigh resolutionspatial and temporal mapping of traffic-related air pollutantsrdquoInternational Journal of Environmental Research and PublicHealth vol 12 no 4 pp 3646ndash3666 2015

[18] J Eliasson M Borjesson D van Amelsfort K Brundell-Freijand L Engelson ldquoAccuracy of congestion pricing forecastsrdquoTransportation Research Part A Policy and Practice vol 52 pp34ndash46 2013

[19] J Eliasson ldquoThe role of attitude structures direct experienceand reframing for the success of congestion pricingrdquo Trans-portation Research Part A Policy and Practice vol 67 pp 81ndash952014

[20] H X Yang J D Li H Zhang and S Q Liu ldquoResearch on thegovernance of urban traffic jam based on system dynamicsrdquoSystems EngineeringTheory and Practice vol 34 no 8 pp 2135ndash2143 2014 (Chinese)

[21] M H Zhu Research on Socio-Economic Impact of UrbanTrafficCongestion [PhD thesis] Beijing JiaotongUniversity 2013(Chinese)

[22] B Zeng Research on Modeling Technologies of Grey Prediction[PhD thesis] Nanjing University of Aeronautics and Astronau-tics 2011 (Chinese)

[23] S F Liu Y J Yang and L F Wu Grey System Theory andApplication Science Press Beijing China 2017

[24] S W Jia K Yang J J Zhao and G L Yan ldquoThe traffic-congestion charging fee management model based on thesystem dynamics approachrdquo Mathematical Problems in Engi-neering vol 2017 Article ID 3024898 13 pages 2017

6 Discrete Dynamics in Nature and Society

Second introduce the second-order average weakeningoperator 1198632 as

119883(0)1198632 = (119909(0) (1) 1198892 119909(0) (2) 1198892 119909(0) (10) 1198892) (16)

wherein

119909(0) (119896) 1198892 = 110 minus 119896 + 1 [119909(0) (119896) 119889 + 119909(0) (119896 + 1) 119889

+ + 119909(0) (10) 119889] 119909(0) (119896) 119889 = 1

10 minus 119896 + 1 [119909(0) (119896) + 119909(0) (119896 + 1) + + 119909(0) (10)] 119896 = 1 2 3 10

(17)

Obtain

119883(0)1198632 = (191742 195978 200266 20465 209105 213463 21769 221898 225937 230146) ≜ 119883= (119909 (1) 119909 (2) 119909 (3) 119909 (10)) (18)

Step 2 Calculate the 1-AGO sequence of sequence 119883 andobtain sequence 119883(1)

119883(1) = (119909(1) (1) 119909(1) (2) 119909(1) (3) 119909(1) (10))= (191742 38772 587986 792636 1001741 1215204 1432894 1654792 1880729 2110875) (19)

Step 3 Calculate its simulative sequence based on the greyGM (11) prediction model

According to Definition 1 the grey GM (11) predictionmodel is used to obtain the time response formula as follows

and119909(1) (119896 + 1) = 9728182119890002119896 minus 953644and119884 (119896 + 1) = and119909(0) (119896 + 1) = and119909(1) (119896 + 1) minus and119909(1) (119896)

(20)

The simulative sequence can then be calculated as

and119883= (and119909 (1) and119909 (2) and119909 (10))= (191742 196536 2005157 204576 2087185 2129448 2172568 2216561 2261444 2307236)

(21)

Step 4 (accuracy test) According to Steps 1 and 3 the originalsequence and its simulative sequence were respectivelycalculated as follows

119883 =[[[[[[[[[[

119909 (1)119909 (2)119909 (3)

119909 (10)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[[[[[[[[[

191742195978200266204650209105213463217690221898225937230146

]]]]]]]]]]]]]]]]]]]]]]]

and119883 =

[[[[[[[[[[[[[

and119909 (1)and119909 (2)and119909 (3)

and119909 (10)

]]]]]]]]]]]]]

=

[[[[[[[[[[[[[[[[[[[[[[[

191742196536020051572045760208718521294482172568221656122614442307236

]]]]]]]]]]]]]]]]]]]]]]]

(22)

Therefore one can calculate

|119904| =10038161003816100381610038161003816100381610038161003816100381610038169sum119896=2

[119909 (119896) minus 119909 (1)] + 12 [119909 (10) minus 119909 (1)]

1003816100381610038161003816100381610038161003816100381610038161003816

Discrete Dynamics in Nature and Society 7

Table 5 Reference list of accuracy test grade

Accuracy grade Grade 1 Grade 2 Grade 3 Grade 4Degree of grey incidence 1205760 090 080 070 060

Table 6 Amount of GDP and its growth rate

Time Amount of GDP (t) Growth rate Time Amount of GDP (t) Growth rate2005 69695e+011 --- 2013 198008e+012 010752006 81178e+011 01648 2014 213308e+012 007732007 98468e+011 02130 2015 230146e+012 007892008 11115e+012 01288 2016 2353956e+012 0022812009 12153e+012 00934 2017 2401622e+012 0020302010 141136e+012 01613 2018 2450253e+012 0020252011 162519e+012 01515 2019 2499868e+012 0020242012 178794e+012 01001 2020 2550488e+012 0020249

= 1742531003816100381610038161003816100381610038161003816and1199041003816100381610038161003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816100381610038169sum119896=2

[and119909 (119896) minus and119909 (1)] + 12 [and119909 (10) minus and119909 (1)]

1003816100381610038161003816100381610038161003816100381610038161003816= 1739031

1003816100381610038161003816100381610038161003816and119904 minus1199041003816100381610038161003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816100381610038169sum119896=2

[119909 (119896) minus 119909 (1) minus (and119909 (119896) minus and119909 (1))]

+ 12 [119909 (10) minus 119909 (1) minus (and119909 (10) minus and119909 (1))]

1003816100381610038161003816100381610038161003816100381610038161003816 = 3499(23)

such that

120585 = 1 + |119904| + 1003816100381610038161003816100381610038161003816and1199041003816100381610038161003816100381610038161003816

1 + |119904| + 1003816100381610038161003816100381610038161003816and1199041003816100381610038161003816100381610038161003816 +

1003816100381610038161003816100381610038161003816and119904 minus1199041003816100381610038161003816100381610038161003816

asymp 09990 (24)

Similarly 119903 = 09993 when 120579 = 05 exist1205760 = 09 therebydefining

120576 = 120579120585 + (1 minus 120579) 119903 = 09991 gt 09 = 1205760 (25)

Therefore this model is defined as the qualified verificationof the degree of grey incidence

Step 5 (predict future data) According to

and119909(1) (119896 + 1) = 9728182119890002119896 minus 953644and119909(0) (119896 + 1) = and119909(1) (119896 + 1) minus and119909(1) (119896)

(26)

a prediction of the next five steps was calculated as follows

and119883=

[[[[[[[[[[[[[[

and119909(0) (11)and119909(0) (12)and119909(0) (13)and119909(0) (14)and119909(0) (15)

]]]]]]]]]]]]]]

=[[[[[[[[[

23539562401622245025324998682550488

]]]]]]]]]

(27)

Step 6 (establish the graphical function) The GDP gross andits growth rate (2005-2020) were calculated using the abovesteps See Table 6 for specific results

Therefore onemay establish the graphical function of thegrowth of GDP

Graphical function of the growth of GDP= WITHLOOKUP (Amount of GDP ([(8e+011 0)- (3e+012 03)](81178e+011 01648) (98468e+011 0213) (11115e+01201288) (12153e+012 00934) (141136e+012 01613)(162519e+012 01515) (178794e+012 01001) (198008e+012 01075) (213308e+012 00773) (230146e+012 00789)(235396e+012 002281) (240162e+012 00203) (245025e+012 002025) (249987e+012 002024) (255049e+0120020249)))

Similarly onemay establish the Graphical function aboutthe growth rate of vehicle ownership See Appendix B forspecific results

(3)ThirdMethodThe purpose of this method is to determinesome variables with nonlinear characteristics because theyare difficult to define directly such as degree of air pollutionand air pollution control In the actual situation estimationswere conducted by utilizing data from the official website(M1) and the first two prediction methods Main basisSlightly adjust the change trend of the variables to meetthe actual change rules that have been observed in Beijingin recent years As a result several variables have been

8 Discrete Dynamics in Nature and Society

Table 7 Estimated values of pollution degree of NOx and PMx in Beijing

Time Amount of motor vehicles (vehicle) ANOG (t) APMG (t) Actual pollution degree2014 5591e+006 11182e+005 22364e+005 Serious pollution2013 5437e+006 10874e+005 21748e+005 Serious pollution2012 5200e+006 10400e+005 20800e+005 Moderate pollution2011 4983e+006 9966e+004 19932e+005 Moderate pollution2010 4809e+006 9618e+004 19236e+005 Moderate pollution2009 4019e+006 8038e+004 16076e+005 Mild pollution2008 3504e+006 7008e+004 14016e+005 Mild pollution2007 3072e+006 6144e+004 12288e+005 Mild pollution2006 2754e+006 5508e+004 11016e+005 Mild pollution

confirmed including the attraction degree of the city netmigration rate degree of air pollution air pollution controlattraction degree of vehicle trips attraction degree of growthof the vehicles and growth rate ofmotor vehiclesThe presentstudy characterized the degree of air pollution as an example

(a) Estimation of Degree of Air Pollution The present studyestimated the degree of air pollution mainly based on theamount of NOx generation (ANOG) and amount of PMxgeneration (APMG) in accordance with historical data inStatistical Yearbook of Beijing from 2006 to 2014 In additionthe methods were also combined to estimate the ANOG andAPMG See Table 7 for detailed results

According to the actual situation of air pollution causedby motor vehicle exhaust emission in Beijing serious pol-lution was observed from 2013 to 2014 moderate pollutionwas generated between 2010 and 2012 and mild pollutionoccurred before 2009Therefore this paper defines the degreeof air pollution caused by ANOG as follows

(I)The degree of air pollution exhibited a value range thatis defined as (0 1) wherein a value of 08 and above indicatesserious pollution a value lower than 08 but higher than 05means moderate pollution and a value lower than 05 meansmild pollution

(II) From 2013 to 2014 Beijing exhibited a very seriousdegree of air pollution such that the estimated value ofNOx pollution was characterized between 08 and 1 at acorresponding ANOG of 108740 t to 111820 t From 2010 to2012 the degree of air pollution was moderate such that theestimated value of pollution NOx was within the interval of(05 08) at a corresponding ANOG of 96180 t to 104000 tFrom 2006 to 2009 the pollution degree was mild such thatthe estimated value of NOx pollution was lower than 05

According to the provisions above establish the logicalfunction of pollution degree of NOx

Pollution degree of NOx = IF THEN ELSE (Amount ofNOxgenerationgt= 11182e+005 09 IFTHENELSE (Amountof NOx generationgt= 10874e+005 08 IF THEN ELSE(Amount of NOx generationgt= 10400e+005 07 IF THENELSE (Amount of NOx generationgt= 9966e+004 06 IFTHENELSE (Amount of NOx generationgt= 9618e+004 05IF THEN ELSE (Amount of NOx generationgt= 8038e+00403 IF THEN ELSE (Amount of NOx generationgt=7008e+004 025 IF THEN ELSE (Amount of NOx

generationgt= 6144e+004 02 IF THEN ELSE (Amount ofNOx generationgt= 5508e+004 015 01 )))))))))

In the same way one can establish the logical function ofpollution degree of PMx

Pollution degree of PMx = IF THEN ELSE (Amountof PMx generationgt= 22364e+005 09 IF THEN ELSE(Amount of PMx generationgt= 21748e+005 08 IF THENELSE (Amount of PMx generationgt= 20800e+005 07 IFTHEN ELSE (Amount of PMx generationgt= 19932e+00506 IF THEN ELSE (Amount of PMx generationgt=19236e+005 05 IF THEN ELSE (Amount of PMxgenerationgt= 16076e+005 03 IF THEN ELSE (Amountof PMx generationgt= 14016e+005 025 IF THEN ELSE(Amount of PMx generationgt= 12288e+005 02 IF THENELSE (Amount of PMx generationgt= 11016e+005 015 01)))))))))

Therefore

119863119890119892119903119890119890 119900119891 119886119894119903 119901119900119897119897119906119905119894119900119899= 120573 lowast 119901119900119897119897119906119905119894119900119899 119889119890119892119903119890119890 119900119891 119873119874119909 + 120574

lowast 119901119900119897119897119906119905119894119900119899 119889119890119892119903119890119890 119900119891 119875119872119909(28)

wherein 120573 refers to the weight ratio of NOx 120574 refers to weightratio of PMx and 120573 + 120574 = 1(b) Estimation of Net Migration Rate According to Jia et al(2017) the attraction degree in Beijing was calculated to beabout 07056 [24]

According to Table 2 the permanent resident populationin Beijing exhibited a mechanical increase from 2009 to2014 respectively 112163 109091 129313 107072 109656and 74654 persons Therefore the net migration rates wererespectively calculated as 603 556 641 517 519and 347 A continuously decreasing trend was observeddue to registered residence migration and settlement policiesin Beijing In addition the net migration rate (mean value)of 531 must be adjusted given that it is obviously higherthan 347 and is inconsistent with the actual conditionsin Beijing Therefore the present study set the followingconditions

119873119890119905 119898119894119892119903119886119905119894119900119899 119903119886119905119890= 119899119890119905 119898119894119892119903119886119905119894119900119899 119903119886119905119890119898119890119886119899 V119886119897119906119890

Discrete Dynamics in Nature and Society 9

(a) APMG APCF=5(a) APMG APCF=100(a) APMG APCF=1000

100000

125000

150000

175000

200000

ton

2011 2013 2015 2017 20192009Time (year)

(a) APMG

(b) ANOG APCF=5(b) ANOG APCF=100(b) ANOG APCF=1000

2011 2013 2015 2017 20192009Time (year)

80000

110000

140000

170000

200000

ton

(b) ANOG

(c) AMVT APCF=5(c) AMVT APCF=100(c) AMVT APCF=1000

2011 2013 2015 2017 20192009Time (year)

2 M

25 M

3 M

35 M

4 M

vehi

cle

(c) AMVT

Figure 3 Extreme condition test (a) APMG (b) ANOG (c) AMVT

times 119886119905119905119903119886119888119905119894119900119899 119889119890119892119903119890119890 119900119891 119888119894119905119910120572(29)

where 120572 refers to the impact factor of policy Based on thiscalculation 120572 = 15 generates calculations that are close tothe actual value See the appendixes for descriptions of theother variables and main equations

3 Simulation and Result Analysis

31 Model Test

311 Extreme Condition Test The extreme condition testmainly aims to inspect the stability applicability in extremeconditions and accuracy of the equations in the test modelto represent the change trends of the realistic system and theintentions of the decision maker

According to Figure 3(a) the APMG exhibited a continu-ous decrease following an increase in the APCF In particularthe minimum value of APMG was obtained when the APCFwas at the limit value (1000 yuandaysdotvehicle) In additionwhen APCF was equal to 5 the maximum APMG value wasobtained which is consistent with the actual laws therebyconfirming the stability of the model in extreme conditions

A deeper analysis indicated a larger interval between curves1 and 2 and a shorter interval between curves 2 and curve3 thereby indicating that the APCF did not exceed 100yuandaysdotvehicle

The change rules presented in Figures 3(b) and 3(c) weresimilar to those in Figure 3(a)

312 Sensitivity Test The model behaviors exhibited dif-ferent and sensitive results at different parameter valuesSpecifically the behavior model changed following an appro-priate change of parameter In addition the policies generatedthrough the model analysis changed following a change inparameters

According to Figure 4(a) with time all the curves firstrose and then slowly descended Specifically in the earlyperiod of policy implementation (before 2014) the effect wasnot obvious because part-time drivers may not have had adeep understanding of the purpose of the implementationand the significance of the APCF policy thereby resultingin a continuous increase in AMVT due to sharp increasein motor vehicle ownership The AMVT growth rate wasmore effectively controlled following a longer period due tocontinuous policy implementation and fulfilment After 2016the growth rate continuously decreased thereby allowing

10 Discrete Dynamics in Nature and Society

(a) AMVT APCF=5(a) AMVT APCF=10(a) AMVT APCF=20(a) AMVT APCF=30(a) AMVT APCF=40(a) AMVT APCF=50(a) AMVT APCF=60(a) AMVT APCF=70(a) AMVT APCF=80(a) AMVT APCF=90(a) AMVT APCF=100

2 M

25 M

3 M

35 M

4 Mve

hicle

2011 2013 2015 2017 20192009Time (year)

(a) AMVT

(b) APMG APCF=5(b) APMG APCF=10(b) APMG APCF=20(b) APMG APCF=30(b) APMG APCF=40(b) APMG APCF=50(b) APMG APCF=60(b) APMG APCF=70(b) APMG APCF=80(b) APMG APCF=90(b) APMG APCF=100

100000

125000

150000

175000

200000

ton

2011 2013 2015 2017 20192009Time (year)

(b) APMG

(c) ANOG APCF=5(c) ANOG APCF=10(c) ANOG APCF=20(c) ANOG APCF=30(c) ANOG APCF=40(c) ANOG APCF=50(c) ANOG APCF=60(c) ANOG APCF=70(c) ANOG APCF=80(c) ANOG APCF=90(c) ANOG APCF=100

80000

110000

140000

170000

200000

ton

2011 2013 2015 2017 20192009Time (year)

(c) ANOG

Figure 4 Sensitivity test (a) AMVT (b) APMG (c) ANOG

the APCF policy to exhibit good effects based on long-termpractice improvement and fulfilment

Following further analysis the AMVT exhibited amarginal decreasing effect following an increase in APCFfrom curve 1 to curve 6 especially in curves 3ndash6 whichindicates that a larger APCF is not always better The analysisresults are presented in Figures 4(b) and 4(c)

In conclusion the APCF value range was observed withinthe interval of [30 50] based on the above analysis from the

perspective of AMVT reduction (alleviate traffic jam) as wellas APMG and ANOG emission reduction Table 8 presentsthe detailed analysis results

32 Analysis of Results The AMVT exhibited a continuousdecrease following an increase in APCF which indicates theability of this policy to restrict increases in AMVT Specif-ically obvious changes were in the intervals of [5 10] and[10 20] wherein theAMVTexhibited a decrease of 166649

Discrete Dynamics in Nature and Society 11

and 105055 respectively The AMVT exhibited a decreaseof 35103 24912 and 16793 in the intervals of [20 30][30 40] and [40 50] respectivelyHoweverminimal changeswere observed in the interval of 50 yuandaysdotvehicle aboveIn addition the APMG exhibited a decrease of 13967789137 28538 20987 and 14128 respectively in theabove intervals and exhibited very minimal changes in theinterval of 50 above The ANOG exhibited similar changerules

Therefore the interval [30 50] is deemed a reasonablevalue range based on the analysis on the degree of effect ofdifferent APCFs on the AMVT APMG and ANOG

In particular the change trends of AMVT APMG andANOG were generally consistent as presented in Figure 6specifically Figure 5(d) Figures 5(a)ndash5(c) exhibited obviousdecreasing trend rates that were continuously weakened inthe interval of [30 50] In addition the change was verylimited as the APCF exceeded 50 yuandaysdotvehicle

Therefore an effective APCF range of [30 50]was chosenbased on the development trends analysis of the change ratesof the main variables

33 Model Validation Historical data (2009-2015) on theamount of motor vehicles and population in Beijing arepresented in Table 9 wherein the conformance of theirrespective GSID was tested

331 Qualified Verification of the Degree of Grey Incidenceon the Population of Beijing The original sequence and itssimulation value sequence are respectively presented asfollows

1198830 =[[[[[[[[[[

1199090 (1)1199090 (2)1199090 (3)

1199090 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

18600119890 + 00719619119890 + 00720186119890 + 00720693119890 + 00721148119890 + 00721516119890 + 00721705119890 + 007

]]]]]]]]]]]]]]]

1198831 =[[[[[[[[[[

1199091 (1)1199091 (2)1199091 (3)

1199091 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

186000119890 + 007187390119890 + 007188790119890 + 007190200119890 + 007191621119890 + 007193053119890 + 007194495119890 + 007

]]]]]]]]]]]]]]]

(30)

The following was derived based on their calculations

100381610038161003816100381611990401003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

11990900 (119896) + 1211990900 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 117145

100381610038161003816100381611990411003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

11990901 (119896) + 1211990901 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 025295

10038161003816100381610038161199040 minus 11990411003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

(11990901 (119896) minus 11990900 (119896)) + 12 (11990901 (7) minus 11990900 (7))

1003816100381610038161003816100381610038161003816100381610038161003816= 09185

(31)

Therefore we are able to obtain the value of the GAID

12058501 = 1 + 100381610038161003816100381611990401003816100381610038161003816 + 1003816100381610038161003816119904110038161003816100381610038161 + 100381610038161003816100381611990401003816100381610038161003816 + 100381610038161003816100381611990411003816100381610038161003816 + 10038161003816100381610038161199040 minus 11990411003816100381610038161003816= 1 + 117145 + 025295

1 + 117145 + 025295 + 09185 asymp 07275(32)

In a similar way

100381610038161003816100381610038161199041015840010038161003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

119909101584000 (119896) + 12119909101584000 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 062985100381610038161003816100381610038161199041015840110038161003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

119909101584001 (119896) + 12119909101584001 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 0136051003816100381610038161003816100381611990410158400 minus 1199041015840110038161003816100381610038161003816

=10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

(119909101584001 (119896) minus 119909101584000 (119896)) + 12 (119909101584001 (7) minus 119909101584000 (7))

1003816100381610038161003816100381610038161003816100381610038161003816= 04938

(33)

Therefore GRID is

11990301 = 1 + 100381610038161003816100381610038161199041015840010038161003816100381610038161003816 + 1003816100381610038161003816100381611990410158401100381610038161003816100381610038161 + 1003816100381610038161003816119904101584001003816100381610038161003816 + 1003816100381610038161003816119904101584011003816100381610038161003816 + 100381610038161003816100381611990410158400 minus 119904101584011003816100381610038161003816= 1 + 062985 + 013605

1 + 062985 + 013605 + 04938 asymp 07815(34)

When 120579 = 05 and exist1205760 = 07 then12057601 = 12057912058501 + (1 minus 120579) 11990301 = 05 times 07275 + 05 times 07815

= 07545 gt 07 = 1205760 (35)

Therefore according to Table 5 the accuracy was determinedto be between grade 2 and grade 3

332 Qualified Verification of the Degree of Grey Incidenceon the Amount of Motor Vehicles in Beijing The original

12 Discrete Dynamics in Nature and Society

Table 8 The effects of different APCFs on AMVT APNG and ANOG

APCF AMVT Trend Variation APMG Trend Variation ANOG Trend Variation() () ()

5 345229e+006 -- -- 161737 -- -- 154899 -- --10 287697e+006 darr -166649 139146 darr -139677 137782 darr -11050420 257473e+006 darr -105055 126743 darr -89137 128122 darr -7011130 248435e+006 darr -35103 123126 darr -28538 125306 darr -2197940 242246e+006 darr -24912 120542 darr -20987 123272 darr -1623250 238178e+006 darr -16793 118839 darr -14128 121928 darr -1090360 235237e+006 darr -12348 117604 darr -10392 120952 darr -0800570 232979e+006 darr -09599 116655 darr -08069 120202 darr -0620180 231171e+006 darr -07760 115894 darr -06524 119599 darr -0501790 229680e+006 darr -06450 115265 darr -05427 119101 darr -04164100 228421e+006 darr -05482 114734 darr -04607 118680 darr -03535

Table 9 Historical data and their simulation values (2009-2015)

Time Amount of motor vehicles (vehicle) Amount of population (person)Actual value Simulation value Actual value Simulation value

2009 4019e+006 401900e+006 18600e+007 186000e+0072010 4809e+006 457571e+006 19619e+007 187390e+0072011 4983e+006 528216e+006 20186e+007 188790e+0072012 5200e+006 560956e+006 20693e+007 190200e+0072013 5437e+006 577509e+006 21148e+007 191621e+0072014 5591e+006 584424e+006 21516e+007 193053e+0072015 5619e+006 591422e+006 21705e+007 194495e+007

sequence and its simulation value sequence were respec-tively calculated as follows

119883119894 =[[[[[[[[[[

119909119894 (1)119909119894 (2)119909119894 (3)

119909119894 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

4019119890 + 0064809119890 + 0064983119890 + 0065200119890 + 0065437119890 + 0065591119890 + 0065619119890 + 006

]]]]]]]]]]]]]]]

119883119895 =[[[[[[[[[[

119909119895 (1)119909119895 (2)119909119895 (3)

119909119895 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

401900119890 + 006457571119890 + 006528216119890 + 006560956119890 + 006577509119890 + 006584424119890 + 006591422119890 + 006

]]]]]]]]]]]]]]]

(36)

TheGAID andGRIDwere respectively calculated as follows

120585119894119895 asymp 09235119903119894119895 asymp 09390 (37)

Hence when exist1205760 = 09 and 120579 = 05120576119894119895 = 120579120585119894119895 + (1 minus 120579) 119903119894119895 = 09313 gt 09 = 1205760 (38)

Therefore according to Definition 3 and Table 5 thismodel verified the degree of grey incidence and exhibited anaccuracy belonging to grade 1

34 Policy Simulation Analysis and Discussion

341 Horizontal Analysis According to the horizontal anal-ysis the curves exhibited different changes with time Thespecific analysis results are presented as follows

Following the adoption of the low charge policy egAPCF = 5 yuandaysdotvehicle the AMVT (curve 1) exhibiteda decrease since about 2014 as exhibited in Figure 6(a)Although the growth rates of ANOG and APMG exhibited adecrease the total emissions maintained an increasing trendthereby resulting in high DAP levels (curve 4) The analysisresults indicate the inability of the low charge policy toeffectively reduce the DAP

According to Figure 6(f) curve 1 first exhibited aslow rise (before 2013) and a subsequent sharp descentfollowing the adoption of the high charge policy (APCF= 50 yuandaylowastvehicle) As a result the AMVT valuesdescended until 2013 wherein its descending range continu-ously increased Curve 3 terminated its previously continuousrise and instead descended slowly Similarly the rising rate

Discrete Dynamics in Nature and Society 13

0

2

4

6

8

10

12

14

16

18A

MV

T (

)

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

(a) AMVT

0

2

4

6

8

10

12

14

APM

G (

)

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

(b) APMG

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

0

2

4

6

8

10

12

AN

OG

()

(c) ANOG

AMVT ()APMG ()ANOG ()

0

2

4

6

8

10

12

14

16

18

5 20 8010 50 60 7030 9040 100

(d) Trend comparison

Figure 5 Development trends of the change rates of the main variables (a) AMVT (b) APMG (c) ANOG (d) Trend comparison

Table 10 The comparison of different policies

Variable APCF (yuandaylowastvehicle) Trend Variation ()5 50

AMVT (vehicle) 345229e+006 238178e+006 darr -3101APMG (t) 161737e+005 118839e+005 darr -2652ANOG (t) 154899e+005 121928e+005 darr -2129DAP 06 0525 darr -1250

of curve 2 slowed down relatively These results indicatethe effective control on the increase of APMG and ANOGafter which the values began to descend slowly Curve 4exhibited three phases specifically a rapid rise between 2011and 2014 a slow rise in rate between 2014 and 2018 and a slowdescent after 2018These results indicate the presence of DAPimprovements which exhibited gradual descent after 2018

The analysis results in Figures 6(b)ndash6(e) were similar tothose presented above

342 Vertical Analysis According to Figures 6(a)ndash6(f) theAPCF exhibited a continuous increase thereby generating achange in the rules of all the curves as follows

(i) AMVT (curve 1)TheAMVT exhibited a continuousdecrease Within a certain range the increase inAPCF aided in the descent of the AMVT therebyfurther alleviating the traffic pressures

(ii) APMG (curve 3) and ANOG (curve 2) A charge ofmore than 30 (Figures 6(d)ndash6(f)) generated a slowdescent in APMGMeanwhile the increase in ANOGalso exhibited effective restraint

(iii) DAP (curve 4)TheDAP exhibited an overall declineespecially following the implementation of a highcharge policy (APCF isin [40 50]) A subsequentdescending trend was later observed in the period ofanalogue simulation as presented in Figures 6(e) and6(f)

343 Comparison of Policies According to Table 10 in thepresence of a low charge policy (APCF=5) the AMVTAPMG ANOG and DAP under a high charge pol-icy exhibited an obvious decrease which indicates thatthe implementation of a high charge policy effectivelyreduced motor vehicle exhaust emissions to restrain the

14 Discrete Dynamics in Nature and Society

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

083 M

10000004

2 M00

2011 2013 2015 2017 20192009Time (year)

AMVT APCF=5ANOG APCF=5APMG APCF=5DAP APCF=5

vehicletontonDmnl

(a)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=10ANOG APCF=10APMG APCF=10DAP APCF=10

vehicletontonDmnl

(b)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=20ANOG APCF=20APMG APCF=20DAP APCF=20

vehicletontonDmnl

(c)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=30ANOG APCF=30APMG APCF=30DAP APCF=30

vehicletontonDmnl

(d)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=40ANOG APCF=40APMG APCF=40DAP APCF=40

vehicletontonDmnl

(e)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=50ANOG APCF=50APMG APCF=50DAP APCF=50

vehicletontonDmnl

(f)

Figure 6 Policy simulation (a) APCF=5 (b) APCF=10 (c) APCF=20 (d) APCF=30 (e) APCF=40 (f) APCF=50

intensification of ldquohazerdquo pollution degree in Beijing Specif-ically the gap between curves 1 and 2 exhibited a continuouswidening as presented in Figure 7(a) After 2013 curve 2exhibited an obvious descent Therefore the APCF policyeffectively reduced the AMVT and enabled an about 3101decrease in 2020

The results in Figures 7(b)ndash7(d) were similarly analyzed

In conclusion the adoption of a low charge policygenerated increasing APMG and ANOG trends as presentedin Figures 6(a) and 6(b) thereby suggesting the inabilityof the low charge policy to effectively reduce the DAP Anincrease of the fee to a certain extent especially followingthe implementation of a high charge policy (Figures 6(e) and6(f)) not only reduced the AMVT and alleviated traffic jams

Discrete Dynamics in Nature and Society 15

APCF=5

APCF=50

x 106

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 20202009Time (year)

2

25

3

35ve

hicle

(a) AMVT

APCF=5

APCF=50

x 105

20182017 2019 20202015 2016201420122011 201320102009Time (year)

11

12

13

14

15

16

17

ton

(b) APMG

APCF=5

APCF=50

x 105

08

09

1

11

12

13

14

15

16

ton

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 20202009Time (year)

(c) ANOG

02

APCF=5

APCF=50

2009 2011 20122010 20142013 2016 2017 20182015 20202019Time (year)

025

03

035

04

045

05

055D

mnl

(d) DAP

Figure 7 Comparison of the policies (a) AVT (b) APMG (c) ANOG (d) DAP

in cities but also effectively reduced the APMG and ANOGthereby reducing the DAP

According to a comparison on the different schemes atthe end of the analogue simulation period the high chargepolicy functioned as follows in terms of the emission reduc-tion of the motor vehicle exhaust the APMG and ANOGexhibited reductions of 2652 and 2129 respectively interms of alleviating traffic jams the AMVT exhibited a 3101decrease and in terms of reducing the degree of air pollutionthe DAP exhibited a 1250 decrease

4 Conclusions

41 Main Conclusions To resolve the air pollution problemsgenerated by motor vehicle exhaust emission the presentstudy introduced the charging mechanism and built a motorvehicle exhaust emission reduction strategy managementmodel using economic means and the SD-GM approach to

generate the following conclusions based on tests validationof the models and the simulation analysis of policies

(1)Within a certain range the reduction effects of APMGandANOGexhibited continuous enhancements following anincrease in APCF However the APCF did not always followthe principle ldquobigger means betterrdquo because the emissionreduction effect which was generated by an increase inthe APCF exhibited a marginal decreasing effect Accord-ing to the sensitivity analysis a pollution charge of 30ndash50yuandaysdotvehicle for the motor vehicles in Beijing was withinthe relatively reasonable range

(2) Three high charge policy functions were generatedbased on a comparison of the simulation results of thedifferent charging schemes the implementation of highcharge policies not only reduced the AMVT and alleviatedtraffic jams (Figures 6(e) 6(f) and 7(a) Table 10) but alsoeffectively reduced the APMG andANOG (Figures 6(e) 6(f)7(b) and 7(c) Tables 5 and 10) thereby further reducing theDAP (Figures 6(e) 6(f) and 7(d) Table 10) According to the

16 Discrete Dynamics in Nature and Society

contrastive analysis the DAP exhibited a decrease of about1250

(3) However the following problems were encounteredfollowing the implementation of the APCF policy (a) Theimplementation of the APCF policy increased the cost ofmotor vehicle trips and urged part-time drivers to take publictransportation which increased the burden of public trans-portation The subsidy policy and other applicable policiesmust be introduced to improve the public transport supplylevel and service quality Otherwise the trip demands ofpassengers will be difficult to satisfy which will influencethe implementation of the APCF policy (b) In the earlyperiods of APCF policy implementation an increase in thecost of motor vehicle trips due to the insufficient publicunderstanding and utilization of the APCF policy loweredits public support rate The government must strengthenits public relations work especially regarding the purposeand significance of its implementation to improve publicawareness and acknowledgment (c) The purpose of thesepolicies must be supervised and managed to gather APCFincome and improve public transportation infrastructures

42 Deficiencies and Future Work The present study consid-ered NOx and PMx as the principal motor vehicle emissionpollutants Future research must fully consider other com-ponents such as SO2 airborne particles hydrocarbons COand CO2 Secondly the implementation of a single chargingmeasure can reduce the supply level of public transportationFuture research should consider a subsidy mechanism toimprove the service quality Thirdly the function and effectof a single policy are limited Future work must considerthe integration of multiple policies to improve the emissionreduction effect For example future work may focus priorityon public transportation improvement of fuel quality vigor-ous promotion of new energy vehicles and improvements inemission standards

Appendix

A

See Table 11

B

Summary of the major variables and equations(1) Cost of motor vehicle trips = Air pollution charging

feelowast (1+ Air pollution control)(2) Amount ofNOx generation = INTEG (NOx emissions

- Annual dissipation of NOx 80380)(3) NOx emissions = Per vehicle annual of NOx

emissionslowast Amount of motor vehicle tripslowast Contributionrate of NOx from vehicle

(4) Contribution rate of NOx from vehicle = 05(5) Dissipation rate of NOx = 02(6) Annual dissipation of NOx = Amount of NOx

generationlowast Dissipation rate of NOx(7) Per vehicle annual of NOx emissions = 002

(8) Amount of PMx generation = INTEG (PMxemissions- Annual dissipation of PMx 160760)

(9) PMx emissions = Amount of motor vehicle tripslowastContribution rate of PMx from vehiclelowast Per vehicle annualof PMx emissions

(10) Contribution rate of PMx from vehicle = 05(11) Per vehicle annual of PMx emissions = 004(12) Annual dissipation of PMx = Amount of PMx

generationlowast Dissipation and control rate of PMx(13) Dissipation and control rate of PMx = 05(14) Pollution degree of NOx = IF THEN ELSE (Amount

of NOx generationgt= 11182e+005 09 IF THEN ELSE(Amount of NOx generationgt= 10874e+005 08 IF THENELSE (Amount of NOx generationgt= 10400e+005 07 IFTHEN ELSE (Amount of NOx generationgt= 9966e+00406 IF THEN ELSE (Amount of NOx generationgt=9618e+004 05 IF THEN ELSE (Amount of NOxgenerationgt= 8038e+004 03 IF THEN ELSE (Amountof NOx generationgt= 7008e+004 025 IF THEN ELSE(Amount of NOx generationgt= 6144e+004 02 IF THENELSE (Amount of NOx generationgt= 5508e+004 015 01)))))))))

(15) Pollution degree of PMx = IF THEN ELSE (Amountof PMx generationgt= 22364e+005 09 IF THEN ELSE(Amount of PMx generationgt= 21748e+005 08 IF THENELSE (Amount of PMx generationgt= 20800e+005 07 IFTHEN ELSE (Amount of PMx generationgt= 19932e+00506 IF THEN ELSE (Amount of PMx generationgt=19236e+005 05 IF THEN ELSE (Amount of PMxgenerationgt= 16076e+005 03 IF THEN ELSE (Amountof PMx generationgt= 14016e+005 025 IF THEN ELSE(Amount of PMx generationgt= 12288e+005 02 IF THENELSE (Amount of PMx generationgt= 11016e+005 015 01)))))))))

(16) Ratio of motor vehicle trips = 055(17) Amount of motor vehicle trips = Amount of motor

vehicleslowast Ratio of motor vehicle trips(18) Degree of air pollution = Weight ratio of NOxlowast

Pollution degree of NOx+ Weight ratio of PMxlowast Pollutiondegree of PMx

(19) Weight ratio of PMx = 05(20) Weight ratio of NOx = 05(21) Air pollution control = IF THEN ELSE (Degree of air

pollutiongt= 07 1 IF THEN ELSE (Degree of air pollutiongt=06 08 IF THEN ELSE (Degree of air pollutiongt= 05 07IF THEN ELSE (Degree of air pollutiongt= 04 06 IF THENELSE (Degree of air pollutiongt= 03 05 IF THEN ELSE(Degree of air pollutiongt= 025 045 IF THENELSE (Degreeof air pollutiongt= 02 04 IF THEN ELSE (Degree of airpollutiongt= 015 035 03))))))))

(22) Attraction degree of the growth of vehicles= (1-Airpollution control)lowast 055+ Attraction degree of vehicle tripslowast045

(23) Per capita annual income = Amount of GDPAmount of population

(24) Amount of population = INTEG (Growth of popu-lation+ Net migration- Population reduction 186e+007)

(25) Birth rate = Adjustment coefficient of birth ratelowastPredictive value of birth rate

Discrete Dynamics in Nature and Society 17

Table 11 Description of main variables in stock flow diagram

Signicant variable Unit Variable type Data sourceAir pollution charging fee yuandaysdotvehicle ConstantAir pollution control Dmnl Auxiliary variable M1+M3Amount of GDP yuan Level M1Amount of motor vehicles vehicle Level M1Amount of motor vehicle trips vehicle Auxiliary variableAmount of NOx (PMx) generation ton Level M1Amount of population person Level M1Annual dissipation of NOx (PMx) tonyear FlowAnnual scrapped vehicleyear FlowAttraction degree of city Constant M2Attraction degree of the growth of vehicles Auxiliary variable M1+M3Attraction degree of vehicle trips Auxiliary variable M1+M3Birth rate 1year Constant M3Contribution rate of NOx (PMx) from vehicle Constant M2Cost of motor vehicle trips yuandaysdotvehicle Auxiliary variable M3Death rate 1year Constant M3Degree of air pollution Dmnl Auxiliary variable M3Dissipation and control rate of NOx (PMx) 1year Constant M2Graphical function of the growth of GDP Dmnl Auxiliary variable M3Growth of GDP yuanyear FlowGrowth rate of motor vehicles 1year Auxiliary variable M1+M3Growth of motor vehicles vehicleyear FlowGrowth of population personyear FlowGrowth rate of vehicle ownership Dmnl Auxiliary variable M1+M3Impact factor of policy Dmnl Constant M3Net migration personyear FlowNet migration rate 1year Constant M1+M3NOx (PMx) emissions tonyear FlowPer capita annual income yuanperson Auxiliary variablePer vehicle annual of NOx (PMx) emissions tonyearsdotvehicle Constant M2Pollution degree of NOx (PMx) Dmnl Auxiliary variable M1+M3Population reduction personyear FlowRatio of motor vehicle trips Constant M2Scrap rate 1year Constant M2The average of net migration rate 1year Constant M1Weight ratio of PMx (NOx) Auxiliary variable M3

(26) Predictive value of birth rate = 000925(27) Death rate = Adjustment coefficient of death ratelowast

Predictive value of death rate(28) Predictive value of death rate = 000494(29) Net migration = Amount of populationlowastNet migra-

tion rate(30) Net migration rate = The average of net migration

ratelowast Attraction degree of cityand(Impact factor of policy)(31) Impact factor of policy = 15(32) The average of net migration rate = 000531(33) Attraction degree of city = 07056(34) Amount of GDP = INTEG (Growth of GDP

12153e+012)

(35) Graphical function of the growth of GDP = WITHLOOKUP (Amount of GDP ([(8e+011 0)- (3e+ 012 03)](81178e+011 01648) (98468e+011 0213) (11115e+01201288) (12153e+012 00934) (141136e+012 01613)(162519e+012 01515) (178794e+012 01001) (198008e+01201075) (213308e+012 00773) (230146e+012 00789)(235396e+012 002281) (240162e+012 00203) (245025e+012 002025) (249987e+012 002024) (255049e+0120020249)))

(36) Growth rate of GDP = Graphical function of thegrowth of GDPlowast Impact factor of the growth of GDP

(37) Amount of motor vehicles = INTEG (Growth ofmotor vehicles- Annual scrapped 4019e+006)

18 Discrete Dynamics in Nature and Society

(38) Annual scrapped = Amount of motor vehicleslowastScrap rate

(39) Scrap rate = 0067

Conflicts of Interest

The author declares no conflicts of interest

Acknowledgments

This work has been partially supported by the NationalNatural Science Foundation of China (71571119) ShanghaiFirst-Class Academic Discipline Project (S1201YLXK) andChina Postdoctoral Science Foundation (2018M630404)Theauthor would like to thank LetPub (httpwwwletpubcom)for providing linguistic assistance during the preparation ofthis manuscript

References

[1] X Liu S Ma J Tian N Jia and G Li ldquoA system dynamicsapproach to scenario analysis for urban passenger transportenergy consumption and CO2 emissions A case study ofBeijingrdquo Energy Policy vol 85 pp 253ndash270 2015

[2] B Xu L Luo and B Lin ldquoA dynamic analysis of air pollutionemissions in China Evidence from nonparametric additiveregression modelsrdquo Ecological Indicators vol 63 pp 346ndash3582016

[3] S Leinert H Daly B Hyde and B O Gallachoir ldquoCo-benefitsNot always Quantifying the negative effect of a CO2-reducingcar taxation policy on NOx emissionsrdquo Energy Policy vol 63pp 1151ndash1159 2013

[4] Z Cheng L Li and J Liu ldquoIdentifying the spatial effects anddriving factors of urban PM25 pollution in Chinardquo EcologicalIndicators vol 82 pp 61ndash75 2017

[5] N Kaida and K Kaida ldquoSpillover effect of congestion chargingon pro-environmental behaviorrdquo Environment Developmentand Sustainability vol 17 no 3 pp 409ndash421 2015

[6] R Penabaena-Niebles V Cantillo and J L Moura ldquoImpactof transition between signal timing plans in social cost basedin delay fuel consumption and air emissionsrdquo TransportationResearch Part D Transport and Environment vol 41 pp 445ndash456 2015

[7] DDing andB Shuai ldquoA traffic restriction scheme for enhancingcarpoolingrdquoDiscreteDynamics inNature and Society Article ID9626938 9 pages 2017

[8] D Kong X Guo B Yang and D Wu ldquoAnalyzing the Impactof Trucks on Traffic Flow Based on an Improved CellularAutomaton Modelrdquo Discrete Dynamics in Nature and Societyvol 2016 pp 1ndash14 2016

[9] S Cakmak C Hebbern J D Cakmak and J Vanos ldquoThemodifying effect of socioeconomic status on the relationshipbetween traffic air pollution and respiratory health in elemen-tary schoolchildrenrdquo Journal of Environmental Managementvol 177 pp 1ndash8 2016

[10] L Song H Song J Lin et al ldquoPM25 emissions from differenttypes of heavy-duty truck a case study and meta-analysis ofthe Beijing-Tianjin-Hebei regionrdquo Environmental Science andPollution Research vol 24 no 12 pp 11206ndash11214 2017

[11] Z Hu S Kang C Li et al ldquoLight absorption of biomassburning and vehicle emission-sourced carbonaceous aerosolsof the Tibetan Plateaurdquo Environmental Science and PollutionResearch vol 24 no 18 pp 15369ndash15378 2017

[12] X Cen H K Lo and L Li ldquoA framework for estimating trafficemissions The development of Passenger Car Emission UnitrdquoTransportation Research Part D Transport and Environmentvol 44 pp 78ndash92 2016

[13] S Wang X Liu C Zhou J Hu and J Ou ldquoExamining theimpacts of socioeconomic factors urban form and transporta-tion networks on CO2 emissions in Chinarsquos megacitiesrdquoAppliedEnergy vol 185 pp 189ndash200 2017

[14] Q Wang K Hubacek K Feng Y-M Wei and Q-M LiangldquoDistributional effects of carbon taxationrdquo Applied Energy vol184 pp 1123ndash1131 2016

[15] C Johansson L Burman and B Forsberg ldquoThe effects ofcongestions tax on air quality and healthrdquo Atmospheric Envi-ronment vol 43 no 31 pp 4843ndash4854 2009

[16] A Rakowska K C Wong T Townsend et al ldquoImpact of trafficvolume and composition on the air quality and pedestrianexposure in urban street canyonrdquo Atmospheric Environmentvol 98 pp 260ndash270 2014

[17] S Batterman R Ganguly and P Harbin ldquoHigh resolutionspatial and temporal mapping of traffic-related air pollutantsrdquoInternational Journal of Environmental Research and PublicHealth vol 12 no 4 pp 3646ndash3666 2015

[18] J Eliasson M Borjesson D van Amelsfort K Brundell-Freijand L Engelson ldquoAccuracy of congestion pricing forecastsrdquoTransportation Research Part A Policy and Practice vol 52 pp34ndash46 2013

[19] J Eliasson ldquoThe role of attitude structures direct experienceand reframing for the success of congestion pricingrdquo Trans-portation Research Part A Policy and Practice vol 67 pp 81ndash952014

[20] H X Yang J D Li H Zhang and S Q Liu ldquoResearch on thegovernance of urban traffic jam based on system dynamicsrdquoSystems EngineeringTheory and Practice vol 34 no 8 pp 2135ndash2143 2014 (Chinese)

[21] M H Zhu Research on Socio-Economic Impact of UrbanTrafficCongestion [PhD thesis] Beijing JiaotongUniversity 2013(Chinese)

[22] B Zeng Research on Modeling Technologies of Grey Prediction[PhD thesis] Nanjing University of Aeronautics and Astronau-tics 2011 (Chinese)

[23] S F Liu Y J Yang and L F Wu Grey System Theory andApplication Science Press Beijing China 2017

[24] S W Jia K Yang J J Zhao and G L Yan ldquoThe traffic-congestion charging fee management model based on thesystem dynamics approachrdquo Mathematical Problems in Engi-neering vol 2017 Article ID 3024898 13 pages 2017

Discrete Dynamics in Nature and Society 7

Table 5 Reference list of accuracy test grade

Accuracy grade Grade 1 Grade 2 Grade 3 Grade 4Degree of grey incidence 1205760 090 080 070 060

Table 6 Amount of GDP and its growth rate

Time Amount of GDP (t) Growth rate Time Amount of GDP (t) Growth rate2005 69695e+011 --- 2013 198008e+012 010752006 81178e+011 01648 2014 213308e+012 007732007 98468e+011 02130 2015 230146e+012 007892008 11115e+012 01288 2016 2353956e+012 0022812009 12153e+012 00934 2017 2401622e+012 0020302010 141136e+012 01613 2018 2450253e+012 0020252011 162519e+012 01515 2019 2499868e+012 0020242012 178794e+012 01001 2020 2550488e+012 0020249

= 1742531003816100381610038161003816100381610038161003816and1199041003816100381610038161003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816100381610038169sum119896=2

[and119909 (119896) minus and119909 (1)] + 12 [and119909 (10) minus and119909 (1)]

1003816100381610038161003816100381610038161003816100381610038161003816= 1739031

1003816100381610038161003816100381610038161003816and119904 minus1199041003816100381610038161003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816100381610038169sum119896=2

[119909 (119896) minus 119909 (1) minus (and119909 (119896) minus and119909 (1))]

+ 12 [119909 (10) minus 119909 (1) minus (and119909 (10) minus and119909 (1))]

1003816100381610038161003816100381610038161003816100381610038161003816 = 3499(23)

such that

120585 = 1 + |119904| + 1003816100381610038161003816100381610038161003816and1199041003816100381610038161003816100381610038161003816

1 + |119904| + 1003816100381610038161003816100381610038161003816and1199041003816100381610038161003816100381610038161003816 +

1003816100381610038161003816100381610038161003816and119904 minus1199041003816100381610038161003816100381610038161003816

asymp 09990 (24)

Similarly 119903 = 09993 when 120579 = 05 exist1205760 = 09 therebydefining

120576 = 120579120585 + (1 minus 120579) 119903 = 09991 gt 09 = 1205760 (25)

Therefore this model is defined as the qualified verificationof the degree of grey incidence

Step 5 (predict future data) According to

and119909(1) (119896 + 1) = 9728182119890002119896 minus 953644and119909(0) (119896 + 1) = and119909(1) (119896 + 1) minus and119909(1) (119896)

(26)

a prediction of the next five steps was calculated as follows

and119883=

[[[[[[[[[[[[[[

and119909(0) (11)and119909(0) (12)and119909(0) (13)and119909(0) (14)and119909(0) (15)

]]]]]]]]]]]]]]

=[[[[[[[[[

23539562401622245025324998682550488

]]]]]]]]]

(27)

Step 6 (establish the graphical function) The GDP gross andits growth rate (2005-2020) were calculated using the abovesteps See Table 6 for specific results

Therefore onemay establish the graphical function of thegrowth of GDP

Graphical function of the growth of GDP= WITHLOOKUP (Amount of GDP ([(8e+011 0)- (3e+012 03)](81178e+011 01648) (98468e+011 0213) (11115e+01201288) (12153e+012 00934) (141136e+012 01613)(162519e+012 01515) (178794e+012 01001) (198008e+012 01075) (213308e+012 00773) (230146e+012 00789)(235396e+012 002281) (240162e+012 00203) (245025e+012 002025) (249987e+012 002024) (255049e+0120020249)))

Similarly onemay establish the Graphical function aboutthe growth rate of vehicle ownership See Appendix B forspecific results

(3)ThirdMethodThe purpose of this method is to determinesome variables with nonlinear characteristics because theyare difficult to define directly such as degree of air pollutionand air pollution control In the actual situation estimationswere conducted by utilizing data from the official website(M1) and the first two prediction methods Main basisSlightly adjust the change trend of the variables to meetthe actual change rules that have been observed in Beijingin recent years As a result several variables have been

8 Discrete Dynamics in Nature and Society

Table 7 Estimated values of pollution degree of NOx and PMx in Beijing

Time Amount of motor vehicles (vehicle) ANOG (t) APMG (t) Actual pollution degree2014 5591e+006 11182e+005 22364e+005 Serious pollution2013 5437e+006 10874e+005 21748e+005 Serious pollution2012 5200e+006 10400e+005 20800e+005 Moderate pollution2011 4983e+006 9966e+004 19932e+005 Moderate pollution2010 4809e+006 9618e+004 19236e+005 Moderate pollution2009 4019e+006 8038e+004 16076e+005 Mild pollution2008 3504e+006 7008e+004 14016e+005 Mild pollution2007 3072e+006 6144e+004 12288e+005 Mild pollution2006 2754e+006 5508e+004 11016e+005 Mild pollution

confirmed including the attraction degree of the city netmigration rate degree of air pollution air pollution controlattraction degree of vehicle trips attraction degree of growthof the vehicles and growth rate ofmotor vehiclesThe presentstudy characterized the degree of air pollution as an example

(a) Estimation of Degree of Air Pollution The present studyestimated the degree of air pollution mainly based on theamount of NOx generation (ANOG) and amount of PMxgeneration (APMG) in accordance with historical data inStatistical Yearbook of Beijing from 2006 to 2014 In additionthe methods were also combined to estimate the ANOG andAPMG See Table 7 for detailed results

According to the actual situation of air pollution causedby motor vehicle exhaust emission in Beijing serious pol-lution was observed from 2013 to 2014 moderate pollutionwas generated between 2010 and 2012 and mild pollutionoccurred before 2009Therefore this paper defines the degreeof air pollution caused by ANOG as follows

(I)The degree of air pollution exhibited a value range thatis defined as (0 1) wherein a value of 08 and above indicatesserious pollution a value lower than 08 but higher than 05means moderate pollution and a value lower than 05 meansmild pollution

(II) From 2013 to 2014 Beijing exhibited a very seriousdegree of air pollution such that the estimated value ofNOx pollution was characterized between 08 and 1 at acorresponding ANOG of 108740 t to 111820 t From 2010 to2012 the degree of air pollution was moderate such that theestimated value of pollution NOx was within the interval of(05 08) at a corresponding ANOG of 96180 t to 104000 tFrom 2006 to 2009 the pollution degree was mild such thatthe estimated value of NOx pollution was lower than 05

According to the provisions above establish the logicalfunction of pollution degree of NOx

Pollution degree of NOx = IF THEN ELSE (Amount ofNOxgenerationgt= 11182e+005 09 IFTHENELSE (Amountof NOx generationgt= 10874e+005 08 IF THEN ELSE(Amount of NOx generationgt= 10400e+005 07 IF THENELSE (Amount of NOx generationgt= 9966e+004 06 IFTHENELSE (Amount of NOx generationgt= 9618e+004 05IF THEN ELSE (Amount of NOx generationgt= 8038e+00403 IF THEN ELSE (Amount of NOx generationgt=7008e+004 025 IF THEN ELSE (Amount of NOx

generationgt= 6144e+004 02 IF THEN ELSE (Amount ofNOx generationgt= 5508e+004 015 01 )))))))))

In the same way one can establish the logical function ofpollution degree of PMx

Pollution degree of PMx = IF THEN ELSE (Amountof PMx generationgt= 22364e+005 09 IF THEN ELSE(Amount of PMx generationgt= 21748e+005 08 IF THENELSE (Amount of PMx generationgt= 20800e+005 07 IFTHEN ELSE (Amount of PMx generationgt= 19932e+00506 IF THEN ELSE (Amount of PMx generationgt=19236e+005 05 IF THEN ELSE (Amount of PMxgenerationgt= 16076e+005 03 IF THEN ELSE (Amountof PMx generationgt= 14016e+005 025 IF THEN ELSE(Amount of PMx generationgt= 12288e+005 02 IF THENELSE (Amount of PMx generationgt= 11016e+005 015 01)))))))))

Therefore

119863119890119892119903119890119890 119900119891 119886119894119903 119901119900119897119897119906119905119894119900119899= 120573 lowast 119901119900119897119897119906119905119894119900119899 119889119890119892119903119890119890 119900119891 119873119874119909 + 120574

lowast 119901119900119897119897119906119905119894119900119899 119889119890119892119903119890119890 119900119891 119875119872119909(28)

wherein 120573 refers to the weight ratio of NOx 120574 refers to weightratio of PMx and 120573 + 120574 = 1(b) Estimation of Net Migration Rate According to Jia et al(2017) the attraction degree in Beijing was calculated to beabout 07056 [24]

According to Table 2 the permanent resident populationin Beijing exhibited a mechanical increase from 2009 to2014 respectively 112163 109091 129313 107072 109656and 74654 persons Therefore the net migration rates wererespectively calculated as 603 556 641 517 519and 347 A continuously decreasing trend was observeddue to registered residence migration and settlement policiesin Beijing In addition the net migration rate (mean value)of 531 must be adjusted given that it is obviously higherthan 347 and is inconsistent with the actual conditionsin Beijing Therefore the present study set the followingconditions

119873119890119905 119898119894119892119903119886119905119894119900119899 119903119886119905119890= 119899119890119905 119898119894119892119903119886119905119894119900119899 119903119886119905119890119898119890119886119899 V119886119897119906119890

Discrete Dynamics in Nature and Society 9

(a) APMG APCF=5(a) APMG APCF=100(a) APMG APCF=1000

100000

125000

150000

175000

200000

ton

2011 2013 2015 2017 20192009Time (year)

(a) APMG

(b) ANOG APCF=5(b) ANOG APCF=100(b) ANOG APCF=1000

2011 2013 2015 2017 20192009Time (year)

80000

110000

140000

170000

200000

ton

(b) ANOG

(c) AMVT APCF=5(c) AMVT APCF=100(c) AMVT APCF=1000

2011 2013 2015 2017 20192009Time (year)

2 M

25 M

3 M

35 M

4 M

vehi

cle

(c) AMVT

Figure 3 Extreme condition test (a) APMG (b) ANOG (c) AMVT

times 119886119905119905119903119886119888119905119894119900119899 119889119890119892119903119890119890 119900119891 119888119894119905119910120572(29)

where 120572 refers to the impact factor of policy Based on thiscalculation 120572 = 15 generates calculations that are close tothe actual value See the appendixes for descriptions of theother variables and main equations

3 Simulation and Result Analysis

31 Model Test

311 Extreme Condition Test The extreme condition testmainly aims to inspect the stability applicability in extremeconditions and accuracy of the equations in the test modelto represent the change trends of the realistic system and theintentions of the decision maker

According to Figure 3(a) the APMG exhibited a continu-ous decrease following an increase in the APCF In particularthe minimum value of APMG was obtained when the APCFwas at the limit value (1000 yuandaysdotvehicle) In additionwhen APCF was equal to 5 the maximum APMG value wasobtained which is consistent with the actual laws therebyconfirming the stability of the model in extreme conditions

A deeper analysis indicated a larger interval between curves1 and 2 and a shorter interval between curves 2 and curve3 thereby indicating that the APCF did not exceed 100yuandaysdotvehicle

The change rules presented in Figures 3(b) and 3(c) weresimilar to those in Figure 3(a)

312 Sensitivity Test The model behaviors exhibited dif-ferent and sensitive results at different parameter valuesSpecifically the behavior model changed following an appro-priate change of parameter In addition the policies generatedthrough the model analysis changed following a change inparameters

According to Figure 4(a) with time all the curves firstrose and then slowly descended Specifically in the earlyperiod of policy implementation (before 2014) the effect wasnot obvious because part-time drivers may not have had adeep understanding of the purpose of the implementationand the significance of the APCF policy thereby resultingin a continuous increase in AMVT due to sharp increasein motor vehicle ownership The AMVT growth rate wasmore effectively controlled following a longer period due tocontinuous policy implementation and fulfilment After 2016the growth rate continuously decreased thereby allowing

10 Discrete Dynamics in Nature and Society

(a) AMVT APCF=5(a) AMVT APCF=10(a) AMVT APCF=20(a) AMVT APCF=30(a) AMVT APCF=40(a) AMVT APCF=50(a) AMVT APCF=60(a) AMVT APCF=70(a) AMVT APCF=80(a) AMVT APCF=90(a) AMVT APCF=100

2 M

25 M

3 M

35 M

4 Mve

hicle

2011 2013 2015 2017 20192009Time (year)

(a) AMVT

(b) APMG APCF=5(b) APMG APCF=10(b) APMG APCF=20(b) APMG APCF=30(b) APMG APCF=40(b) APMG APCF=50(b) APMG APCF=60(b) APMG APCF=70(b) APMG APCF=80(b) APMG APCF=90(b) APMG APCF=100

100000

125000

150000

175000

200000

ton

2011 2013 2015 2017 20192009Time (year)

(b) APMG

(c) ANOG APCF=5(c) ANOG APCF=10(c) ANOG APCF=20(c) ANOG APCF=30(c) ANOG APCF=40(c) ANOG APCF=50(c) ANOG APCF=60(c) ANOG APCF=70(c) ANOG APCF=80(c) ANOG APCF=90(c) ANOG APCF=100

80000

110000

140000

170000

200000

ton

2011 2013 2015 2017 20192009Time (year)

(c) ANOG

Figure 4 Sensitivity test (a) AMVT (b) APMG (c) ANOG

the APCF policy to exhibit good effects based on long-termpractice improvement and fulfilment

Following further analysis the AMVT exhibited amarginal decreasing effect following an increase in APCFfrom curve 1 to curve 6 especially in curves 3ndash6 whichindicates that a larger APCF is not always better The analysisresults are presented in Figures 4(b) and 4(c)

In conclusion the APCF value range was observed withinthe interval of [30 50] based on the above analysis from the

perspective of AMVT reduction (alleviate traffic jam) as wellas APMG and ANOG emission reduction Table 8 presentsthe detailed analysis results

32 Analysis of Results The AMVT exhibited a continuousdecrease following an increase in APCF which indicates theability of this policy to restrict increases in AMVT Specif-ically obvious changes were in the intervals of [5 10] and[10 20] wherein theAMVTexhibited a decrease of 166649

Discrete Dynamics in Nature and Society 11

and 105055 respectively The AMVT exhibited a decreaseof 35103 24912 and 16793 in the intervals of [20 30][30 40] and [40 50] respectivelyHoweverminimal changeswere observed in the interval of 50 yuandaysdotvehicle aboveIn addition the APMG exhibited a decrease of 13967789137 28538 20987 and 14128 respectively in theabove intervals and exhibited very minimal changes in theinterval of 50 above The ANOG exhibited similar changerules

Therefore the interval [30 50] is deemed a reasonablevalue range based on the analysis on the degree of effect ofdifferent APCFs on the AMVT APMG and ANOG

In particular the change trends of AMVT APMG andANOG were generally consistent as presented in Figure 6specifically Figure 5(d) Figures 5(a)ndash5(c) exhibited obviousdecreasing trend rates that were continuously weakened inthe interval of [30 50] In addition the change was verylimited as the APCF exceeded 50 yuandaysdotvehicle

Therefore an effective APCF range of [30 50]was chosenbased on the development trends analysis of the change ratesof the main variables

33 Model Validation Historical data (2009-2015) on theamount of motor vehicles and population in Beijing arepresented in Table 9 wherein the conformance of theirrespective GSID was tested

331 Qualified Verification of the Degree of Grey Incidenceon the Population of Beijing The original sequence and itssimulation value sequence are respectively presented asfollows

1198830 =[[[[[[[[[[

1199090 (1)1199090 (2)1199090 (3)

1199090 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

18600119890 + 00719619119890 + 00720186119890 + 00720693119890 + 00721148119890 + 00721516119890 + 00721705119890 + 007

]]]]]]]]]]]]]]]

1198831 =[[[[[[[[[[

1199091 (1)1199091 (2)1199091 (3)

1199091 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

186000119890 + 007187390119890 + 007188790119890 + 007190200119890 + 007191621119890 + 007193053119890 + 007194495119890 + 007

]]]]]]]]]]]]]]]

(30)

The following was derived based on their calculations

100381610038161003816100381611990401003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

11990900 (119896) + 1211990900 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 117145

100381610038161003816100381611990411003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

11990901 (119896) + 1211990901 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 025295

10038161003816100381610038161199040 minus 11990411003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

(11990901 (119896) minus 11990900 (119896)) + 12 (11990901 (7) minus 11990900 (7))

1003816100381610038161003816100381610038161003816100381610038161003816= 09185

(31)

Therefore we are able to obtain the value of the GAID

12058501 = 1 + 100381610038161003816100381611990401003816100381610038161003816 + 1003816100381610038161003816119904110038161003816100381610038161 + 100381610038161003816100381611990401003816100381610038161003816 + 100381610038161003816100381611990411003816100381610038161003816 + 10038161003816100381610038161199040 minus 11990411003816100381610038161003816= 1 + 117145 + 025295

1 + 117145 + 025295 + 09185 asymp 07275(32)

In a similar way

100381610038161003816100381610038161199041015840010038161003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

119909101584000 (119896) + 12119909101584000 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 062985100381610038161003816100381610038161199041015840110038161003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

119909101584001 (119896) + 12119909101584001 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 0136051003816100381610038161003816100381611990410158400 minus 1199041015840110038161003816100381610038161003816

=10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

(119909101584001 (119896) minus 119909101584000 (119896)) + 12 (119909101584001 (7) minus 119909101584000 (7))

1003816100381610038161003816100381610038161003816100381610038161003816= 04938

(33)

Therefore GRID is

11990301 = 1 + 100381610038161003816100381610038161199041015840010038161003816100381610038161003816 + 1003816100381610038161003816100381611990410158401100381610038161003816100381610038161 + 1003816100381610038161003816119904101584001003816100381610038161003816 + 1003816100381610038161003816119904101584011003816100381610038161003816 + 100381610038161003816100381611990410158400 minus 119904101584011003816100381610038161003816= 1 + 062985 + 013605

1 + 062985 + 013605 + 04938 asymp 07815(34)

When 120579 = 05 and exist1205760 = 07 then12057601 = 12057912058501 + (1 minus 120579) 11990301 = 05 times 07275 + 05 times 07815

= 07545 gt 07 = 1205760 (35)

Therefore according to Table 5 the accuracy was determinedto be between grade 2 and grade 3

332 Qualified Verification of the Degree of Grey Incidenceon the Amount of Motor Vehicles in Beijing The original

12 Discrete Dynamics in Nature and Society

Table 8 The effects of different APCFs on AMVT APNG and ANOG

APCF AMVT Trend Variation APMG Trend Variation ANOG Trend Variation() () ()

5 345229e+006 -- -- 161737 -- -- 154899 -- --10 287697e+006 darr -166649 139146 darr -139677 137782 darr -11050420 257473e+006 darr -105055 126743 darr -89137 128122 darr -7011130 248435e+006 darr -35103 123126 darr -28538 125306 darr -2197940 242246e+006 darr -24912 120542 darr -20987 123272 darr -1623250 238178e+006 darr -16793 118839 darr -14128 121928 darr -1090360 235237e+006 darr -12348 117604 darr -10392 120952 darr -0800570 232979e+006 darr -09599 116655 darr -08069 120202 darr -0620180 231171e+006 darr -07760 115894 darr -06524 119599 darr -0501790 229680e+006 darr -06450 115265 darr -05427 119101 darr -04164100 228421e+006 darr -05482 114734 darr -04607 118680 darr -03535

Table 9 Historical data and their simulation values (2009-2015)

Time Amount of motor vehicles (vehicle) Amount of population (person)Actual value Simulation value Actual value Simulation value

2009 4019e+006 401900e+006 18600e+007 186000e+0072010 4809e+006 457571e+006 19619e+007 187390e+0072011 4983e+006 528216e+006 20186e+007 188790e+0072012 5200e+006 560956e+006 20693e+007 190200e+0072013 5437e+006 577509e+006 21148e+007 191621e+0072014 5591e+006 584424e+006 21516e+007 193053e+0072015 5619e+006 591422e+006 21705e+007 194495e+007

sequence and its simulation value sequence were respec-tively calculated as follows

119883119894 =[[[[[[[[[[

119909119894 (1)119909119894 (2)119909119894 (3)

119909119894 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

4019119890 + 0064809119890 + 0064983119890 + 0065200119890 + 0065437119890 + 0065591119890 + 0065619119890 + 006

]]]]]]]]]]]]]]]

119883119895 =[[[[[[[[[[

119909119895 (1)119909119895 (2)119909119895 (3)

119909119895 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

401900119890 + 006457571119890 + 006528216119890 + 006560956119890 + 006577509119890 + 006584424119890 + 006591422119890 + 006

]]]]]]]]]]]]]]]

(36)

TheGAID andGRIDwere respectively calculated as follows

120585119894119895 asymp 09235119903119894119895 asymp 09390 (37)

Hence when exist1205760 = 09 and 120579 = 05120576119894119895 = 120579120585119894119895 + (1 minus 120579) 119903119894119895 = 09313 gt 09 = 1205760 (38)

Therefore according to Definition 3 and Table 5 thismodel verified the degree of grey incidence and exhibited anaccuracy belonging to grade 1

34 Policy Simulation Analysis and Discussion

341 Horizontal Analysis According to the horizontal anal-ysis the curves exhibited different changes with time Thespecific analysis results are presented as follows

Following the adoption of the low charge policy egAPCF = 5 yuandaysdotvehicle the AMVT (curve 1) exhibiteda decrease since about 2014 as exhibited in Figure 6(a)Although the growth rates of ANOG and APMG exhibited adecrease the total emissions maintained an increasing trendthereby resulting in high DAP levels (curve 4) The analysisresults indicate the inability of the low charge policy toeffectively reduce the DAP

According to Figure 6(f) curve 1 first exhibited aslow rise (before 2013) and a subsequent sharp descentfollowing the adoption of the high charge policy (APCF= 50 yuandaylowastvehicle) As a result the AMVT valuesdescended until 2013 wherein its descending range continu-ously increased Curve 3 terminated its previously continuousrise and instead descended slowly Similarly the rising rate

Discrete Dynamics in Nature and Society 13

0

2

4

6

8

10

12

14

16

18A

MV

T (

)

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

(a) AMVT

0

2

4

6

8

10

12

14

APM

G (

)

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

(b) APMG

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

0

2

4

6

8

10

12

AN

OG

()

(c) ANOG

AMVT ()APMG ()ANOG ()

0

2

4

6

8

10

12

14

16

18

5 20 8010 50 60 7030 9040 100

(d) Trend comparison

Figure 5 Development trends of the change rates of the main variables (a) AMVT (b) APMG (c) ANOG (d) Trend comparison

Table 10 The comparison of different policies

Variable APCF (yuandaylowastvehicle) Trend Variation ()5 50

AMVT (vehicle) 345229e+006 238178e+006 darr -3101APMG (t) 161737e+005 118839e+005 darr -2652ANOG (t) 154899e+005 121928e+005 darr -2129DAP 06 0525 darr -1250

of curve 2 slowed down relatively These results indicatethe effective control on the increase of APMG and ANOGafter which the values began to descend slowly Curve 4exhibited three phases specifically a rapid rise between 2011and 2014 a slow rise in rate between 2014 and 2018 and a slowdescent after 2018These results indicate the presence of DAPimprovements which exhibited gradual descent after 2018

The analysis results in Figures 6(b)ndash6(e) were similar tothose presented above

342 Vertical Analysis According to Figures 6(a)ndash6(f) theAPCF exhibited a continuous increase thereby generating achange in the rules of all the curves as follows

(i) AMVT (curve 1)TheAMVT exhibited a continuousdecrease Within a certain range the increase inAPCF aided in the descent of the AMVT therebyfurther alleviating the traffic pressures

(ii) APMG (curve 3) and ANOG (curve 2) A charge ofmore than 30 (Figures 6(d)ndash6(f)) generated a slowdescent in APMGMeanwhile the increase in ANOGalso exhibited effective restraint

(iii) DAP (curve 4)TheDAP exhibited an overall declineespecially following the implementation of a highcharge policy (APCF isin [40 50]) A subsequentdescending trend was later observed in the period ofanalogue simulation as presented in Figures 6(e) and6(f)

343 Comparison of Policies According to Table 10 in thepresence of a low charge policy (APCF=5) the AMVTAPMG ANOG and DAP under a high charge pol-icy exhibited an obvious decrease which indicates thatthe implementation of a high charge policy effectivelyreduced motor vehicle exhaust emissions to restrain the

14 Discrete Dynamics in Nature and Society

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

083 M

10000004

2 M00

2011 2013 2015 2017 20192009Time (year)

AMVT APCF=5ANOG APCF=5APMG APCF=5DAP APCF=5

vehicletontonDmnl

(a)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=10ANOG APCF=10APMG APCF=10DAP APCF=10

vehicletontonDmnl

(b)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=20ANOG APCF=20APMG APCF=20DAP APCF=20

vehicletontonDmnl

(c)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=30ANOG APCF=30APMG APCF=30DAP APCF=30

vehicletontonDmnl

(d)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=40ANOG APCF=40APMG APCF=40DAP APCF=40

vehicletontonDmnl

(e)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=50ANOG APCF=50APMG APCF=50DAP APCF=50

vehicletontonDmnl

(f)

Figure 6 Policy simulation (a) APCF=5 (b) APCF=10 (c) APCF=20 (d) APCF=30 (e) APCF=40 (f) APCF=50

intensification of ldquohazerdquo pollution degree in Beijing Specif-ically the gap between curves 1 and 2 exhibited a continuouswidening as presented in Figure 7(a) After 2013 curve 2exhibited an obvious descent Therefore the APCF policyeffectively reduced the AMVT and enabled an about 3101decrease in 2020

The results in Figures 7(b)ndash7(d) were similarly analyzed

In conclusion the adoption of a low charge policygenerated increasing APMG and ANOG trends as presentedin Figures 6(a) and 6(b) thereby suggesting the inabilityof the low charge policy to effectively reduce the DAP Anincrease of the fee to a certain extent especially followingthe implementation of a high charge policy (Figures 6(e) and6(f)) not only reduced the AMVT and alleviated traffic jams

Discrete Dynamics in Nature and Society 15

APCF=5

APCF=50

x 106

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 20202009Time (year)

2

25

3

35ve

hicle

(a) AMVT

APCF=5

APCF=50

x 105

20182017 2019 20202015 2016201420122011 201320102009Time (year)

11

12

13

14

15

16

17

ton

(b) APMG

APCF=5

APCF=50

x 105

08

09

1

11

12

13

14

15

16

ton

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 20202009Time (year)

(c) ANOG

02

APCF=5

APCF=50

2009 2011 20122010 20142013 2016 2017 20182015 20202019Time (year)

025

03

035

04

045

05

055D

mnl

(d) DAP

Figure 7 Comparison of the policies (a) AVT (b) APMG (c) ANOG (d) DAP

in cities but also effectively reduced the APMG and ANOGthereby reducing the DAP

According to a comparison on the different schemes atthe end of the analogue simulation period the high chargepolicy functioned as follows in terms of the emission reduc-tion of the motor vehicle exhaust the APMG and ANOGexhibited reductions of 2652 and 2129 respectively interms of alleviating traffic jams the AMVT exhibited a 3101decrease and in terms of reducing the degree of air pollutionthe DAP exhibited a 1250 decrease

4 Conclusions

41 Main Conclusions To resolve the air pollution problemsgenerated by motor vehicle exhaust emission the presentstudy introduced the charging mechanism and built a motorvehicle exhaust emission reduction strategy managementmodel using economic means and the SD-GM approach to

generate the following conclusions based on tests validationof the models and the simulation analysis of policies

(1)Within a certain range the reduction effects of APMGandANOGexhibited continuous enhancements following anincrease in APCF However the APCF did not always followthe principle ldquobigger means betterrdquo because the emissionreduction effect which was generated by an increase inthe APCF exhibited a marginal decreasing effect Accord-ing to the sensitivity analysis a pollution charge of 30ndash50yuandaysdotvehicle for the motor vehicles in Beijing was withinthe relatively reasonable range

(2) Three high charge policy functions were generatedbased on a comparison of the simulation results of thedifferent charging schemes the implementation of highcharge policies not only reduced the AMVT and alleviatedtraffic jams (Figures 6(e) 6(f) and 7(a) Table 10) but alsoeffectively reduced the APMG andANOG (Figures 6(e) 6(f)7(b) and 7(c) Tables 5 and 10) thereby further reducing theDAP (Figures 6(e) 6(f) and 7(d) Table 10) According to the

16 Discrete Dynamics in Nature and Society

contrastive analysis the DAP exhibited a decrease of about1250

(3) However the following problems were encounteredfollowing the implementation of the APCF policy (a) Theimplementation of the APCF policy increased the cost ofmotor vehicle trips and urged part-time drivers to take publictransportation which increased the burden of public trans-portation The subsidy policy and other applicable policiesmust be introduced to improve the public transport supplylevel and service quality Otherwise the trip demands ofpassengers will be difficult to satisfy which will influencethe implementation of the APCF policy (b) In the earlyperiods of APCF policy implementation an increase in thecost of motor vehicle trips due to the insufficient publicunderstanding and utilization of the APCF policy loweredits public support rate The government must strengthenits public relations work especially regarding the purposeand significance of its implementation to improve publicawareness and acknowledgment (c) The purpose of thesepolicies must be supervised and managed to gather APCFincome and improve public transportation infrastructures

42 Deficiencies and Future Work The present study consid-ered NOx and PMx as the principal motor vehicle emissionpollutants Future research must fully consider other com-ponents such as SO2 airborne particles hydrocarbons COand CO2 Secondly the implementation of a single chargingmeasure can reduce the supply level of public transportationFuture research should consider a subsidy mechanism toimprove the service quality Thirdly the function and effectof a single policy are limited Future work must considerthe integration of multiple policies to improve the emissionreduction effect For example future work may focus priorityon public transportation improvement of fuel quality vigor-ous promotion of new energy vehicles and improvements inemission standards

Appendix

A

See Table 11

B

Summary of the major variables and equations(1) Cost of motor vehicle trips = Air pollution charging

feelowast (1+ Air pollution control)(2) Amount ofNOx generation = INTEG (NOx emissions

- Annual dissipation of NOx 80380)(3) NOx emissions = Per vehicle annual of NOx

emissionslowast Amount of motor vehicle tripslowast Contributionrate of NOx from vehicle

(4) Contribution rate of NOx from vehicle = 05(5) Dissipation rate of NOx = 02(6) Annual dissipation of NOx = Amount of NOx

generationlowast Dissipation rate of NOx(7) Per vehicle annual of NOx emissions = 002

(8) Amount of PMx generation = INTEG (PMxemissions- Annual dissipation of PMx 160760)

(9) PMx emissions = Amount of motor vehicle tripslowastContribution rate of PMx from vehiclelowast Per vehicle annualof PMx emissions

(10) Contribution rate of PMx from vehicle = 05(11) Per vehicle annual of PMx emissions = 004(12) Annual dissipation of PMx = Amount of PMx

generationlowast Dissipation and control rate of PMx(13) Dissipation and control rate of PMx = 05(14) Pollution degree of NOx = IF THEN ELSE (Amount

of NOx generationgt= 11182e+005 09 IF THEN ELSE(Amount of NOx generationgt= 10874e+005 08 IF THENELSE (Amount of NOx generationgt= 10400e+005 07 IFTHEN ELSE (Amount of NOx generationgt= 9966e+00406 IF THEN ELSE (Amount of NOx generationgt=9618e+004 05 IF THEN ELSE (Amount of NOxgenerationgt= 8038e+004 03 IF THEN ELSE (Amountof NOx generationgt= 7008e+004 025 IF THEN ELSE(Amount of NOx generationgt= 6144e+004 02 IF THENELSE (Amount of NOx generationgt= 5508e+004 015 01)))))))))

(15) Pollution degree of PMx = IF THEN ELSE (Amountof PMx generationgt= 22364e+005 09 IF THEN ELSE(Amount of PMx generationgt= 21748e+005 08 IF THENELSE (Amount of PMx generationgt= 20800e+005 07 IFTHEN ELSE (Amount of PMx generationgt= 19932e+00506 IF THEN ELSE (Amount of PMx generationgt=19236e+005 05 IF THEN ELSE (Amount of PMxgenerationgt= 16076e+005 03 IF THEN ELSE (Amountof PMx generationgt= 14016e+005 025 IF THEN ELSE(Amount of PMx generationgt= 12288e+005 02 IF THENELSE (Amount of PMx generationgt= 11016e+005 015 01)))))))))

(16) Ratio of motor vehicle trips = 055(17) Amount of motor vehicle trips = Amount of motor

vehicleslowast Ratio of motor vehicle trips(18) Degree of air pollution = Weight ratio of NOxlowast

Pollution degree of NOx+ Weight ratio of PMxlowast Pollutiondegree of PMx

(19) Weight ratio of PMx = 05(20) Weight ratio of NOx = 05(21) Air pollution control = IF THEN ELSE (Degree of air

pollutiongt= 07 1 IF THEN ELSE (Degree of air pollutiongt=06 08 IF THEN ELSE (Degree of air pollutiongt= 05 07IF THEN ELSE (Degree of air pollutiongt= 04 06 IF THENELSE (Degree of air pollutiongt= 03 05 IF THEN ELSE(Degree of air pollutiongt= 025 045 IF THENELSE (Degreeof air pollutiongt= 02 04 IF THEN ELSE (Degree of airpollutiongt= 015 035 03))))))))

(22) Attraction degree of the growth of vehicles= (1-Airpollution control)lowast 055+ Attraction degree of vehicle tripslowast045

(23) Per capita annual income = Amount of GDPAmount of population

(24) Amount of population = INTEG (Growth of popu-lation+ Net migration- Population reduction 186e+007)

(25) Birth rate = Adjustment coefficient of birth ratelowastPredictive value of birth rate

Discrete Dynamics in Nature and Society 17

Table 11 Description of main variables in stock flow diagram

Signicant variable Unit Variable type Data sourceAir pollution charging fee yuandaysdotvehicle ConstantAir pollution control Dmnl Auxiliary variable M1+M3Amount of GDP yuan Level M1Amount of motor vehicles vehicle Level M1Amount of motor vehicle trips vehicle Auxiliary variableAmount of NOx (PMx) generation ton Level M1Amount of population person Level M1Annual dissipation of NOx (PMx) tonyear FlowAnnual scrapped vehicleyear FlowAttraction degree of city Constant M2Attraction degree of the growth of vehicles Auxiliary variable M1+M3Attraction degree of vehicle trips Auxiliary variable M1+M3Birth rate 1year Constant M3Contribution rate of NOx (PMx) from vehicle Constant M2Cost of motor vehicle trips yuandaysdotvehicle Auxiliary variable M3Death rate 1year Constant M3Degree of air pollution Dmnl Auxiliary variable M3Dissipation and control rate of NOx (PMx) 1year Constant M2Graphical function of the growth of GDP Dmnl Auxiliary variable M3Growth of GDP yuanyear FlowGrowth rate of motor vehicles 1year Auxiliary variable M1+M3Growth of motor vehicles vehicleyear FlowGrowth of population personyear FlowGrowth rate of vehicle ownership Dmnl Auxiliary variable M1+M3Impact factor of policy Dmnl Constant M3Net migration personyear FlowNet migration rate 1year Constant M1+M3NOx (PMx) emissions tonyear FlowPer capita annual income yuanperson Auxiliary variablePer vehicle annual of NOx (PMx) emissions tonyearsdotvehicle Constant M2Pollution degree of NOx (PMx) Dmnl Auxiliary variable M1+M3Population reduction personyear FlowRatio of motor vehicle trips Constant M2Scrap rate 1year Constant M2The average of net migration rate 1year Constant M1Weight ratio of PMx (NOx) Auxiliary variable M3

(26) Predictive value of birth rate = 000925(27) Death rate = Adjustment coefficient of death ratelowast

Predictive value of death rate(28) Predictive value of death rate = 000494(29) Net migration = Amount of populationlowastNet migra-

tion rate(30) Net migration rate = The average of net migration

ratelowast Attraction degree of cityand(Impact factor of policy)(31) Impact factor of policy = 15(32) The average of net migration rate = 000531(33) Attraction degree of city = 07056(34) Amount of GDP = INTEG (Growth of GDP

12153e+012)

(35) Graphical function of the growth of GDP = WITHLOOKUP (Amount of GDP ([(8e+011 0)- (3e+ 012 03)](81178e+011 01648) (98468e+011 0213) (11115e+01201288) (12153e+012 00934) (141136e+012 01613)(162519e+012 01515) (178794e+012 01001) (198008e+01201075) (213308e+012 00773) (230146e+012 00789)(235396e+012 002281) (240162e+012 00203) (245025e+012 002025) (249987e+012 002024) (255049e+0120020249)))

(36) Growth rate of GDP = Graphical function of thegrowth of GDPlowast Impact factor of the growth of GDP

(37) Amount of motor vehicles = INTEG (Growth ofmotor vehicles- Annual scrapped 4019e+006)

18 Discrete Dynamics in Nature and Society

(38) Annual scrapped = Amount of motor vehicleslowastScrap rate

(39) Scrap rate = 0067

Conflicts of Interest

The author declares no conflicts of interest

Acknowledgments

This work has been partially supported by the NationalNatural Science Foundation of China (71571119) ShanghaiFirst-Class Academic Discipline Project (S1201YLXK) andChina Postdoctoral Science Foundation (2018M630404)Theauthor would like to thank LetPub (httpwwwletpubcom)for providing linguistic assistance during the preparation ofthis manuscript

References

[1] X Liu S Ma J Tian N Jia and G Li ldquoA system dynamicsapproach to scenario analysis for urban passenger transportenergy consumption and CO2 emissions A case study ofBeijingrdquo Energy Policy vol 85 pp 253ndash270 2015

[2] B Xu L Luo and B Lin ldquoA dynamic analysis of air pollutionemissions in China Evidence from nonparametric additiveregression modelsrdquo Ecological Indicators vol 63 pp 346ndash3582016

[3] S Leinert H Daly B Hyde and B O Gallachoir ldquoCo-benefitsNot always Quantifying the negative effect of a CO2-reducingcar taxation policy on NOx emissionsrdquo Energy Policy vol 63pp 1151ndash1159 2013

[4] Z Cheng L Li and J Liu ldquoIdentifying the spatial effects anddriving factors of urban PM25 pollution in Chinardquo EcologicalIndicators vol 82 pp 61ndash75 2017

[5] N Kaida and K Kaida ldquoSpillover effect of congestion chargingon pro-environmental behaviorrdquo Environment Developmentand Sustainability vol 17 no 3 pp 409ndash421 2015

[6] R Penabaena-Niebles V Cantillo and J L Moura ldquoImpactof transition between signal timing plans in social cost basedin delay fuel consumption and air emissionsrdquo TransportationResearch Part D Transport and Environment vol 41 pp 445ndash456 2015

[7] DDing andB Shuai ldquoA traffic restriction scheme for enhancingcarpoolingrdquoDiscreteDynamics inNature and Society Article ID9626938 9 pages 2017

[8] D Kong X Guo B Yang and D Wu ldquoAnalyzing the Impactof Trucks on Traffic Flow Based on an Improved CellularAutomaton Modelrdquo Discrete Dynamics in Nature and Societyvol 2016 pp 1ndash14 2016

[9] S Cakmak C Hebbern J D Cakmak and J Vanos ldquoThemodifying effect of socioeconomic status on the relationshipbetween traffic air pollution and respiratory health in elemen-tary schoolchildrenrdquo Journal of Environmental Managementvol 177 pp 1ndash8 2016

[10] L Song H Song J Lin et al ldquoPM25 emissions from differenttypes of heavy-duty truck a case study and meta-analysis ofthe Beijing-Tianjin-Hebei regionrdquo Environmental Science andPollution Research vol 24 no 12 pp 11206ndash11214 2017

[11] Z Hu S Kang C Li et al ldquoLight absorption of biomassburning and vehicle emission-sourced carbonaceous aerosolsof the Tibetan Plateaurdquo Environmental Science and PollutionResearch vol 24 no 18 pp 15369ndash15378 2017

[12] X Cen H K Lo and L Li ldquoA framework for estimating trafficemissions The development of Passenger Car Emission UnitrdquoTransportation Research Part D Transport and Environmentvol 44 pp 78ndash92 2016

[13] S Wang X Liu C Zhou J Hu and J Ou ldquoExamining theimpacts of socioeconomic factors urban form and transporta-tion networks on CO2 emissions in Chinarsquos megacitiesrdquoAppliedEnergy vol 185 pp 189ndash200 2017

[14] Q Wang K Hubacek K Feng Y-M Wei and Q-M LiangldquoDistributional effects of carbon taxationrdquo Applied Energy vol184 pp 1123ndash1131 2016

[15] C Johansson L Burman and B Forsberg ldquoThe effects ofcongestions tax on air quality and healthrdquo Atmospheric Envi-ronment vol 43 no 31 pp 4843ndash4854 2009

[16] A Rakowska K C Wong T Townsend et al ldquoImpact of trafficvolume and composition on the air quality and pedestrianexposure in urban street canyonrdquo Atmospheric Environmentvol 98 pp 260ndash270 2014

[17] S Batterman R Ganguly and P Harbin ldquoHigh resolutionspatial and temporal mapping of traffic-related air pollutantsrdquoInternational Journal of Environmental Research and PublicHealth vol 12 no 4 pp 3646ndash3666 2015

[18] J Eliasson M Borjesson D van Amelsfort K Brundell-Freijand L Engelson ldquoAccuracy of congestion pricing forecastsrdquoTransportation Research Part A Policy and Practice vol 52 pp34ndash46 2013

[19] J Eliasson ldquoThe role of attitude structures direct experienceand reframing for the success of congestion pricingrdquo Trans-portation Research Part A Policy and Practice vol 67 pp 81ndash952014

[20] H X Yang J D Li H Zhang and S Q Liu ldquoResearch on thegovernance of urban traffic jam based on system dynamicsrdquoSystems EngineeringTheory and Practice vol 34 no 8 pp 2135ndash2143 2014 (Chinese)

[21] M H Zhu Research on Socio-Economic Impact of UrbanTrafficCongestion [PhD thesis] Beijing JiaotongUniversity 2013(Chinese)

[22] B Zeng Research on Modeling Technologies of Grey Prediction[PhD thesis] Nanjing University of Aeronautics and Astronau-tics 2011 (Chinese)

[23] S F Liu Y J Yang and L F Wu Grey System Theory andApplication Science Press Beijing China 2017

[24] S W Jia K Yang J J Zhao and G L Yan ldquoThe traffic-congestion charging fee management model based on thesystem dynamics approachrdquo Mathematical Problems in Engi-neering vol 2017 Article ID 3024898 13 pages 2017

8 Discrete Dynamics in Nature and Society

Table 7 Estimated values of pollution degree of NOx and PMx in Beijing

Time Amount of motor vehicles (vehicle) ANOG (t) APMG (t) Actual pollution degree2014 5591e+006 11182e+005 22364e+005 Serious pollution2013 5437e+006 10874e+005 21748e+005 Serious pollution2012 5200e+006 10400e+005 20800e+005 Moderate pollution2011 4983e+006 9966e+004 19932e+005 Moderate pollution2010 4809e+006 9618e+004 19236e+005 Moderate pollution2009 4019e+006 8038e+004 16076e+005 Mild pollution2008 3504e+006 7008e+004 14016e+005 Mild pollution2007 3072e+006 6144e+004 12288e+005 Mild pollution2006 2754e+006 5508e+004 11016e+005 Mild pollution

confirmed including the attraction degree of the city netmigration rate degree of air pollution air pollution controlattraction degree of vehicle trips attraction degree of growthof the vehicles and growth rate ofmotor vehiclesThe presentstudy characterized the degree of air pollution as an example

(a) Estimation of Degree of Air Pollution The present studyestimated the degree of air pollution mainly based on theamount of NOx generation (ANOG) and amount of PMxgeneration (APMG) in accordance with historical data inStatistical Yearbook of Beijing from 2006 to 2014 In additionthe methods were also combined to estimate the ANOG andAPMG See Table 7 for detailed results

According to the actual situation of air pollution causedby motor vehicle exhaust emission in Beijing serious pol-lution was observed from 2013 to 2014 moderate pollutionwas generated between 2010 and 2012 and mild pollutionoccurred before 2009Therefore this paper defines the degreeof air pollution caused by ANOG as follows

(I)The degree of air pollution exhibited a value range thatis defined as (0 1) wherein a value of 08 and above indicatesserious pollution a value lower than 08 but higher than 05means moderate pollution and a value lower than 05 meansmild pollution

(II) From 2013 to 2014 Beijing exhibited a very seriousdegree of air pollution such that the estimated value ofNOx pollution was characterized between 08 and 1 at acorresponding ANOG of 108740 t to 111820 t From 2010 to2012 the degree of air pollution was moderate such that theestimated value of pollution NOx was within the interval of(05 08) at a corresponding ANOG of 96180 t to 104000 tFrom 2006 to 2009 the pollution degree was mild such thatthe estimated value of NOx pollution was lower than 05

According to the provisions above establish the logicalfunction of pollution degree of NOx

Pollution degree of NOx = IF THEN ELSE (Amount ofNOxgenerationgt= 11182e+005 09 IFTHENELSE (Amountof NOx generationgt= 10874e+005 08 IF THEN ELSE(Amount of NOx generationgt= 10400e+005 07 IF THENELSE (Amount of NOx generationgt= 9966e+004 06 IFTHENELSE (Amount of NOx generationgt= 9618e+004 05IF THEN ELSE (Amount of NOx generationgt= 8038e+00403 IF THEN ELSE (Amount of NOx generationgt=7008e+004 025 IF THEN ELSE (Amount of NOx

generationgt= 6144e+004 02 IF THEN ELSE (Amount ofNOx generationgt= 5508e+004 015 01 )))))))))

In the same way one can establish the logical function ofpollution degree of PMx

Pollution degree of PMx = IF THEN ELSE (Amountof PMx generationgt= 22364e+005 09 IF THEN ELSE(Amount of PMx generationgt= 21748e+005 08 IF THENELSE (Amount of PMx generationgt= 20800e+005 07 IFTHEN ELSE (Amount of PMx generationgt= 19932e+00506 IF THEN ELSE (Amount of PMx generationgt=19236e+005 05 IF THEN ELSE (Amount of PMxgenerationgt= 16076e+005 03 IF THEN ELSE (Amountof PMx generationgt= 14016e+005 025 IF THEN ELSE(Amount of PMx generationgt= 12288e+005 02 IF THENELSE (Amount of PMx generationgt= 11016e+005 015 01)))))))))

Therefore

119863119890119892119903119890119890 119900119891 119886119894119903 119901119900119897119897119906119905119894119900119899= 120573 lowast 119901119900119897119897119906119905119894119900119899 119889119890119892119903119890119890 119900119891 119873119874119909 + 120574

lowast 119901119900119897119897119906119905119894119900119899 119889119890119892119903119890119890 119900119891 119875119872119909(28)

wherein 120573 refers to the weight ratio of NOx 120574 refers to weightratio of PMx and 120573 + 120574 = 1(b) Estimation of Net Migration Rate According to Jia et al(2017) the attraction degree in Beijing was calculated to beabout 07056 [24]

According to Table 2 the permanent resident populationin Beijing exhibited a mechanical increase from 2009 to2014 respectively 112163 109091 129313 107072 109656and 74654 persons Therefore the net migration rates wererespectively calculated as 603 556 641 517 519and 347 A continuously decreasing trend was observeddue to registered residence migration and settlement policiesin Beijing In addition the net migration rate (mean value)of 531 must be adjusted given that it is obviously higherthan 347 and is inconsistent with the actual conditionsin Beijing Therefore the present study set the followingconditions

119873119890119905 119898119894119892119903119886119905119894119900119899 119903119886119905119890= 119899119890119905 119898119894119892119903119886119905119894119900119899 119903119886119905119890119898119890119886119899 V119886119897119906119890

Discrete Dynamics in Nature and Society 9

(a) APMG APCF=5(a) APMG APCF=100(a) APMG APCF=1000

100000

125000

150000

175000

200000

ton

2011 2013 2015 2017 20192009Time (year)

(a) APMG

(b) ANOG APCF=5(b) ANOG APCF=100(b) ANOG APCF=1000

2011 2013 2015 2017 20192009Time (year)

80000

110000

140000

170000

200000

ton

(b) ANOG

(c) AMVT APCF=5(c) AMVT APCF=100(c) AMVT APCF=1000

2011 2013 2015 2017 20192009Time (year)

2 M

25 M

3 M

35 M

4 M

vehi

cle

(c) AMVT

Figure 3 Extreme condition test (a) APMG (b) ANOG (c) AMVT

times 119886119905119905119903119886119888119905119894119900119899 119889119890119892119903119890119890 119900119891 119888119894119905119910120572(29)

where 120572 refers to the impact factor of policy Based on thiscalculation 120572 = 15 generates calculations that are close tothe actual value See the appendixes for descriptions of theother variables and main equations

3 Simulation and Result Analysis

31 Model Test

311 Extreme Condition Test The extreme condition testmainly aims to inspect the stability applicability in extremeconditions and accuracy of the equations in the test modelto represent the change trends of the realistic system and theintentions of the decision maker

According to Figure 3(a) the APMG exhibited a continu-ous decrease following an increase in the APCF In particularthe minimum value of APMG was obtained when the APCFwas at the limit value (1000 yuandaysdotvehicle) In additionwhen APCF was equal to 5 the maximum APMG value wasobtained which is consistent with the actual laws therebyconfirming the stability of the model in extreme conditions

A deeper analysis indicated a larger interval between curves1 and 2 and a shorter interval between curves 2 and curve3 thereby indicating that the APCF did not exceed 100yuandaysdotvehicle

The change rules presented in Figures 3(b) and 3(c) weresimilar to those in Figure 3(a)

312 Sensitivity Test The model behaviors exhibited dif-ferent and sensitive results at different parameter valuesSpecifically the behavior model changed following an appro-priate change of parameter In addition the policies generatedthrough the model analysis changed following a change inparameters

According to Figure 4(a) with time all the curves firstrose and then slowly descended Specifically in the earlyperiod of policy implementation (before 2014) the effect wasnot obvious because part-time drivers may not have had adeep understanding of the purpose of the implementationand the significance of the APCF policy thereby resultingin a continuous increase in AMVT due to sharp increasein motor vehicle ownership The AMVT growth rate wasmore effectively controlled following a longer period due tocontinuous policy implementation and fulfilment After 2016the growth rate continuously decreased thereby allowing

10 Discrete Dynamics in Nature and Society

(a) AMVT APCF=5(a) AMVT APCF=10(a) AMVT APCF=20(a) AMVT APCF=30(a) AMVT APCF=40(a) AMVT APCF=50(a) AMVT APCF=60(a) AMVT APCF=70(a) AMVT APCF=80(a) AMVT APCF=90(a) AMVT APCF=100

2 M

25 M

3 M

35 M

4 Mve

hicle

2011 2013 2015 2017 20192009Time (year)

(a) AMVT

(b) APMG APCF=5(b) APMG APCF=10(b) APMG APCF=20(b) APMG APCF=30(b) APMG APCF=40(b) APMG APCF=50(b) APMG APCF=60(b) APMG APCF=70(b) APMG APCF=80(b) APMG APCF=90(b) APMG APCF=100

100000

125000

150000

175000

200000

ton

2011 2013 2015 2017 20192009Time (year)

(b) APMG

(c) ANOG APCF=5(c) ANOG APCF=10(c) ANOG APCF=20(c) ANOG APCF=30(c) ANOG APCF=40(c) ANOG APCF=50(c) ANOG APCF=60(c) ANOG APCF=70(c) ANOG APCF=80(c) ANOG APCF=90(c) ANOG APCF=100

80000

110000

140000

170000

200000

ton

2011 2013 2015 2017 20192009Time (year)

(c) ANOG

Figure 4 Sensitivity test (a) AMVT (b) APMG (c) ANOG

the APCF policy to exhibit good effects based on long-termpractice improvement and fulfilment

Following further analysis the AMVT exhibited amarginal decreasing effect following an increase in APCFfrom curve 1 to curve 6 especially in curves 3ndash6 whichindicates that a larger APCF is not always better The analysisresults are presented in Figures 4(b) and 4(c)

In conclusion the APCF value range was observed withinthe interval of [30 50] based on the above analysis from the

perspective of AMVT reduction (alleviate traffic jam) as wellas APMG and ANOG emission reduction Table 8 presentsthe detailed analysis results

32 Analysis of Results The AMVT exhibited a continuousdecrease following an increase in APCF which indicates theability of this policy to restrict increases in AMVT Specif-ically obvious changes were in the intervals of [5 10] and[10 20] wherein theAMVTexhibited a decrease of 166649

Discrete Dynamics in Nature and Society 11

and 105055 respectively The AMVT exhibited a decreaseof 35103 24912 and 16793 in the intervals of [20 30][30 40] and [40 50] respectivelyHoweverminimal changeswere observed in the interval of 50 yuandaysdotvehicle aboveIn addition the APMG exhibited a decrease of 13967789137 28538 20987 and 14128 respectively in theabove intervals and exhibited very minimal changes in theinterval of 50 above The ANOG exhibited similar changerules

Therefore the interval [30 50] is deemed a reasonablevalue range based on the analysis on the degree of effect ofdifferent APCFs on the AMVT APMG and ANOG

In particular the change trends of AMVT APMG andANOG were generally consistent as presented in Figure 6specifically Figure 5(d) Figures 5(a)ndash5(c) exhibited obviousdecreasing trend rates that were continuously weakened inthe interval of [30 50] In addition the change was verylimited as the APCF exceeded 50 yuandaysdotvehicle

Therefore an effective APCF range of [30 50]was chosenbased on the development trends analysis of the change ratesof the main variables

33 Model Validation Historical data (2009-2015) on theamount of motor vehicles and population in Beijing arepresented in Table 9 wherein the conformance of theirrespective GSID was tested

331 Qualified Verification of the Degree of Grey Incidenceon the Population of Beijing The original sequence and itssimulation value sequence are respectively presented asfollows

1198830 =[[[[[[[[[[

1199090 (1)1199090 (2)1199090 (3)

1199090 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

18600119890 + 00719619119890 + 00720186119890 + 00720693119890 + 00721148119890 + 00721516119890 + 00721705119890 + 007

]]]]]]]]]]]]]]]

1198831 =[[[[[[[[[[

1199091 (1)1199091 (2)1199091 (3)

1199091 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

186000119890 + 007187390119890 + 007188790119890 + 007190200119890 + 007191621119890 + 007193053119890 + 007194495119890 + 007

]]]]]]]]]]]]]]]

(30)

The following was derived based on their calculations

100381610038161003816100381611990401003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

11990900 (119896) + 1211990900 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 117145

100381610038161003816100381611990411003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

11990901 (119896) + 1211990901 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 025295

10038161003816100381610038161199040 minus 11990411003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

(11990901 (119896) minus 11990900 (119896)) + 12 (11990901 (7) minus 11990900 (7))

1003816100381610038161003816100381610038161003816100381610038161003816= 09185

(31)

Therefore we are able to obtain the value of the GAID

12058501 = 1 + 100381610038161003816100381611990401003816100381610038161003816 + 1003816100381610038161003816119904110038161003816100381610038161 + 100381610038161003816100381611990401003816100381610038161003816 + 100381610038161003816100381611990411003816100381610038161003816 + 10038161003816100381610038161199040 minus 11990411003816100381610038161003816= 1 + 117145 + 025295

1 + 117145 + 025295 + 09185 asymp 07275(32)

In a similar way

100381610038161003816100381610038161199041015840010038161003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

119909101584000 (119896) + 12119909101584000 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 062985100381610038161003816100381610038161199041015840110038161003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

119909101584001 (119896) + 12119909101584001 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 0136051003816100381610038161003816100381611990410158400 minus 1199041015840110038161003816100381610038161003816

=10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

(119909101584001 (119896) minus 119909101584000 (119896)) + 12 (119909101584001 (7) minus 119909101584000 (7))

1003816100381610038161003816100381610038161003816100381610038161003816= 04938

(33)

Therefore GRID is

11990301 = 1 + 100381610038161003816100381610038161199041015840010038161003816100381610038161003816 + 1003816100381610038161003816100381611990410158401100381610038161003816100381610038161 + 1003816100381610038161003816119904101584001003816100381610038161003816 + 1003816100381610038161003816119904101584011003816100381610038161003816 + 100381610038161003816100381611990410158400 minus 119904101584011003816100381610038161003816= 1 + 062985 + 013605

1 + 062985 + 013605 + 04938 asymp 07815(34)

When 120579 = 05 and exist1205760 = 07 then12057601 = 12057912058501 + (1 minus 120579) 11990301 = 05 times 07275 + 05 times 07815

= 07545 gt 07 = 1205760 (35)

Therefore according to Table 5 the accuracy was determinedto be between grade 2 and grade 3

332 Qualified Verification of the Degree of Grey Incidenceon the Amount of Motor Vehicles in Beijing The original

12 Discrete Dynamics in Nature and Society

Table 8 The effects of different APCFs on AMVT APNG and ANOG

APCF AMVT Trend Variation APMG Trend Variation ANOG Trend Variation() () ()

5 345229e+006 -- -- 161737 -- -- 154899 -- --10 287697e+006 darr -166649 139146 darr -139677 137782 darr -11050420 257473e+006 darr -105055 126743 darr -89137 128122 darr -7011130 248435e+006 darr -35103 123126 darr -28538 125306 darr -2197940 242246e+006 darr -24912 120542 darr -20987 123272 darr -1623250 238178e+006 darr -16793 118839 darr -14128 121928 darr -1090360 235237e+006 darr -12348 117604 darr -10392 120952 darr -0800570 232979e+006 darr -09599 116655 darr -08069 120202 darr -0620180 231171e+006 darr -07760 115894 darr -06524 119599 darr -0501790 229680e+006 darr -06450 115265 darr -05427 119101 darr -04164100 228421e+006 darr -05482 114734 darr -04607 118680 darr -03535

Table 9 Historical data and their simulation values (2009-2015)

Time Amount of motor vehicles (vehicle) Amount of population (person)Actual value Simulation value Actual value Simulation value

2009 4019e+006 401900e+006 18600e+007 186000e+0072010 4809e+006 457571e+006 19619e+007 187390e+0072011 4983e+006 528216e+006 20186e+007 188790e+0072012 5200e+006 560956e+006 20693e+007 190200e+0072013 5437e+006 577509e+006 21148e+007 191621e+0072014 5591e+006 584424e+006 21516e+007 193053e+0072015 5619e+006 591422e+006 21705e+007 194495e+007

sequence and its simulation value sequence were respec-tively calculated as follows

119883119894 =[[[[[[[[[[

119909119894 (1)119909119894 (2)119909119894 (3)

119909119894 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

4019119890 + 0064809119890 + 0064983119890 + 0065200119890 + 0065437119890 + 0065591119890 + 0065619119890 + 006

]]]]]]]]]]]]]]]

119883119895 =[[[[[[[[[[

119909119895 (1)119909119895 (2)119909119895 (3)

119909119895 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

401900119890 + 006457571119890 + 006528216119890 + 006560956119890 + 006577509119890 + 006584424119890 + 006591422119890 + 006

]]]]]]]]]]]]]]]

(36)

TheGAID andGRIDwere respectively calculated as follows

120585119894119895 asymp 09235119903119894119895 asymp 09390 (37)

Hence when exist1205760 = 09 and 120579 = 05120576119894119895 = 120579120585119894119895 + (1 minus 120579) 119903119894119895 = 09313 gt 09 = 1205760 (38)

Therefore according to Definition 3 and Table 5 thismodel verified the degree of grey incidence and exhibited anaccuracy belonging to grade 1

34 Policy Simulation Analysis and Discussion

341 Horizontal Analysis According to the horizontal anal-ysis the curves exhibited different changes with time Thespecific analysis results are presented as follows

Following the adoption of the low charge policy egAPCF = 5 yuandaysdotvehicle the AMVT (curve 1) exhibiteda decrease since about 2014 as exhibited in Figure 6(a)Although the growth rates of ANOG and APMG exhibited adecrease the total emissions maintained an increasing trendthereby resulting in high DAP levels (curve 4) The analysisresults indicate the inability of the low charge policy toeffectively reduce the DAP

According to Figure 6(f) curve 1 first exhibited aslow rise (before 2013) and a subsequent sharp descentfollowing the adoption of the high charge policy (APCF= 50 yuandaylowastvehicle) As a result the AMVT valuesdescended until 2013 wherein its descending range continu-ously increased Curve 3 terminated its previously continuousrise and instead descended slowly Similarly the rising rate

Discrete Dynamics in Nature and Society 13

0

2

4

6

8

10

12

14

16

18A

MV

T (

)

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

(a) AMVT

0

2

4

6

8

10

12

14

APM

G (

)

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

(b) APMG

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

0

2

4

6

8

10

12

AN

OG

()

(c) ANOG

AMVT ()APMG ()ANOG ()

0

2

4

6

8

10

12

14

16

18

5 20 8010 50 60 7030 9040 100

(d) Trend comparison

Figure 5 Development trends of the change rates of the main variables (a) AMVT (b) APMG (c) ANOG (d) Trend comparison

Table 10 The comparison of different policies

Variable APCF (yuandaylowastvehicle) Trend Variation ()5 50

AMVT (vehicle) 345229e+006 238178e+006 darr -3101APMG (t) 161737e+005 118839e+005 darr -2652ANOG (t) 154899e+005 121928e+005 darr -2129DAP 06 0525 darr -1250

of curve 2 slowed down relatively These results indicatethe effective control on the increase of APMG and ANOGafter which the values began to descend slowly Curve 4exhibited three phases specifically a rapid rise between 2011and 2014 a slow rise in rate between 2014 and 2018 and a slowdescent after 2018These results indicate the presence of DAPimprovements which exhibited gradual descent after 2018

The analysis results in Figures 6(b)ndash6(e) were similar tothose presented above

342 Vertical Analysis According to Figures 6(a)ndash6(f) theAPCF exhibited a continuous increase thereby generating achange in the rules of all the curves as follows

(i) AMVT (curve 1)TheAMVT exhibited a continuousdecrease Within a certain range the increase inAPCF aided in the descent of the AMVT therebyfurther alleviating the traffic pressures

(ii) APMG (curve 3) and ANOG (curve 2) A charge ofmore than 30 (Figures 6(d)ndash6(f)) generated a slowdescent in APMGMeanwhile the increase in ANOGalso exhibited effective restraint

(iii) DAP (curve 4)TheDAP exhibited an overall declineespecially following the implementation of a highcharge policy (APCF isin [40 50]) A subsequentdescending trend was later observed in the period ofanalogue simulation as presented in Figures 6(e) and6(f)

343 Comparison of Policies According to Table 10 in thepresence of a low charge policy (APCF=5) the AMVTAPMG ANOG and DAP under a high charge pol-icy exhibited an obvious decrease which indicates thatthe implementation of a high charge policy effectivelyreduced motor vehicle exhaust emissions to restrain the

14 Discrete Dynamics in Nature and Society

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

083 M

10000004

2 M00

2011 2013 2015 2017 20192009Time (year)

AMVT APCF=5ANOG APCF=5APMG APCF=5DAP APCF=5

vehicletontonDmnl

(a)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=10ANOG APCF=10APMG APCF=10DAP APCF=10

vehicletontonDmnl

(b)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=20ANOG APCF=20APMG APCF=20DAP APCF=20

vehicletontonDmnl

(c)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=30ANOG APCF=30APMG APCF=30DAP APCF=30

vehicletontonDmnl

(d)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=40ANOG APCF=40APMG APCF=40DAP APCF=40

vehicletontonDmnl

(e)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=50ANOG APCF=50APMG APCF=50DAP APCF=50

vehicletontonDmnl

(f)

Figure 6 Policy simulation (a) APCF=5 (b) APCF=10 (c) APCF=20 (d) APCF=30 (e) APCF=40 (f) APCF=50

intensification of ldquohazerdquo pollution degree in Beijing Specif-ically the gap between curves 1 and 2 exhibited a continuouswidening as presented in Figure 7(a) After 2013 curve 2exhibited an obvious descent Therefore the APCF policyeffectively reduced the AMVT and enabled an about 3101decrease in 2020

The results in Figures 7(b)ndash7(d) were similarly analyzed

In conclusion the adoption of a low charge policygenerated increasing APMG and ANOG trends as presentedin Figures 6(a) and 6(b) thereby suggesting the inabilityof the low charge policy to effectively reduce the DAP Anincrease of the fee to a certain extent especially followingthe implementation of a high charge policy (Figures 6(e) and6(f)) not only reduced the AMVT and alleviated traffic jams

Discrete Dynamics in Nature and Society 15

APCF=5

APCF=50

x 106

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 20202009Time (year)

2

25

3

35ve

hicle

(a) AMVT

APCF=5

APCF=50

x 105

20182017 2019 20202015 2016201420122011 201320102009Time (year)

11

12

13

14

15

16

17

ton

(b) APMG

APCF=5

APCF=50

x 105

08

09

1

11

12

13

14

15

16

ton

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 20202009Time (year)

(c) ANOG

02

APCF=5

APCF=50

2009 2011 20122010 20142013 2016 2017 20182015 20202019Time (year)

025

03

035

04

045

05

055D

mnl

(d) DAP

Figure 7 Comparison of the policies (a) AVT (b) APMG (c) ANOG (d) DAP

in cities but also effectively reduced the APMG and ANOGthereby reducing the DAP

According to a comparison on the different schemes atthe end of the analogue simulation period the high chargepolicy functioned as follows in terms of the emission reduc-tion of the motor vehicle exhaust the APMG and ANOGexhibited reductions of 2652 and 2129 respectively interms of alleviating traffic jams the AMVT exhibited a 3101decrease and in terms of reducing the degree of air pollutionthe DAP exhibited a 1250 decrease

4 Conclusions

41 Main Conclusions To resolve the air pollution problemsgenerated by motor vehicle exhaust emission the presentstudy introduced the charging mechanism and built a motorvehicle exhaust emission reduction strategy managementmodel using economic means and the SD-GM approach to

generate the following conclusions based on tests validationof the models and the simulation analysis of policies

(1)Within a certain range the reduction effects of APMGandANOGexhibited continuous enhancements following anincrease in APCF However the APCF did not always followthe principle ldquobigger means betterrdquo because the emissionreduction effect which was generated by an increase inthe APCF exhibited a marginal decreasing effect Accord-ing to the sensitivity analysis a pollution charge of 30ndash50yuandaysdotvehicle for the motor vehicles in Beijing was withinthe relatively reasonable range

(2) Three high charge policy functions were generatedbased on a comparison of the simulation results of thedifferent charging schemes the implementation of highcharge policies not only reduced the AMVT and alleviatedtraffic jams (Figures 6(e) 6(f) and 7(a) Table 10) but alsoeffectively reduced the APMG andANOG (Figures 6(e) 6(f)7(b) and 7(c) Tables 5 and 10) thereby further reducing theDAP (Figures 6(e) 6(f) and 7(d) Table 10) According to the

16 Discrete Dynamics in Nature and Society

contrastive analysis the DAP exhibited a decrease of about1250

(3) However the following problems were encounteredfollowing the implementation of the APCF policy (a) Theimplementation of the APCF policy increased the cost ofmotor vehicle trips and urged part-time drivers to take publictransportation which increased the burden of public trans-portation The subsidy policy and other applicable policiesmust be introduced to improve the public transport supplylevel and service quality Otherwise the trip demands ofpassengers will be difficult to satisfy which will influencethe implementation of the APCF policy (b) In the earlyperiods of APCF policy implementation an increase in thecost of motor vehicle trips due to the insufficient publicunderstanding and utilization of the APCF policy loweredits public support rate The government must strengthenits public relations work especially regarding the purposeand significance of its implementation to improve publicawareness and acknowledgment (c) The purpose of thesepolicies must be supervised and managed to gather APCFincome and improve public transportation infrastructures

42 Deficiencies and Future Work The present study consid-ered NOx and PMx as the principal motor vehicle emissionpollutants Future research must fully consider other com-ponents such as SO2 airborne particles hydrocarbons COand CO2 Secondly the implementation of a single chargingmeasure can reduce the supply level of public transportationFuture research should consider a subsidy mechanism toimprove the service quality Thirdly the function and effectof a single policy are limited Future work must considerthe integration of multiple policies to improve the emissionreduction effect For example future work may focus priorityon public transportation improvement of fuel quality vigor-ous promotion of new energy vehicles and improvements inemission standards

Appendix

A

See Table 11

B

Summary of the major variables and equations(1) Cost of motor vehicle trips = Air pollution charging

feelowast (1+ Air pollution control)(2) Amount ofNOx generation = INTEG (NOx emissions

- Annual dissipation of NOx 80380)(3) NOx emissions = Per vehicle annual of NOx

emissionslowast Amount of motor vehicle tripslowast Contributionrate of NOx from vehicle

(4) Contribution rate of NOx from vehicle = 05(5) Dissipation rate of NOx = 02(6) Annual dissipation of NOx = Amount of NOx

generationlowast Dissipation rate of NOx(7) Per vehicle annual of NOx emissions = 002

(8) Amount of PMx generation = INTEG (PMxemissions- Annual dissipation of PMx 160760)

(9) PMx emissions = Amount of motor vehicle tripslowastContribution rate of PMx from vehiclelowast Per vehicle annualof PMx emissions

(10) Contribution rate of PMx from vehicle = 05(11) Per vehicle annual of PMx emissions = 004(12) Annual dissipation of PMx = Amount of PMx

generationlowast Dissipation and control rate of PMx(13) Dissipation and control rate of PMx = 05(14) Pollution degree of NOx = IF THEN ELSE (Amount

of NOx generationgt= 11182e+005 09 IF THEN ELSE(Amount of NOx generationgt= 10874e+005 08 IF THENELSE (Amount of NOx generationgt= 10400e+005 07 IFTHEN ELSE (Amount of NOx generationgt= 9966e+00406 IF THEN ELSE (Amount of NOx generationgt=9618e+004 05 IF THEN ELSE (Amount of NOxgenerationgt= 8038e+004 03 IF THEN ELSE (Amountof NOx generationgt= 7008e+004 025 IF THEN ELSE(Amount of NOx generationgt= 6144e+004 02 IF THENELSE (Amount of NOx generationgt= 5508e+004 015 01)))))))))

(15) Pollution degree of PMx = IF THEN ELSE (Amountof PMx generationgt= 22364e+005 09 IF THEN ELSE(Amount of PMx generationgt= 21748e+005 08 IF THENELSE (Amount of PMx generationgt= 20800e+005 07 IFTHEN ELSE (Amount of PMx generationgt= 19932e+00506 IF THEN ELSE (Amount of PMx generationgt=19236e+005 05 IF THEN ELSE (Amount of PMxgenerationgt= 16076e+005 03 IF THEN ELSE (Amountof PMx generationgt= 14016e+005 025 IF THEN ELSE(Amount of PMx generationgt= 12288e+005 02 IF THENELSE (Amount of PMx generationgt= 11016e+005 015 01)))))))))

(16) Ratio of motor vehicle trips = 055(17) Amount of motor vehicle trips = Amount of motor

vehicleslowast Ratio of motor vehicle trips(18) Degree of air pollution = Weight ratio of NOxlowast

Pollution degree of NOx+ Weight ratio of PMxlowast Pollutiondegree of PMx

(19) Weight ratio of PMx = 05(20) Weight ratio of NOx = 05(21) Air pollution control = IF THEN ELSE (Degree of air

pollutiongt= 07 1 IF THEN ELSE (Degree of air pollutiongt=06 08 IF THEN ELSE (Degree of air pollutiongt= 05 07IF THEN ELSE (Degree of air pollutiongt= 04 06 IF THENELSE (Degree of air pollutiongt= 03 05 IF THEN ELSE(Degree of air pollutiongt= 025 045 IF THENELSE (Degreeof air pollutiongt= 02 04 IF THEN ELSE (Degree of airpollutiongt= 015 035 03))))))))

(22) Attraction degree of the growth of vehicles= (1-Airpollution control)lowast 055+ Attraction degree of vehicle tripslowast045

(23) Per capita annual income = Amount of GDPAmount of population

(24) Amount of population = INTEG (Growth of popu-lation+ Net migration- Population reduction 186e+007)

(25) Birth rate = Adjustment coefficient of birth ratelowastPredictive value of birth rate

Discrete Dynamics in Nature and Society 17

Table 11 Description of main variables in stock flow diagram

Signicant variable Unit Variable type Data sourceAir pollution charging fee yuandaysdotvehicle ConstantAir pollution control Dmnl Auxiliary variable M1+M3Amount of GDP yuan Level M1Amount of motor vehicles vehicle Level M1Amount of motor vehicle trips vehicle Auxiliary variableAmount of NOx (PMx) generation ton Level M1Amount of population person Level M1Annual dissipation of NOx (PMx) tonyear FlowAnnual scrapped vehicleyear FlowAttraction degree of city Constant M2Attraction degree of the growth of vehicles Auxiliary variable M1+M3Attraction degree of vehicle trips Auxiliary variable M1+M3Birth rate 1year Constant M3Contribution rate of NOx (PMx) from vehicle Constant M2Cost of motor vehicle trips yuandaysdotvehicle Auxiliary variable M3Death rate 1year Constant M3Degree of air pollution Dmnl Auxiliary variable M3Dissipation and control rate of NOx (PMx) 1year Constant M2Graphical function of the growth of GDP Dmnl Auxiliary variable M3Growth of GDP yuanyear FlowGrowth rate of motor vehicles 1year Auxiliary variable M1+M3Growth of motor vehicles vehicleyear FlowGrowth of population personyear FlowGrowth rate of vehicle ownership Dmnl Auxiliary variable M1+M3Impact factor of policy Dmnl Constant M3Net migration personyear FlowNet migration rate 1year Constant M1+M3NOx (PMx) emissions tonyear FlowPer capita annual income yuanperson Auxiliary variablePer vehicle annual of NOx (PMx) emissions tonyearsdotvehicle Constant M2Pollution degree of NOx (PMx) Dmnl Auxiliary variable M1+M3Population reduction personyear FlowRatio of motor vehicle trips Constant M2Scrap rate 1year Constant M2The average of net migration rate 1year Constant M1Weight ratio of PMx (NOx) Auxiliary variable M3

(26) Predictive value of birth rate = 000925(27) Death rate = Adjustment coefficient of death ratelowast

Predictive value of death rate(28) Predictive value of death rate = 000494(29) Net migration = Amount of populationlowastNet migra-

tion rate(30) Net migration rate = The average of net migration

ratelowast Attraction degree of cityand(Impact factor of policy)(31) Impact factor of policy = 15(32) The average of net migration rate = 000531(33) Attraction degree of city = 07056(34) Amount of GDP = INTEG (Growth of GDP

12153e+012)

(35) Graphical function of the growth of GDP = WITHLOOKUP (Amount of GDP ([(8e+011 0)- (3e+ 012 03)](81178e+011 01648) (98468e+011 0213) (11115e+01201288) (12153e+012 00934) (141136e+012 01613)(162519e+012 01515) (178794e+012 01001) (198008e+01201075) (213308e+012 00773) (230146e+012 00789)(235396e+012 002281) (240162e+012 00203) (245025e+012 002025) (249987e+012 002024) (255049e+0120020249)))

(36) Growth rate of GDP = Graphical function of thegrowth of GDPlowast Impact factor of the growth of GDP

(37) Amount of motor vehicles = INTEG (Growth ofmotor vehicles- Annual scrapped 4019e+006)

18 Discrete Dynamics in Nature and Society

(38) Annual scrapped = Amount of motor vehicleslowastScrap rate

(39) Scrap rate = 0067

Conflicts of Interest

The author declares no conflicts of interest

Acknowledgments

This work has been partially supported by the NationalNatural Science Foundation of China (71571119) ShanghaiFirst-Class Academic Discipline Project (S1201YLXK) andChina Postdoctoral Science Foundation (2018M630404)Theauthor would like to thank LetPub (httpwwwletpubcom)for providing linguistic assistance during the preparation ofthis manuscript

References

[1] X Liu S Ma J Tian N Jia and G Li ldquoA system dynamicsapproach to scenario analysis for urban passenger transportenergy consumption and CO2 emissions A case study ofBeijingrdquo Energy Policy vol 85 pp 253ndash270 2015

[2] B Xu L Luo and B Lin ldquoA dynamic analysis of air pollutionemissions in China Evidence from nonparametric additiveregression modelsrdquo Ecological Indicators vol 63 pp 346ndash3582016

[3] S Leinert H Daly B Hyde and B O Gallachoir ldquoCo-benefitsNot always Quantifying the negative effect of a CO2-reducingcar taxation policy on NOx emissionsrdquo Energy Policy vol 63pp 1151ndash1159 2013

[4] Z Cheng L Li and J Liu ldquoIdentifying the spatial effects anddriving factors of urban PM25 pollution in Chinardquo EcologicalIndicators vol 82 pp 61ndash75 2017

[5] N Kaida and K Kaida ldquoSpillover effect of congestion chargingon pro-environmental behaviorrdquo Environment Developmentand Sustainability vol 17 no 3 pp 409ndash421 2015

[6] R Penabaena-Niebles V Cantillo and J L Moura ldquoImpactof transition between signal timing plans in social cost basedin delay fuel consumption and air emissionsrdquo TransportationResearch Part D Transport and Environment vol 41 pp 445ndash456 2015

[7] DDing andB Shuai ldquoA traffic restriction scheme for enhancingcarpoolingrdquoDiscreteDynamics inNature and Society Article ID9626938 9 pages 2017

[8] D Kong X Guo B Yang and D Wu ldquoAnalyzing the Impactof Trucks on Traffic Flow Based on an Improved CellularAutomaton Modelrdquo Discrete Dynamics in Nature and Societyvol 2016 pp 1ndash14 2016

[9] S Cakmak C Hebbern J D Cakmak and J Vanos ldquoThemodifying effect of socioeconomic status on the relationshipbetween traffic air pollution and respiratory health in elemen-tary schoolchildrenrdquo Journal of Environmental Managementvol 177 pp 1ndash8 2016

[10] L Song H Song J Lin et al ldquoPM25 emissions from differenttypes of heavy-duty truck a case study and meta-analysis ofthe Beijing-Tianjin-Hebei regionrdquo Environmental Science andPollution Research vol 24 no 12 pp 11206ndash11214 2017

[11] Z Hu S Kang C Li et al ldquoLight absorption of biomassburning and vehicle emission-sourced carbonaceous aerosolsof the Tibetan Plateaurdquo Environmental Science and PollutionResearch vol 24 no 18 pp 15369ndash15378 2017

[12] X Cen H K Lo and L Li ldquoA framework for estimating trafficemissions The development of Passenger Car Emission UnitrdquoTransportation Research Part D Transport and Environmentvol 44 pp 78ndash92 2016

[13] S Wang X Liu C Zhou J Hu and J Ou ldquoExamining theimpacts of socioeconomic factors urban form and transporta-tion networks on CO2 emissions in Chinarsquos megacitiesrdquoAppliedEnergy vol 185 pp 189ndash200 2017

[14] Q Wang K Hubacek K Feng Y-M Wei and Q-M LiangldquoDistributional effects of carbon taxationrdquo Applied Energy vol184 pp 1123ndash1131 2016

[15] C Johansson L Burman and B Forsberg ldquoThe effects ofcongestions tax on air quality and healthrdquo Atmospheric Envi-ronment vol 43 no 31 pp 4843ndash4854 2009

[16] A Rakowska K C Wong T Townsend et al ldquoImpact of trafficvolume and composition on the air quality and pedestrianexposure in urban street canyonrdquo Atmospheric Environmentvol 98 pp 260ndash270 2014

[17] S Batterman R Ganguly and P Harbin ldquoHigh resolutionspatial and temporal mapping of traffic-related air pollutantsrdquoInternational Journal of Environmental Research and PublicHealth vol 12 no 4 pp 3646ndash3666 2015

[18] J Eliasson M Borjesson D van Amelsfort K Brundell-Freijand L Engelson ldquoAccuracy of congestion pricing forecastsrdquoTransportation Research Part A Policy and Practice vol 52 pp34ndash46 2013

[19] J Eliasson ldquoThe role of attitude structures direct experienceand reframing for the success of congestion pricingrdquo Trans-portation Research Part A Policy and Practice vol 67 pp 81ndash952014

[20] H X Yang J D Li H Zhang and S Q Liu ldquoResearch on thegovernance of urban traffic jam based on system dynamicsrdquoSystems EngineeringTheory and Practice vol 34 no 8 pp 2135ndash2143 2014 (Chinese)

[21] M H Zhu Research on Socio-Economic Impact of UrbanTrafficCongestion [PhD thesis] Beijing JiaotongUniversity 2013(Chinese)

[22] B Zeng Research on Modeling Technologies of Grey Prediction[PhD thesis] Nanjing University of Aeronautics and Astronau-tics 2011 (Chinese)

[23] S F Liu Y J Yang and L F Wu Grey System Theory andApplication Science Press Beijing China 2017

[24] S W Jia K Yang J J Zhao and G L Yan ldquoThe traffic-congestion charging fee management model based on thesystem dynamics approachrdquo Mathematical Problems in Engi-neering vol 2017 Article ID 3024898 13 pages 2017

Discrete Dynamics in Nature and Society 9

(a) APMG APCF=5(a) APMG APCF=100(a) APMG APCF=1000

100000

125000

150000

175000

200000

ton

2011 2013 2015 2017 20192009Time (year)

(a) APMG

(b) ANOG APCF=5(b) ANOG APCF=100(b) ANOG APCF=1000

2011 2013 2015 2017 20192009Time (year)

80000

110000

140000

170000

200000

ton

(b) ANOG

(c) AMVT APCF=5(c) AMVT APCF=100(c) AMVT APCF=1000

2011 2013 2015 2017 20192009Time (year)

2 M

25 M

3 M

35 M

4 M

vehi

cle

(c) AMVT

Figure 3 Extreme condition test (a) APMG (b) ANOG (c) AMVT

times 119886119905119905119903119886119888119905119894119900119899 119889119890119892119903119890119890 119900119891 119888119894119905119910120572(29)

where 120572 refers to the impact factor of policy Based on thiscalculation 120572 = 15 generates calculations that are close tothe actual value See the appendixes for descriptions of theother variables and main equations

3 Simulation and Result Analysis

31 Model Test

311 Extreme Condition Test The extreme condition testmainly aims to inspect the stability applicability in extremeconditions and accuracy of the equations in the test modelto represent the change trends of the realistic system and theintentions of the decision maker

According to Figure 3(a) the APMG exhibited a continu-ous decrease following an increase in the APCF In particularthe minimum value of APMG was obtained when the APCFwas at the limit value (1000 yuandaysdotvehicle) In additionwhen APCF was equal to 5 the maximum APMG value wasobtained which is consistent with the actual laws therebyconfirming the stability of the model in extreme conditions

A deeper analysis indicated a larger interval between curves1 and 2 and a shorter interval between curves 2 and curve3 thereby indicating that the APCF did not exceed 100yuandaysdotvehicle

The change rules presented in Figures 3(b) and 3(c) weresimilar to those in Figure 3(a)

312 Sensitivity Test The model behaviors exhibited dif-ferent and sensitive results at different parameter valuesSpecifically the behavior model changed following an appro-priate change of parameter In addition the policies generatedthrough the model analysis changed following a change inparameters

According to Figure 4(a) with time all the curves firstrose and then slowly descended Specifically in the earlyperiod of policy implementation (before 2014) the effect wasnot obvious because part-time drivers may not have had adeep understanding of the purpose of the implementationand the significance of the APCF policy thereby resultingin a continuous increase in AMVT due to sharp increasein motor vehicle ownership The AMVT growth rate wasmore effectively controlled following a longer period due tocontinuous policy implementation and fulfilment After 2016the growth rate continuously decreased thereby allowing

10 Discrete Dynamics in Nature and Society

(a) AMVT APCF=5(a) AMVT APCF=10(a) AMVT APCF=20(a) AMVT APCF=30(a) AMVT APCF=40(a) AMVT APCF=50(a) AMVT APCF=60(a) AMVT APCF=70(a) AMVT APCF=80(a) AMVT APCF=90(a) AMVT APCF=100

2 M

25 M

3 M

35 M

4 Mve

hicle

2011 2013 2015 2017 20192009Time (year)

(a) AMVT

(b) APMG APCF=5(b) APMG APCF=10(b) APMG APCF=20(b) APMG APCF=30(b) APMG APCF=40(b) APMG APCF=50(b) APMG APCF=60(b) APMG APCF=70(b) APMG APCF=80(b) APMG APCF=90(b) APMG APCF=100

100000

125000

150000

175000

200000

ton

2011 2013 2015 2017 20192009Time (year)

(b) APMG

(c) ANOG APCF=5(c) ANOG APCF=10(c) ANOG APCF=20(c) ANOG APCF=30(c) ANOG APCF=40(c) ANOG APCF=50(c) ANOG APCF=60(c) ANOG APCF=70(c) ANOG APCF=80(c) ANOG APCF=90(c) ANOG APCF=100

80000

110000

140000

170000

200000

ton

2011 2013 2015 2017 20192009Time (year)

(c) ANOG

Figure 4 Sensitivity test (a) AMVT (b) APMG (c) ANOG

the APCF policy to exhibit good effects based on long-termpractice improvement and fulfilment

Following further analysis the AMVT exhibited amarginal decreasing effect following an increase in APCFfrom curve 1 to curve 6 especially in curves 3ndash6 whichindicates that a larger APCF is not always better The analysisresults are presented in Figures 4(b) and 4(c)

In conclusion the APCF value range was observed withinthe interval of [30 50] based on the above analysis from the

perspective of AMVT reduction (alleviate traffic jam) as wellas APMG and ANOG emission reduction Table 8 presentsthe detailed analysis results

32 Analysis of Results The AMVT exhibited a continuousdecrease following an increase in APCF which indicates theability of this policy to restrict increases in AMVT Specif-ically obvious changes were in the intervals of [5 10] and[10 20] wherein theAMVTexhibited a decrease of 166649

Discrete Dynamics in Nature and Society 11

and 105055 respectively The AMVT exhibited a decreaseof 35103 24912 and 16793 in the intervals of [20 30][30 40] and [40 50] respectivelyHoweverminimal changeswere observed in the interval of 50 yuandaysdotvehicle aboveIn addition the APMG exhibited a decrease of 13967789137 28538 20987 and 14128 respectively in theabove intervals and exhibited very minimal changes in theinterval of 50 above The ANOG exhibited similar changerules

Therefore the interval [30 50] is deemed a reasonablevalue range based on the analysis on the degree of effect ofdifferent APCFs on the AMVT APMG and ANOG

In particular the change trends of AMVT APMG andANOG were generally consistent as presented in Figure 6specifically Figure 5(d) Figures 5(a)ndash5(c) exhibited obviousdecreasing trend rates that were continuously weakened inthe interval of [30 50] In addition the change was verylimited as the APCF exceeded 50 yuandaysdotvehicle

Therefore an effective APCF range of [30 50]was chosenbased on the development trends analysis of the change ratesof the main variables

33 Model Validation Historical data (2009-2015) on theamount of motor vehicles and population in Beijing arepresented in Table 9 wherein the conformance of theirrespective GSID was tested

331 Qualified Verification of the Degree of Grey Incidenceon the Population of Beijing The original sequence and itssimulation value sequence are respectively presented asfollows

1198830 =[[[[[[[[[[

1199090 (1)1199090 (2)1199090 (3)

1199090 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

18600119890 + 00719619119890 + 00720186119890 + 00720693119890 + 00721148119890 + 00721516119890 + 00721705119890 + 007

]]]]]]]]]]]]]]]

1198831 =[[[[[[[[[[

1199091 (1)1199091 (2)1199091 (3)

1199091 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

186000119890 + 007187390119890 + 007188790119890 + 007190200119890 + 007191621119890 + 007193053119890 + 007194495119890 + 007

]]]]]]]]]]]]]]]

(30)

The following was derived based on their calculations

100381610038161003816100381611990401003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

11990900 (119896) + 1211990900 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 117145

100381610038161003816100381611990411003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

11990901 (119896) + 1211990901 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 025295

10038161003816100381610038161199040 minus 11990411003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

(11990901 (119896) minus 11990900 (119896)) + 12 (11990901 (7) minus 11990900 (7))

1003816100381610038161003816100381610038161003816100381610038161003816= 09185

(31)

Therefore we are able to obtain the value of the GAID

12058501 = 1 + 100381610038161003816100381611990401003816100381610038161003816 + 1003816100381610038161003816119904110038161003816100381610038161 + 100381610038161003816100381611990401003816100381610038161003816 + 100381610038161003816100381611990411003816100381610038161003816 + 10038161003816100381610038161199040 minus 11990411003816100381610038161003816= 1 + 117145 + 025295

1 + 117145 + 025295 + 09185 asymp 07275(32)

In a similar way

100381610038161003816100381610038161199041015840010038161003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

119909101584000 (119896) + 12119909101584000 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 062985100381610038161003816100381610038161199041015840110038161003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

119909101584001 (119896) + 12119909101584001 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 0136051003816100381610038161003816100381611990410158400 minus 1199041015840110038161003816100381610038161003816

=10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

(119909101584001 (119896) minus 119909101584000 (119896)) + 12 (119909101584001 (7) minus 119909101584000 (7))

1003816100381610038161003816100381610038161003816100381610038161003816= 04938

(33)

Therefore GRID is

11990301 = 1 + 100381610038161003816100381610038161199041015840010038161003816100381610038161003816 + 1003816100381610038161003816100381611990410158401100381610038161003816100381610038161 + 1003816100381610038161003816119904101584001003816100381610038161003816 + 1003816100381610038161003816119904101584011003816100381610038161003816 + 100381610038161003816100381611990410158400 minus 119904101584011003816100381610038161003816= 1 + 062985 + 013605

1 + 062985 + 013605 + 04938 asymp 07815(34)

When 120579 = 05 and exist1205760 = 07 then12057601 = 12057912058501 + (1 minus 120579) 11990301 = 05 times 07275 + 05 times 07815

= 07545 gt 07 = 1205760 (35)

Therefore according to Table 5 the accuracy was determinedto be between grade 2 and grade 3

332 Qualified Verification of the Degree of Grey Incidenceon the Amount of Motor Vehicles in Beijing The original

12 Discrete Dynamics in Nature and Society

Table 8 The effects of different APCFs on AMVT APNG and ANOG

APCF AMVT Trend Variation APMG Trend Variation ANOG Trend Variation() () ()

5 345229e+006 -- -- 161737 -- -- 154899 -- --10 287697e+006 darr -166649 139146 darr -139677 137782 darr -11050420 257473e+006 darr -105055 126743 darr -89137 128122 darr -7011130 248435e+006 darr -35103 123126 darr -28538 125306 darr -2197940 242246e+006 darr -24912 120542 darr -20987 123272 darr -1623250 238178e+006 darr -16793 118839 darr -14128 121928 darr -1090360 235237e+006 darr -12348 117604 darr -10392 120952 darr -0800570 232979e+006 darr -09599 116655 darr -08069 120202 darr -0620180 231171e+006 darr -07760 115894 darr -06524 119599 darr -0501790 229680e+006 darr -06450 115265 darr -05427 119101 darr -04164100 228421e+006 darr -05482 114734 darr -04607 118680 darr -03535

Table 9 Historical data and their simulation values (2009-2015)

Time Amount of motor vehicles (vehicle) Amount of population (person)Actual value Simulation value Actual value Simulation value

2009 4019e+006 401900e+006 18600e+007 186000e+0072010 4809e+006 457571e+006 19619e+007 187390e+0072011 4983e+006 528216e+006 20186e+007 188790e+0072012 5200e+006 560956e+006 20693e+007 190200e+0072013 5437e+006 577509e+006 21148e+007 191621e+0072014 5591e+006 584424e+006 21516e+007 193053e+0072015 5619e+006 591422e+006 21705e+007 194495e+007

sequence and its simulation value sequence were respec-tively calculated as follows

119883119894 =[[[[[[[[[[

119909119894 (1)119909119894 (2)119909119894 (3)

119909119894 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

4019119890 + 0064809119890 + 0064983119890 + 0065200119890 + 0065437119890 + 0065591119890 + 0065619119890 + 006

]]]]]]]]]]]]]]]

119883119895 =[[[[[[[[[[

119909119895 (1)119909119895 (2)119909119895 (3)

119909119895 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

401900119890 + 006457571119890 + 006528216119890 + 006560956119890 + 006577509119890 + 006584424119890 + 006591422119890 + 006

]]]]]]]]]]]]]]]

(36)

TheGAID andGRIDwere respectively calculated as follows

120585119894119895 asymp 09235119903119894119895 asymp 09390 (37)

Hence when exist1205760 = 09 and 120579 = 05120576119894119895 = 120579120585119894119895 + (1 minus 120579) 119903119894119895 = 09313 gt 09 = 1205760 (38)

Therefore according to Definition 3 and Table 5 thismodel verified the degree of grey incidence and exhibited anaccuracy belonging to grade 1

34 Policy Simulation Analysis and Discussion

341 Horizontal Analysis According to the horizontal anal-ysis the curves exhibited different changes with time Thespecific analysis results are presented as follows

Following the adoption of the low charge policy egAPCF = 5 yuandaysdotvehicle the AMVT (curve 1) exhibiteda decrease since about 2014 as exhibited in Figure 6(a)Although the growth rates of ANOG and APMG exhibited adecrease the total emissions maintained an increasing trendthereby resulting in high DAP levels (curve 4) The analysisresults indicate the inability of the low charge policy toeffectively reduce the DAP

According to Figure 6(f) curve 1 first exhibited aslow rise (before 2013) and a subsequent sharp descentfollowing the adoption of the high charge policy (APCF= 50 yuandaylowastvehicle) As a result the AMVT valuesdescended until 2013 wherein its descending range continu-ously increased Curve 3 terminated its previously continuousrise and instead descended slowly Similarly the rising rate

Discrete Dynamics in Nature and Society 13

0

2

4

6

8

10

12

14

16

18A

MV

T (

)

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

(a) AMVT

0

2

4

6

8

10

12

14

APM

G (

)

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

(b) APMG

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

0

2

4

6

8

10

12

AN

OG

()

(c) ANOG

AMVT ()APMG ()ANOG ()

0

2

4

6

8

10

12

14

16

18

5 20 8010 50 60 7030 9040 100

(d) Trend comparison

Figure 5 Development trends of the change rates of the main variables (a) AMVT (b) APMG (c) ANOG (d) Trend comparison

Table 10 The comparison of different policies

Variable APCF (yuandaylowastvehicle) Trend Variation ()5 50

AMVT (vehicle) 345229e+006 238178e+006 darr -3101APMG (t) 161737e+005 118839e+005 darr -2652ANOG (t) 154899e+005 121928e+005 darr -2129DAP 06 0525 darr -1250

of curve 2 slowed down relatively These results indicatethe effective control on the increase of APMG and ANOGafter which the values began to descend slowly Curve 4exhibited three phases specifically a rapid rise between 2011and 2014 a slow rise in rate between 2014 and 2018 and a slowdescent after 2018These results indicate the presence of DAPimprovements which exhibited gradual descent after 2018

The analysis results in Figures 6(b)ndash6(e) were similar tothose presented above

342 Vertical Analysis According to Figures 6(a)ndash6(f) theAPCF exhibited a continuous increase thereby generating achange in the rules of all the curves as follows

(i) AMVT (curve 1)TheAMVT exhibited a continuousdecrease Within a certain range the increase inAPCF aided in the descent of the AMVT therebyfurther alleviating the traffic pressures

(ii) APMG (curve 3) and ANOG (curve 2) A charge ofmore than 30 (Figures 6(d)ndash6(f)) generated a slowdescent in APMGMeanwhile the increase in ANOGalso exhibited effective restraint

(iii) DAP (curve 4)TheDAP exhibited an overall declineespecially following the implementation of a highcharge policy (APCF isin [40 50]) A subsequentdescending trend was later observed in the period ofanalogue simulation as presented in Figures 6(e) and6(f)

343 Comparison of Policies According to Table 10 in thepresence of a low charge policy (APCF=5) the AMVTAPMG ANOG and DAP under a high charge pol-icy exhibited an obvious decrease which indicates thatthe implementation of a high charge policy effectivelyreduced motor vehicle exhaust emissions to restrain the

14 Discrete Dynamics in Nature and Society

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

083 M

10000004

2 M00

2011 2013 2015 2017 20192009Time (year)

AMVT APCF=5ANOG APCF=5APMG APCF=5DAP APCF=5

vehicletontonDmnl

(a)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=10ANOG APCF=10APMG APCF=10DAP APCF=10

vehicletontonDmnl

(b)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=20ANOG APCF=20APMG APCF=20DAP APCF=20

vehicletontonDmnl

(c)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=30ANOG APCF=30APMG APCF=30DAP APCF=30

vehicletontonDmnl

(d)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=40ANOG APCF=40APMG APCF=40DAP APCF=40

vehicletontonDmnl

(e)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=50ANOG APCF=50APMG APCF=50DAP APCF=50

vehicletontonDmnl

(f)

Figure 6 Policy simulation (a) APCF=5 (b) APCF=10 (c) APCF=20 (d) APCF=30 (e) APCF=40 (f) APCF=50

intensification of ldquohazerdquo pollution degree in Beijing Specif-ically the gap between curves 1 and 2 exhibited a continuouswidening as presented in Figure 7(a) After 2013 curve 2exhibited an obvious descent Therefore the APCF policyeffectively reduced the AMVT and enabled an about 3101decrease in 2020

The results in Figures 7(b)ndash7(d) were similarly analyzed

In conclusion the adoption of a low charge policygenerated increasing APMG and ANOG trends as presentedin Figures 6(a) and 6(b) thereby suggesting the inabilityof the low charge policy to effectively reduce the DAP Anincrease of the fee to a certain extent especially followingthe implementation of a high charge policy (Figures 6(e) and6(f)) not only reduced the AMVT and alleviated traffic jams

Discrete Dynamics in Nature and Society 15

APCF=5

APCF=50

x 106

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 20202009Time (year)

2

25

3

35ve

hicle

(a) AMVT

APCF=5

APCF=50

x 105

20182017 2019 20202015 2016201420122011 201320102009Time (year)

11

12

13

14

15

16

17

ton

(b) APMG

APCF=5

APCF=50

x 105

08

09

1

11

12

13

14

15

16

ton

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 20202009Time (year)

(c) ANOG

02

APCF=5

APCF=50

2009 2011 20122010 20142013 2016 2017 20182015 20202019Time (year)

025

03

035

04

045

05

055D

mnl

(d) DAP

Figure 7 Comparison of the policies (a) AVT (b) APMG (c) ANOG (d) DAP

in cities but also effectively reduced the APMG and ANOGthereby reducing the DAP

According to a comparison on the different schemes atthe end of the analogue simulation period the high chargepolicy functioned as follows in terms of the emission reduc-tion of the motor vehicle exhaust the APMG and ANOGexhibited reductions of 2652 and 2129 respectively interms of alleviating traffic jams the AMVT exhibited a 3101decrease and in terms of reducing the degree of air pollutionthe DAP exhibited a 1250 decrease

4 Conclusions

41 Main Conclusions To resolve the air pollution problemsgenerated by motor vehicle exhaust emission the presentstudy introduced the charging mechanism and built a motorvehicle exhaust emission reduction strategy managementmodel using economic means and the SD-GM approach to

generate the following conclusions based on tests validationof the models and the simulation analysis of policies

(1)Within a certain range the reduction effects of APMGandANOGexhibited continuous enhancements following anincrease in APCF However the APCF did not always followthe principle ldquobigger means betterrdquo because the emissionreduction effect which was generated by an increase inthe APCF exhibited a marginal decreasing effect Accord-ing to the sensitivity analysis a pollution charge of 30ndash50yuandaysdotvehicle for the motor vehicles in Beijing was withinthe relatively reasonable range

(2) Three high charge policy functions were generatedbased on a comparison of the simulation results of thedifferent charging schemes the implementation of highcharge policies not only reduced the AMVT and alleviatedtraffic jams (Figures 6(e) 6(f) and 7(a) Table 10) but alsoeffectively reduced the APMG andANOG (Figures 6(e) 6(f)7(b) and 7(c) Tables 5 and 10) thereby further reducing theDAP (Figures 6(e) 6(f) and 7(d) Table 10) According to the

16 Discrete Dynamics in Nature and Society

contrastive analysis the DAP exhibited a decrease of about1250

(3) However the following problems were encounteredfollowing the implementation of the APCF policy (a) Theimplementation of the APCF policy increased the cost ofmotor vehicle trips and urged part-time drivers to take publictransportation which increased the burden of public trans-portation The subsidy policy and other applicable policiesmust be introduced to improve the public transport supplylevel and service quality Otherwise the trip demands ofpassengers will be difficult to satisfy which will influencethe implementation of the APCF policy (b) In the earlyperiods of APCF policy implementation an increase in thecost of motor vehicle trips due to the insufficient publicunderstanding and utilization of the APCF policy loweredits public support rate The government must strengthenits public relations work especially regarding the purposeand significance of its implementation to improve publicawareness and acknowledgment (c) The purpose of thesepolicies must be supervised and managed to gather APCFincome and improve public transportation infrastructures

42 Deficiencies and Future Work The present study consid-ered NOx and PMx as the principal motor vehicle emissionpollutants Future research must fully consider other com-ponents such as SO2 airborne particles hydrocarbons COand CO2 Secondly the implementation of a single chargingmeasure can reduce the supply level of public transportationFuture research should consider a subsidy mechanism toimprove the service quality Thirdly the function and effectof a single policy are limited Future work must considerthe integration of multiple policies to improve the emissionreduction effect For example future work may focus priorityon public transportation improvement of fuel quality vigor-ous promotion of new energy vehicles and improvements inemission standards

Appendix

A

See Table 11

B

Summary of the major variables and equations(1) Cost of motor vehicle trips = Air pollution charging

feelowast (1+ Air pollution control)(2) Amount ofNOx generation = INTEG (NOx emissions

- Annual dissipation of NOx 80380)(3) NOx emissions = Per vehicle annual of NOx

emissionslowast Amount of motor vehicle tripslowast Contributionrate of NOx from vehicle

(4) Contribution rate of NOx from vehicle = 05(5) Dissipation rate of NOx = 02(6) Annual dissipation of NOx = Amount of NOx

generationlowast Dissipation rate of NOx(7) Per vehicle annual of NOx emissions = 002

(8) Amount of PMx generation = INTEG (PMxemissions- Annual dissipation of PMx 160760)

(9) PMx emissions = Amount of motor vehicle tripslowastContribution rate of PMx from vehiclelowast Per vehicle annualof PMx emissions

(10) Contribution rate of PMx from vehicle = 05(11) Per vehicle annual of PMx emissions = 004(12) Annual dissipation of PMx = Amount of PMx

generationlowast Dissipation and control rate of PMx(13) Dissipation and control rate of PMx = 05(14) Pollution degree of NOx = IF THEN ELSE (Amount

of NOx generationgt= 11182e+005 09 IF THEN ELSE(Amount of NOx generationgt= 10874e+005 08 IF THENELSE (Amount of NOx generationgt= 10400e+005 07 IFTHEN ELSE (Amount of NOx generationgt= 9966e+00406 IF THEN ELSE (Amount of NOx generationgt=9618e+004 05 IF THEN ELSE (Amount of NOxgenerationgt= 8038e+004 03 IF THEN ELSE (Amountof NOx generationgt= 7008e+004 025 IF THEN ELSE(Amount of NOx generationgt= 6144e+004 02 IF THENELSE (Amount of NOx generationgt= 5508e+004 015 01)))))))))

(15) Pollution degree of PMx = IF THEN ELSE (Amountof PMx generationgt= 22364e+005 09 IF THEN ELSE(Amount of PMx generationgt= 21748e+005 08 IF THENELSE (Amount of PMx generationgt= 20800e+005 07 IFTHEN ELSE (Amount of PMx generationgt= 19932e+00506 IF THEN ELSE (Amount of PMx generationgt=19236e+005 05 IF THEN ELSE (Amount of PMxgenerationgt= 16076e+005 03 IF THEN ELSE (Amountof PMx generationgt= 14016e+005 025 IF THEN ELSE(Amount of PMx generationgt= 12288e+005 02 IF THENELSE (Amount of PMx generationgt= 11016e+005 015 01)))))))))

(16) Ratio of motor vehicle trips = 055(17) Amount of motor vehicle trips = Amount of motor

vehicleslowast Ratio of motor vehicle trips(18) Degree of air pollution = Weight ratio of NOxlowast

Pollution degree of NOx+ Weight ratio of PMxlowast Pollutiondegree of PMx

(19) Weight ratio of PMx = 05(20) Weight ratio of NOx = 05(21) Air pollution control = IF THEN ELSE (Degree of air

pollutiongt= 07 1 IF THEN ELSE (Degree of air pollutiongt=06 08 IF THEN ELSE (Degree of air pollutiongt= 05 07IF THEN ELSE (Degree of air pollutiongt= 04 06 IF THENELSE (Degree of air pollutiongt= 03 05 IF THEN ELSE(Degree of air pollutiongt= 025 045 IF THENELSE (Degreeof air pollutiongt= 02 04 IF THEN ELSE (Degree of airpollutiongt= 015 035 03))))))))

(22) Attraction degree of the growth of vehicles= (1-Airpollution control)lowast 055+ Attraction degree of vehicle tripslowast045

(23) Per capita annual income = Amount of GDPAmount of population

(24) Amount of population = INTEG (Growth of popu-lation+ Net migration- Population reduction 186e+007)

(25) Birth rate = Adjustment coefficient of birth ratelowastPredictive value of birth rate

Discrete Dynamics in Nature and Society 17

Table 11 Description of main variables in stock flow diagram

Signicant variable Unit Variable type Data sourceAir pollution charging fee yuandaysdotvehicle ConstantAir pollution control Dmnl Auxiliary variable M1+M3Amount of GDP yuan Level M1Amount of motor vehicles vehicle Level M1Amount of motor vehicle trips vehicle Auxiliary variableAmount of NOx (PMx) generation ton Level M1Amount of population person Level M1Annual dissipation of NOx (PMx) tonyear FlowAnnual scrapped vehicleyear FlowAttraction degree of city Constant M2Attraction degree of the growth of vehicles Auxiliary variable M1+M3Attraction degree of vehicle trips Auxiliary variable M1+M3Birth rate 1year Constant M3Contribution rate of NOx (PMx) from vehicle Constant M2Cost of motor vehicle trips yuandaysdotvehicle Auxiliary variable M3Death rate 1year Constant M3Degree of air pollution Dmnl Auxiliary variable M3Dissipation and control rate of NOx (PMx) 1year Constant M2Graphical function of the growth of GDP Dmnl Auxiliary variable M3Growth of GDP yuanyear FlowGrowth rate of motor vehicles 1year Auxiliary variable M1+M3Growth of motor vehicles vehicleyear FlowGrowth of population personyear FlowGrowth rate of vehicle ownership Dmnl Auxiliary variable M1+M3Impact factor of policy Dmnl Constant M3Net migration personyear FlowNet migration rate 1year Constant M1+M3NOx (PMx) emissions tonyear FlowPer capita annual income yuanperson Auxiliary variablePer vehicle annual of NOx (PMx) emissions tonyearsdotvehicle Constant M2Pollution degree of NOx (PMx) Dmnl Auxiliary variable M1+M3Population reduction personyear FlowRatio of motor vehicle trips Constant M2Scrap rate 1year Constant M2The average of net migration rate 1year Constant M1Weight ratio of PMx (NOx) Auxiliary variable M3

(26) Predictive value of birth rate = 000925(27) Death rate = Adjustment coefficient of death ratelowast

Predictive value of death rate(28) Predictive value of death rate = 000494(29) Net migration = Amount of populationlowastNet migra-

tion rate(30) Net migration rate = The average of net migration

ratelowast Attraction degree of cityand(Impact factor of policy)(31) Impact factor of policy = 15(32) The average of net migration rate = 000531(33) Attraction degree of city = 07056(34) Amount of GDP = INTEG (Growth of GDP

12153e+012)

(35) Graphical function of the growth of GDP = WITHLOOKUP (Amount of GDP ([(8e+011 0)- (3e+ 012 03)](81178e+011 01648) (98468e+011 0213) (11115e+01201288) (12153e+012 00934) (141136e+012 01613)(162519e+012 01515) (178794e+012 01001) (198008e+01201075) (213308e+012 00773) (230146e+012 00789)(235396e+012 002281) (240162e+012 00203) (245025e+012 002025) (249987e+012 002024) (255049e+0120020249)))

(36) Growth rate of GDP = Graphical function of thegrowth of GDPlowast Impact factor of the growth of GDP

(37) Amount of motor vehicles = INTEG (Growth ofmotor vehicles- Annual scrapped 4019e+006)

18 Discrete Dynamics in Nature and Society

(38) Annual scrapped = Amount of motor vehicleslowastScrap rate

(39) Scrap rate = 0067

Conflicts of Interest

The author declares no conflicts of interest

Acknowledgments

This work has been partially supported by the NationalNatural Science Foundation of China (71571119) ShanghaiFirst-Class Academic Discipline Project (S1201YLXK) andChina Postdoctoral Science Foundation (2018M630404)Theauthor would like to thank LetPub (httpwwwletpubcom)for providing linguistic assistance during the preparation ofthis manuscript

References

[1] X Liu S Ma J Tian N Jia and G Li ldquoA system dynamicsapproach to scenario analysis for urban passenger transportenergy consumption and CO2 emissions A case study ofBeijingrdquo Energy Policy vol 85 pp 253ndash270 2015

[2] B Xu L Luo and B Lin ldquoA dynamic analysis of air pollutionemissions in China Evidence from nonparametric additiveregression modelsrdquo Ecological Indicators vol 63 pp 346ndash3582016

[3] S Leinert H Daly B Hyde and B O Gallachoir ldquoCo-benefitsNot always Quantifying the negative effect of a CO2-reducingcar taxation policy on NOx emissionsrdquo Energy Policy vol 63pp 1151ndash1159 2013

[4] Z Cheng L Li and J Liu ldquoIdentifying the spatial effects anddriving factors of urban PM25 pollution in Chinardquo EcologicalIndicators vol 82 pp 61ndash75 2017

[5] N Kaida and K Kaida ldquoSpillover effect of congestion chargingon pro-environmental behaviorrdquo Environment Developmentand Sustainability vol 17 no 3 pp 409ndash421 2015

[6] R Penabaena-Niebles V Cantillo and J L Moura ldquoImpactof transition between signal timing plans in social cost basedin delay fuel consumption and air emissionsrdquo TransportationResearch Part D Transport and Environment vol 41 pp 445ndash456 2015

[7] DDing andB Shuai ldquoA traffic restriction scheme for enhancingcarpoolingrdquoDiscreteDynamics inNature and Society Article ID9626938 9 pages 2017

[8] D Kong X Guo B Yang and D Wu ldquoAnalyzing the Impactof Trucks on Traffic Flow Based on an Improved CellularAutomaton Modelrdquo Discrete Dynamics in Nature and Societyvol 2016 pp 1ndash14 2016

[9] S Cakmak C Hebbern J D Cakmak and J Vanos ldquoThemodifying effect of socioeconomic status on the relationshipbetween traffic air pollution and respiratory health in elemen-tary schoolchildrenrdquo Journal of Environmental Managementvol 177 pp 1ndash8 2016

[10] L Song H Song J Lin et al ldquoPM25 emissions from differenttypes of heavy-duty truck a case study and meta-analysis ofthe Beijing-Tianjin-Hebei regionrdquo Environmental Science andPollution Research vol 24 no 12 pp 11206ndash11214 2017

[11] Z Hu S Kang C Li et al ldquoLight absorption of biomassburning and vehicle emission-sourced carbonaceous aerosolsof the Tibetan Plateaurdquo Environmental Science and PollutionResearch vol 24 no 18 pp 15369ndash15378 2017

[12] X Cen H K Lo and L Li ldquoA framework for estimating trafficemissions The development of Passenger Car Emission UnitrdquoTransportation Research Part D Transport and Environmentvol 44 pp 78ndash92 2016

[13] S Wang X Liu C Zhou J Hu and J Ou ldquoExamining theimpacts of socioeconomic factors urban form and transporta-tion networks on CO2 emissions in Chinarsquos megacitiesrdquoAppliedEnergy vol 185 pp 189ndash200 2017

[14] Q Wang K Hubacek K Feng Y-M Wei and Q-M LiangldquoDistributional effects of carbon taxationrdquo Applied Energy vol184 pp 1123ndash1131 2016

[15] C Johansson L Burman and B Forsberg ldquoThe effects ofcongestions tax on air quality and healthrdquo Atmospheric Envi-ronment vol 43 no 31 pp 4843ndash4854 2009

[16] A Rakowska K C Wong T Townsend et al ldquoImpact of trafficvolume and composition on the air quality and pedestrianexposure in urban street canyonrdquo Atmospheric Environmentvol 98 pp 260ndash270 2014

[17] S Batterman R Ganguly and P Harbin ldquoHigh resolutionspatial and temporal mapping of traffic-related air pollutantsrdquoInternational Journal of Environmental Research and PublicHealth vol 12 no 4 pp 3646ndash3666 2015

[18] J Eliasson M Borjesson D van Amelsfort K Brundell-Freijand L Engelson ldquoAccuracy of congestion pricing forecastsrdquoTransportation Research Part A Policy and Practice vol 52 pp34ndash46 2013

[19] J Eliasson ldquoThe role of attitude structures direct experienceand reframing for the success of congestion pricingrdquo Trans-portation Research Part A Policy and Practice vol 67 pp 81ndash952014

[20] H X Yang J D Li H Zhang and S Q Liu ldquoResearch on thegovernance of urban traffic jam based on system dynamicsrdquoSystems EngineeringTheory and Practice vol 34 no 8 pp 2135ndash2143 2014 (Chinese)

[21] M H Zhu Research on Socio-Economic Impact of UrbanTrafficCongestion [PhD thesis] Beijing JiaotongUniversity 2013(Chinese)

[22] B Zeng Research on Modeling Technologies of Grey Prediction[PhD thesis] Nanjing University of Aeronautics and Astronau-tics 2011 (Chinese)

[23] S F Liu Y J Yang and L F Wu Grey System Theory andApplication Science Press Beijing China 2017

[24] S W Jia K Yang J J Zhao and G L Yan ldquoThe traffic-congestion charging fee management model based on thesystem dynamics approachrdquo Mathematical Problems in Engi-neering vol 2017 Article ID 3024898 13 pages 2017

10 Discrete Dynamics in Nature and Society

(a) AMVT APCF=5(a) AMVT APCF=10(a) AMVT APCF=20(a) AMVT APCF=30(a) AMVT APCF=40(a) AMVT APCF=50(a) AMVT APCF=60(a) AMVT APCF=70(a) AMVT APCF=80(a) AMVT APCF=90(a) AMVT APCF=100

2 M

25 M

3 M

35 M

4 Mve

hicle

2011 2013 2015 2017 20192009Time (year)

(a) AMVT

(b) APMG APCF=5(b) APMG APCF=10(b) APMG APCF=20(b) APMG APCF=30(b) APMG APCF=40(b) APMG APCF=50(b) APMG APCF=60(b) APMG APCF=70(b) APMG APCF=80(b) APMG APCF=90(b) APMG APCF=100

100000

125000

150000

175000

200000

ton

2011 2013 2015 2017 20192009Time (year)

(b) APMG

(c) ANOG APCF=5(c) ANOG APCF=10(c) ANOG APCF=20(c) ANOG APCF=30(c) ANOG APCF=40(c) ANOG APCF=50(c) ANOG APCF=60(c) ANOG APCF=70(c) ANOG APCF=80(c) ANOG APCF=90(c) ANOG APCF=100

80000

110000

140000

170000

200000

ton

2011 2013 2015 2017 20192009Time (year)

(c) ANOG

Figure 4 Sensitivity test (a) AMVT (b) APMG (c) ANOG

the APCF policy to exhibit good effects based on long-termpractice improvement and fulfilment

Following further analysis the AMVT exhibited amarginal decreasing effect following an increase in APCFfrom curve 1 to curve 6 especially in curves 3ndash6 whichindicates that a larger APCF is not always better The analysisresults are presented in Figures 4(b) and 4(c)

In conclusion the APCF value range was observed withinthe interval of [30 50] based on the above analysis from the

perspective of AMVT reduction (alleviate traffic jam) as wellas APMG and ANOG emission reduction Table 8 presentsthe detailed analysis results

32 Analysis of Results The AMVT exhibited a continuousdecrease following an increase in APCF which indicates theability of this policy to restrict increases in AMVT Specif-ically obvious changes were in the intervals of [5 10] and[10 20] wherein theAMVTexhibited a decrease of 166649

Discrete Dynamics in Nature and Society 11

and 105055 respectively The AMVT exhibited a decreaseof 35103 24912 and 16793 in the intervals of [20 30][30 40] and [40 50] respectivelyHoweverminimal changeswere observed in the interval of 50 yuandaysdotvehicle aboveIn addition the APMG exhibited a decrease of 13967789137 28538 20987 and 14128 respectively in theabove intervals and exhibited very minimal changes in theinterval of 50 above The ANOG exhibited similar changerules

Therefore the interval [30 50] is deemed a reasonablevalue range based on the analysis on the degree of effect ofdifferent APCFs on the AMVT APMG and ANOG

In particular the change trends of AMVT APMG andANOG were generally consistent as presented in Figure 6specifically Figure 5(d) Figures 5(a)ndash5(c) exhibited obviousdecreasing trend rates that were continuously weakened inthe interval of [30 50] In addition the change was verylimited as the APCF exceeded 50 yuandaysdotvehicle

Therefore an effective APCF range of [30 50]was chosenbased on the development trends analysis of the change ratesof the main variables

33 Model Validation Historical data (2009-2015) on theamount of motor vehicles and population in Beijing arepresented in Table 9 wherein the conformance of theirrespective GSID was tested

331 Qualified Verification of the Degree of Grey Incidenceon the Population of Beijing The original sequence and itssimulation value sequence are respectively presented asfollows

1198830 =[[[[[[[[[[

1199090 (1)1199090 (2)1199090 (3)

1199090 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

18600119890 + 00719619119890 + 00720186119890 + 00720693119890 + 00721148119890 + 00721516119890 + 00721705119890 + 007

]]]]]]]]]]]]]]]

1198831 =[[[[[[[[[[

1199091 (1)1199091 (2)1199091 (3)

1199091 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

186000119890 + 007187390119890 + 007188790119890 + 007190200119890 + 007191621119890 + 007193053119890 + 007194495119890 + 007

]]]]]]]]]]]]]]]

(30)

The following was derived based on their calculations

100381610038161003816100381611990401003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

11990900 (119896) + 1211990900 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 117145

100381610038161003816100381611990411003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

11990901 (119896) + 1211990901 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 025295

10038161003816100381610038161199040 minus 11990411003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

(11990901 (119896) minus 11990900 (119896)) + 12 (11990901 (7) minus 11990900 (7))

1003816100381610038161003816100381610038161003816100381610038161003816= 09185

(31)

Therefore we are able to obtain the value of the GAID

12058501 = 1 + 100381610038161003816100381611990401003816100381610038161003816 + 1003816100381610038161003816119904110038161003816100381610038161 + 100381610038161003816100381611990401003816100381610038161003816 + 100381610038161003816100381611990411003816100381610038161003816 + 10038161003816100381610038161199040 minus 11990411003816100381610038161003816= 1 + 117145 + 025295

1 + 117145 + 025295 + 09185 asymp 07275(32)

In a similar way

100381610038161003816100381610038161199041015840010038161003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

119909101584000 (119896) + 12119909101584000 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 062985100381610038161003816100381610038161199041015840110038161003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

119909101584001 (119896) + 12119909101584001 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 0136051003816100381610038161003816100381611990410158400 minus 1199041015840110038161003816100381610038161003816

=10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

(119909101584001 (119896) minus 119909101584000 (119896)) + 12 (119909101584001 (7) minus 119909101584000 (7))

1003816100381610038161003816100381610038161003816100381610038161003816= 04938

(33)

Therefore GRID is

11990301 = 1 + 100381610038161003816100381610038161199041015840010038161003816100381610038161003816 + 1003816100381610038161003816100381611990410158401100381610038161003816100381610038161 + 1003816100381610038161003816119904101584001003816100381610038161003816 + 1003816100381610038161003816119904101584011003816100381610038161003816 + 100381610038161003816100381611990410158400 minus 119904101584011003816100381610038161003816= 1 + 062985 + 013605

1 + 062985 + 013605 + 04938 asymp 07815(34)

When 120579 = 05 and exist1205760 = 07 then12057601 = 12057912058501 + (1 minus 120579) 11990301 = 05 times 07275 + 05 times 07815

= 07545 gt 07 = 1205760 (35)

Therefore according to Table 5 the accuracy was determinedto be between grade 2 and grade 3

332 Qualified Verification of the Degree of Grey Incidenceon the Amount of Motor Vehicles in Beijing The original

12 Discrete Dynamics in Nature and Society

Table 8 The effects of different APCFs on AMVT APNG and ANOG

APCF AMVT Trend Variation APMG Trend Variation ANOG Trend Variation() () ()

5 345229e+006 -- -- 161737 -- -- 154899 -- --10 287697e+006 darr -166649 139146 darr -139677 137782 darr -11050420 257473e+006 darr -105055 126743 darr -89137 128122 darr -7011130 248435e+006 darr -35103 123126 darr -28538 125306 darr -2197940 242246e+006 darr -24912 120542 darr -20987 123272 darr -1623250 238178e+006 darr -16793 118839 darr -14128 121928 darr -1090360 235237e+006 darr -12348 117604 darr -10392 120952 darr -0800570 232979e+006 darr -09599 116655 darr -08069 120202 darr -0620180 231171e+006 darr -07760 115894 darr -06524 119599 darr -0501790 229680e+006 darr -06450 115265 darr -05427 119101 darr -04164100 228421e+006 darr -05482 114734 darr -04607 118680 darr -03535

Table 9 Historical data and their simulation values (2009-2015)

Time Amount of motor vehicles (vehicle) Amount of population (person)Actual value Simulation value Actual value Simulation value

2009 4019e+006 401900e+006 18600e+007 186000e+0072010 4809e+006 457571e+006 19619e+007 187390e+0072011 4983e+006 528216e+006 20186e+007 188790e+0072012 5200e+006 560956e+006 20693e+007 190200e+0072013 5437e+006 577509e+006 21148e+007 191621e+0072014 5591e+006 584424e+006 21516e+007 193053e+0072015 5619e+006 591422e+006 21705e+007 194495e+007

sequence and its simulation value sequence were respec-tively calculated as follows

119883119894 =[[[[[[[[[[

119909119894 (1)119909119894 (2)119909119894 (3)

119909119894 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

4019119890 + 0064809119890 + 0064983119890 + 0065200119890 + 0065437119890 + 0065591119890 + 0065619119890 + 006

]]]]]]]]]]]]]]]

119883119895 =[[[[[[[[[[

119909119895 (1)119909119895 (2)119909119895 (3)

119909119895 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

401900119890 + 006457571119890 + 006528216119890 + 006560956119890 + 006577509119890 + 006584424119890 + 006591422119890 + 006

]]]]]]]]]]]]]]]

(36)

TheGAID andGRIDwere respectively calculated as follows

120585119894119895 asymp 09235119903119894119895 asymp 09390 (37)

Hence when exist1205760 = 09 and 120579 = 05120576119894119895 = 120579120585119894119895 + (1 minus 120579) 119903119894119895 = 09313 gt 09 = 1205760 (38)

Therefore according to Definition 3 and Table 5 thismodel verified the degree of grey incidence and exhibited anaccuracy belonging to grade 1

34 Policy Simulation Analysis and Discussion

341 Horizontal Analysis According to the horizontal anal-ysis the curves exhibited different changes with time Thespecific analysis results are presented as follows

Following the adoption of the low charge policy egAPCF = 5 yuandaysdotvehicle the AMVT (curve 1) exhibiteda decrease since about 2014 as exhibited in Figure 6(a)Although the growth rates of ANOG and APMG exhibited adecrease the total emissions maintained an increasing trendthereby resulting in high DAP levels (curve 4) The analysisresults indicate the inability of the low charge policy toeffectively reduce the DAP

According to Figure 6(f) curve 1 first exhibited aslow rise (before 2013) and a subsequent sharp descentfollowing the adoption of the high charge policy (APCF= 50 yuandaylowastvehicle) As a result the AMVT valuesdescended until 2013 wherein its descending range continu-ously increased Curve 3 terminated its previously continuousrise and instead descended slowly Similarly the rising rate

Discrete Dynamics in Nature and Society 13

0

2

4

6

8

10

12

14

16

18A

MV

T (

)

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

(a) AMVT

0

2

4

6

8

10

12

14

APM

G (

)

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

(b) APMG

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

0

2

4

6

8

10

12

AN

OG

()

(c) ANOG

AMVT ()APMG ()ANOG ()

0

2

4

6

8

10

12

14

16

18

5 20 8010 50 60 7030 9040 100

(d) Trend comparison

Figure 5 Development trends of the change rates of the main variables (a) AMVT (b) APMG (c) ANOG (d) Trend comparison

Table 10 The comparison of different policies

Variable APCF (yuandaylowastvehicle) Trend Variation ()5 50

AMVT (vehicle) 345229e+006 238178e+006 darr -3101APMG (t) 161737e+005 118839e+005 darr -2652ANOG (t) 154899e+005 121928e+005 darr -2129DAP 06 0525 darr -1250

of curve 2 slowed down relatively These results indicatethe effective control on the increase of APMG and ANOGafter which the values began to descend slowly Curve 4exhibited three phases specifically a rapid rise between 2011and 2014 a slow rise in rate between 2014 and 2018 and a slowdescent after 2018These results indicate the presence of DAPimprovements which exhibited gradual descent after 2018

The analysis results in Figures 6(b)ndash6(e) were similar tothose presented above

342 Vertical Analysis According to Figures 6(a)ndash6(f) theAPCF exhibited a continuous increase thereby generating achange in the rules of all the curves as follows

(i) AMVT (curve 1)TheAMVT exhibited a continuousdecrease Within a certain range the increase inAPCF aided in the descent of the AMVT therebyfurther alleviating the traffic pressures

(ii) APMG (curve 3) and ANOG (curve 2) A charge ofmore than 30 (Figures 6(d)ndash6(f)) generated a slowdescent in APMGMeanwhile the increase in ANOGalso exhibited effective restraint

(iii) DAP (curve 4)TheDAP exhibited an overall declineespecially following the implementation of a highcharge policy (APCF isin [40 50]) A subsequentdescending trend was later observed in the period ofanalogue simulation as presented in Figures 6(e) and6(f)

343 Comparison of Policies According to Table 10 in thepresence of a low charge policy (APCF=5) the AMVTAPMG ANOG and DAP under a high charge pol-icy exhibited an obvious decrease which indicates thatthe implementation of a high charge policy effectivelyreduced motor vehicle exhaust emissions to restrain the

14 Discrete Dynamics in Nature and Society

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

083 M

10000004

2 M00

2011 2013 2015 2017 20192009Time (year)

AMVT APCF=5ANOG APCF=5APMG APCF=5DAP APCF=5

vehicletontonDmnl

(a)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=10ANOG APCF=10APMG APCF=10DAP APCF=10

vehicletontonDmnl

(b)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=20ANOG APCF=20APMG APCF=20DAP APCF=20

vehicletontonDmnl

(c)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=30ANOG APCF=30APMG APCF=30DAP APCF=30

vehicletontonDmnl

(d)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=40ANOG APCF=40APMG APCF=40DAP APCF=40

vehicletontonDmnl

(e)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=50ANOG APCF=50APMG APCF=50DAP APCF=50

vehicletontonDmnl

(f)

Figure 6 Policy simulation (a) APCF=5 (b) APCF=10 (c) APCF=20 (d) APCF=30 (e) APCF=40 (f) APCF=50

intensification of ldquohazerdquo pollution degree in Beijing Specif-ically the gap between curves 1 and 2 exhibited a continuouswidening as presented in Figure 7(a) After 2013 curve 2exhibited an obvious descent Therefore the APCF policyeffectively reduced the AMVT and enabled an about 3101decrease in 2020

The results in Figures 7(b)ndash7(d) were similarly analyzed

In conclusion the adoption of a low charge policygenerated increasing APMG and ANOG trends as presentedin Figures 6(a) and 6(b) thereby suggesting the inabilityof the low charge policy to effectively reduce the DAP Anincrease of the fee to a certain extent especially followingthe implementation of a high charge policy (Figures 6(e) and6(f)) not only reduced the AMVT and alleviated traffic jams

Discrete Dynamics in Nature and Society 15

APCF=5

APCF=50

x 106

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 20202009Time (year)

2

25

3

35ve

hicle

(a) AMVT

APCF=5

APCF=50

x 105

20182017 2019 20202015 2016201420122011 201320102009Time (year)

11

12

13

14

15

16

17

ton

(b) APMG

APCF=5

APCF=50

x 105

08

09

1

11

12

13

14

15

16

ton

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 20202009Time (year)

(c) ANOG

02

APCF=5

APCF=50

2009 2011 20122010 20142013 2016 2017 20182015 20202019Time (year)

025

03

035

04

045

05

055D

mnl

(d) DAP

Figure 7 Comparison of the policies (a) AVT (b) APMG (c) ANOG (d) DAP

in cities but also effectively reduced the APMG and ANOGthereby reducing the DAP

According to a comparison on the different schemes atthe end of the analogue simulation period the high chargepolicy functioned as follows in terms of the emission reduc-tion of the motor vehicle exhaust the APMG and ANOGexhibited reductions of 2652 and 2129 respectively interms of alleviating traffic jams the AMVT exhibited a 3101decrease and in terms of reducing the degree of air pollutionthe DAP exhibited a 1250 decrease

4 Conclusions

41 Main Conclusions To resolve the air pollution problemsgenerated by motor vehicle exhaust emission the presentstudy introduced the charging mechanism and built a motorvehicle exhaust emission reduction strategy managementmodel using economic means and the SD-GM approach to

generate the following conclusions based on tests validationof the models and the simulation analysis of policies

(1)Within a certain range the reduction effects of APMGandANOGexhibited continuous enhancements following anincrease in APCF However the APCF did not always followthe principle ldquobigger means betterrdquo because the emissionreduction effect which was generated by an increase inthe APCF exhibited a marginal decreasing effect Accord-ing to the sensitivity analysis a pollution charge of 30ndash50yuandaysdotvehicle for the motor vehicles in Beijing was withinthe relatively reasonable range

(2) Three high charge policy functions were generatedbased on a comparison of the simulation results of thedifferent charging schemes the implementation of highcharge policies not only reduced the AMVT and alleviatedtraffic jams (Figures 6(e) 6(f) and 7(a) Table 10) but alsoeffectively reduced the APMG andANOG (Figures 6(e) 6(f)7(b) and 7(c) Tables 5 and 10) thereby further reducing theDAP (Figures 6(e) 6(f) and 7(d) Table 10) According to the

16 Discrete Dynamics in Nature and Society

contrastive analysis the DAP exhibited a decrease of about1250

(3) However the following problems were encounteredfollowing the implementation of the APCF policy (a) Theimplementation of the APCF policy increased the cost ofmotor vehicle trips and urged part-time drivers to take publictransportation which increased the burden of public trans-portation The subsidy policy and other applicable policiesmust be introduced to improve the public transport supplylevel and service quality Otherwise the trip demands ofpassengers will be difficult to satisfy which will influencethe implementation of the APCF policy (b) In the earlyperiods of APCF policy implementation an increase in thecost of motor vehicle trips due to the insufficient publicunderstanding and utilization of the APCF policy loweredits public support rate The government must strengthenits public relations work especially regarding the purposeand significance of its implementation to improve publicawareness and acknowledgment (c) The purpose of thesepolicies must be supervised and managed to gather APCFincome and improve public transportation infrastructures

42 Deficiencies and Future Work The present study consid-ered NOx and PMx as the principal motor vehicle emissionpollutants Future research must fully consider other com-ponents such as SO2 airborne particles hydrocarbons COand CO2 Secondly the implementation of a single chargingmeasure can reduce the supply level of public transportationFuture research should consider a subsidy mechanism toimprove the service quality Thirdly the function and effectof a single policy are limited Future work must considerthe integration of multiple policies to improve the emissionreduction effect For example future work may focus priorityon public transportation improvement of fuel quality vigor-ous promotion of new energy vehicles and improvements inemission standards

Appendix

A

See Table 11

B

Summary of the major variables and equations(1) Cost of motor vehicle trips = Air pollution charging

feelowast (1+ Air pollution control)(2) Amount ofNOx generation = INTEG (NOx emissions

- Annual dissipation of NOx 80380)(3) NOx emissions = Per vehicle annual of NOx

emissionslowast Amount of motor vehicle tripslowast Contributionrate of NOx from vehicle

(4) Contribution rate of NOx from vehicle = 05(5) Dissipation rate of NOx = 02(6) Annual dissipation of NOx = Amount of NOx

generationlowast Dissipation rate of NOx(7) Per vehicle annual of NOx emissions = 002

(8) Amount of PMx generation = INTEG (PMxemissions- Annual dissipation of PMx 160760)

(9) PMx emissions = Amount of motor vehicle tripslowastContribution rate of PMx from vehiclelowast Per vehicle annualof PMx emissions

(10) Contribution rate of PMx from vehicle = 05(11) Per vehicle annual of PMx emissions = 004(12) Annual dissipation of PMx = Amount of PMx

generationlowast Dissipation and control rate of PMx(13) Dissipation and control rate of PMx = 05(14) Pollution degree of NOx = IF THEN ELSE (Amount

of NOx generationgt= 11182e+005 09 IF THEN ELSE(Amount of NOx generationgt= 10874e+005 08 IF THENELSE (Amount of NOx generationgt= 10400e+005 07 IFTHEN ELSE (Amount of NOx generationgt= 9966e+00406 IF THEN ELSE (Amount of NOx generationgt=9618e+004 05 IF THEN ELSE (Amount of NOxgenerationgt= 8038e+004 03 IF THEN ELSE (Amountof NOx generationgt= 7008e+004 025 IF THEN ELSE(Amount of NOx generationgt= 6144e+004 02 IF THENELSE (Amount of NOx generationgt= 5508e+004 015 01)))))))))

(15) Pollution degree of PMx = IF THEN ELSE (Amountof PMx generationgt= 22364e+005 09 IF THEN ELSE(Amount of PMx generationgt= 21748e+005 08 IF THENELSE (Amount of PMx generationgt= 20800e+005 07 IFTHEN ELSE (Amount of PMx generationgt= 19932e+00506 IF THEN ELSE (Amount of PMx generationgt=19236e+005 05 IF THEN ELSE (Amount of PMxgenerationgt= 16076e+005 03 IF THEN ELSE (Amountof PMx generationgt= 14016e+005 025 IF THEN ELSE(Amount of PMx generationgt= 12288e+005 02 IF THENELSE (Amount of PMx generationgt= 11016e+005 015 01)))))))))

(16) Ratio of motor vehicle trips = 055(17) Amount of motor vehicle trips = Amount of motor

vehicleslowast Ratio of motor vehicle trips(18) Degree of air pollution = Weight ratio of NOxlowast

Pollution degree of NOx+ Weight ratio of PMxlowast Pollutiondegree of PMx

(19) Weight ratio of PMx = 05(20) Weight ratio of NOx = 05(21) Air pollution control = IF THEN ELSE (Degree of air

pollutiongt= 07 1 IF THEN ELSE (Degree of air pollutiongt=06 08 IF THEN ELSE (Degree of air pollutiongt= 05 07IF THEN ELSE (Degree of air pollutiongt= 04 06 IF THENELSE (Degree of air pollutiongt= 03 05 IF THEN ELSE(Degree of air pollutiongt= 025 045 IF THENELSE (Degreeof air pollutiongt= 02 04 IF THEN ELSE (Degree of airpollutiongt= 015 035 03))))))))

(22) Attraction degree of the growth of vehicles= (1-Airpollution control)lowast 055+ Attraction degree of vehicle tripslowast045

(23) Per capita annual income = Amount of GDPAmount of population

(24) Amount of population = INTEG (Growth of popu-lation+ Net migration- Population reduction 186e+007)

(25) Birth rate = Adjustment coefficient of birth ratelowastPredictive value of birth rate

Discrete Dynamics in Nature and Society 17

Table 11 Description of main variables in stock flow diagram

Signicant variable Unit Variable type Data sourceAir pollution charging fee yuandaysdotvehicle ConstantAir pollution control Dmnl Auxiliary variable M1+M3Amount of GDP yuan Level M1Amount of motor vehicles vehicle Level M1Amount of motor vehicle trips vehicle Auxiliary variableAmount of NOx (PMx) generation ton Level M1Amount of population person Level M1Annual dissipation of NOx (PMx) tonyear FlowAnnual scrapped vehicleyear FlowAttraction degree of city Constant M2Attraction degree of the growth of vehicles Auxiliary variable M1+M3Attraction degree of vehicle trips Auxiliary variable M1+M3Birth rate 1year Constant M3Contribution rate of NOx (PMx) from vehicle Constant M2Cost of motor vehicle trips yuandaysdotvehicle Auxiliary variable M3Death rate 1year Constant M3Degree of air pollution Dmnl Auxiliary variable M3Dissipation and control rate of NOx (PMx) 1year Constant M2Graphical function of the growth of GDP Dmnl Auxiliary variable M3Growth of GDP yuanyear FlowGrowth rate of motor vehicles 1year Auxiliary variable M1+M3Growth of motor vehicles vehicleyear FlowGrowth of population personyear FlowGrowth rate of vehicle ownership Dmnl Auxiliary variable M1+M3Impact factor of policy Dmnl Constant M3Net migration personyear FlowNet migration rate 1year Constant M1+M3NOx (PMx) emissions tonyear FlowPer capita annual income yuanperson Auxiliary variablePer vehicle annual of NOx (PMx) emissions tonyearsdotvehicle Constant M2Pollution degree of NOx (PMx) Dmnl Auxiliary variable M1+M3Population reduction personyear FlowRatio of motor vehicle trips Constant M2Scrap rate 1year Constant M2The average of net migration rate 1year Constant M1Weight ratio of PMx (NOx) Auxiliary variable M3

(26) Predictive value of birth rate = 000925(27) Death rate = Adjustment coefficient of death ratelowast

Predictive value of death rate(28) Predictive value of death rate = 000494(29) Net migration = Amount of populationlowastNet migra-

tion rate(30) Net migration rate = The average of net migration

ratelowast Attraction degree of cityand(Impact factor of policy)(31) Impact factor of policy = 15(32) The average of net migration rate = 000531(33) Attraction degree of city = 07056(34) Amount of GDP = INTEG (Growth of GDP

12153e+012)

(35) Graphical function of the growth of GDP = WITHLOOKUP (Amount of GDP ([(8e+011 0)- (3e+ 012 03)](81178e+011 01648) (98468e+011 0213) (11115e+01201288) (12153e+012 00934) (141136e+012 01613)(162519e+012 01515) (178794e+012 01001) (198008e+01201075) (213308e+012 00773) (230146e+012 00789)(235396e+012 002281) (240162e+012 00203) (245025e+012 002025) (249987e+012 002024) (255049e+0120020249)))

(36) Growth rate of GDP = Graphical function of thegrowth of GDPlowast Impact factor of the growth of GDP

(37) Amount of motor vehicles = INTEG (Growth ofmotor vehicles- Annual scrapped 4019e+006)

18 Discrete Dynamics in Nature and Society

(38) Annual scrapped = Amount of motor vehicleslowastScrap rate

(39) Scrap rate = 0067

Conflicts of Interest

The author declares no conflicts of interest

Acknowledgments

This work has been partially supported by the NationalNatural Science Foundation of China (71571119) ShanghaiFirst-Class Academic Discipline Project (S1201YLXK) andChina Postdoctoral Science Foundation (2018M630404)Theauthor would like to thank LetPub (httpwwwletpubcom)for providing linguistic assistance during the preparation ofthis manuscript

References

[1] X Liu S Ma J Tian N Jia and G Li ldquoA system dynamicsapproach to scenario analysis for urban passenger transportenergy consumption and CO2 emissions A case study ofBeijingrdquo Energy Policy vol 85 pp 253ndash270 2015

[2] B Xu L Luo and B Lin ldquoA dynamic analysis of air pollutionemissions in China Evidence from nonparametric additiveregression modelsrdquo Ecological Indicators vol 63 pp 346ndash3582016

[3] S Leinert H Daly B Hyde and B O Gallachoir ldquoCo-benefitsNot always Quantifying the negative effect of a CO2-reducingcar taxation policy on NOx emissionsrdquo Energy Policy vol 63pp 1151ndash1159 2013

[4] Z Cheng L Li and J Liu ldquoIdentifying the spatial effects anddriving factors of urban PM25 pollution in Chinardquo EcologicalIndicators vol 82 pp 61ndash75 2017

[5] N Kaida and K Kaida ldquoSpillover effect of congestion chargingon pro-environmental behaviorrdquo Environment Developmentand Sustainability vol 17 no 3 pp 409ndash421 2015

[6] R Penabaena-Niebles V Cantillo and J L Moura ldquoImpactof transition between signal timing plans in social cost basedin delay fuel consumption and air emissionsrdquo TransportationResearch Part D Transport and Environment vol 41 pp 445ndash456 2015

[7] DDing andB Shuai ldquoA traffic restriction scheme for enhancingcarpoolingrdquoDiscreteDynamics inNature and Society Article ID9626938 9 pages 2017

[8] D Kong X Guo B Yang and D Wu ldquoAnalyzing the Impactof Trucks on Traffic Flow Based on an Improved CellularAutomaton Modelrdquo Discrete Dynamics in Nature and Societyvol 2016 pp 1ndash14 2016

[9] S Cakmak C Hebbern J D Cakmak and J Vanos ldquoThemodifying effect of socioeconomic status on the relationshipbetween traffic air pollution and respiratory health in elemen-tary schoolchildrenrdquo Journal of Environmental Managementvol 177 pp 1ndash8 2016

[10] L Song H Song J Lin et al ldquoPM25 emissions from differenttypes of heavy-duty truck a case study and meta-analysis ofthe Beijing-Tianjin-Hebei regionrdquo Environmental Science andPollution Research vol 24 no 12 pp 11206ndash11214 2017

[11] Z Hu S Kang C Li et al ldquoLight absorption of biomassburning and vehicle emission-sourced carbonaceous aerosolsof the Tibetan Plateaurdquo Environmental Science and PollutionResearch vol 24 no 18 pp 15369ndash15378 2017

[12] X Cen H K Lo and L Li ldquoA framework for estimating trafficemissions The development of Passenger Car Emission UnitrdquoTransportation Research Part D Transport and Environmentvol 44 pp 78ndash92 2016

[13] S Wang X Liu C Zhou J Hu and J Ou ldquoExamining theimpacts of socioeconomic factors urban form and transporta-tion networks on CO2 emissions in Chinarsquos megacitiesrdquoAppliedEnergy vol 185 pp 189ndash200 2017

[14] Q Wang K Hubacek K Feng Y-M Wei and Q-M LiangldquoDistributional effects of carbon taxationrdquo Applied Energy vol184 pp 1123ndash1131 2016

[15] C Johansson L Burman and B Forsberg ldquoThe effects ofcongestions tax on air quality and healthrdquo Atmospheric Envi-ronment vol 43 no 31 pp 4843ndash4854 2009

[16] A Rakowska K C Wong T Townsend et al ldquoImpact of trafficvolume and composition on the air quality and pedestrianexposure in urban street canyonrdquo Atmospheric Environmentvol 98 pp 260ndash270 2014

[17] S Batterman R Ganguly and P Harbin ldquoHigh resolutionspatial and temporal mapping of traffic-related air pollutantsrdquoInternational Journal of Environmental Research and PublicHealth vol 12 no 4 pp 3646ndash3666 2015

[18] J Eliasson M Borjesson D van Amelsfort K Brundell-Freijand L Engelson ldquoAccuracy of congestion pricing forecastsrdquoTransportation Research Part A Policy and Practice vol 52 pp34ndash46 2013

[19] J Eliasson ldquoThe role of attitude structures direct experienceand reframing for the success of congestion pricingrdquo Trans-portation Research Part A Policy and Practice vol 67 pp 81ndash952014

[20] H X Yang J D Li H Zhang and S Q Liu ldquoResearch on thegovernance of urban traffic jam based on system dynamicsrdquoSystems EngineeringTheory and Practice vol 34 no 8 pp 2135ndash2143 2014 (Chinese)

[21] M H Zhu Research on Socio-Economic Impact of UrbanTrafficCongestion [PhD thesis] Beijing JiaotongUniversity 2013(Chinese)

[22] B Zeng Research on Modeling Technologies of Grey Prediction[PhD thesis] Nanjing University of Aeronautics and Astronau-tics 2011 (Chinese)

[23] S F Liu Y J Yang and L F Wu Grey System Theory andApplication Science Press Beijing China 2017

[24] S W Jia K Yang J J Zhao and G L Yan ldquoThe traffic-congestion charging fee management model based on thesystem dynamics approachrdquo Mathematical Problems in Engi-neering vol 2017 Article ID 3024898 13 pages 2017

Discrete Dynamics in Nature and Society 11

and 105055 respectively The AMVT exhibited a decreaseof 35103 24912 and 16793 in the intervals of [20 30][30 40] and [40 50] respectivelyHoweverminimal changeswere observed in the interval of 50 yuandaysdotvehicle aboveIn addition the APMG exhibited a decrease of 13967789137 28538 20987 and 14128 respectively in theabove intervals and exhibited very minimal changes in theinterval of 50 above The ANOG exhibited similar changerules

Therefore the interval [30 50] is deemed a reasonablevalue range based on the analysis on the degree of effect ofdifferent APCFs on the AMVT APMG and ANOG

In particular the change trends of AMVT APMG andANOG were generally consistent as presented in Figure 6specifically Figure 5(d) Figures 5(a)ndash5(c) exhibited obviousdecreasing trend rates that were continuously weakened inthe interval of [30 50] In addition the change was verylimited as the APCF exceeded 50 yuandaysdotvehicle

Therefore an effective APCF range of [30 50]was chosenbased on the development trends analysis of the change ratesof the main variables

33 Model Validation Historical data (2009-2015) on theamount of motor vehicles and population in Beijing arepresented in Table 9 wherein the conformance of theirrespective GSID was tested

331 Qualified Verification of the Degree of Grey Incidenceon the Population of Beijing The original sequence and itssimulation value sequence are respectively presented asfollows

1198830 =[[[[[[[[[[

1199090 (1)1199090 (2)1199090 (3)

1199090 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

18600119890 + 00719619119890 + 00720186119890 + 00720693119890 + 00721148119890 + 00721516119890 + 00721705119890 + 007

]]]]]]]]]]]]]]]

1198831 =[[[[[[[[[[

1199091 (1)1199091 (2)1199091 (3)

1199091 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

186000119890 + 007187390119890 + 007188790119890 + 007190200119890 + 007191621119890 + 007193053119890 + 007194495119890 + 007

]]]]]]]]]]]]]]]

(30)

The following was derived based on their calculations

100381610038161003816100381611990401003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

11990900 (119896) + 1211990900 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 117145

100381610038161003816100381611990411003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

11990901 (119896) + 1211990901 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 025295

10038161003816100381610038161199040 minus 11990411003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

(11990901 (119896) minus 11990900 (119896)) + 12 (11990901 (7) minus 11990900 (7))

1003816100381610038161003816100381610038161003816100381610038161003816= 09185

(31)

Therefore we are able to obtain the value of the GAID

12058501 = 1 + 100381610038161003816100381611990401003816100381610038161003816 + 1003816100381610038161003816119904110038161003816100381610038161 + 100381610038161003816100381611990401003816100381610038161003816 + 100381610038161003816100381611990411003816100381610038161003816 + 10038161003816100381610038161199040 minus 11990411003816100381610038161003816= 1 + 117145 + 025295

1 + 117145 + 025295 + 09185 asymp 07275(32)

In a similar way

100381610038161003816100381610038161199041015840010038161003816100381610038161003816 =10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

119909101584000 (119896) + 12119909101584000 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 062985100381610038161003816100381610038161199041015840110038161003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

119909101584001 (119896) + 12119909101584001 (7)

1003816100381610038161003816100381610038161003816100381610038161003816 = 0136051003816100381610038161003816100381611990410158400 minus 1199041015840110038161003816100381610038161003816

=10038161003816100381610038161003816100381610038161003816100381610038166sum119896=2

(119909101584001 (119896) minus 119909101584000 (119896)) + 12 (119909101584001 (7) minus 119909101584000 (7))

1003816100381610038161003816100381610038161003816100381610038161003816= 04938

(33)

Therefore GRID is

11990301 = 1 + 100381610038161003816100381610038161199041015840010038161003816100381610038161003816 + 1003816100381610038161003816100381611990410158401100381610038161003816100381610038161 + 1003816100381610038161003816119904101584001003816100381610038161003816 + 1003816100381610038161003816119904101584011003816100381610038161003816 + 100381610038161003816100381611990410158400 minus 119904101584011003816100381610038161003816= 1 + 062985 + 013605

1 + 062985 + 013605 + 04938 asymp 07815(34)

When 120579 = 05 and exist1205760 = 07 then12057601 = 12057912058501 + (1 minus 120579) 11990301 = 05 times 07275 + 05 times 07815

= 07545 gt 07 = 1205760 (35)

Therefore according to Table 5 the accuracy was determinedto be between grade 2 and grade 3

332 Qualified Verification of the Degree of Grey Incidenceon the Amount of Motor Vehicles in Beijing The original

12 Discrete Dynamics in Nature and Society

Table 8 The effects of different APCFs on AMVT APNG and ANOG

APCF AMVT Trend Variation APMG Trend Variation ANOG Trend Variation() () ()

5 345229e+006 -- -- 161737 -- -- 154899 -- --10 287697e+006 darr -166649 139146 darr -139677 137782 darr -11050420 257473e+006 darr -105055 126743 darr -89137 128122 darr -7011130 248435e+006 darr -35103 123126 darr -28538 125306 darr -2197940 242246e+006 darr -24912 120542 darr -20987 123272 darr -1623250 238178e+006 darr -16793 118839 darr -14128 121928 darr -1090360 235237e+006 darr -12348 117604 darr -10392 120952 darr -0800570 232979e+006 darr -09599 116655 darr -08069 120202 darr -0620180 231171e+006 darr -07760 115894 darr -06524 119599 darr -0501790 229680e+006 darr -06450 115265 darr -05427 119101 darr -04164100 228421e+006 darr -05482 114734 darr -04607 118680 darr -03535

Table 9 Historical data and their simulation values (2009-2015)

Time Amount of motor vehicles (vehicle) Amount of population (person)Actual value Simulation value Actual value Simulation value

2009 4019e+006 401900e+006 18600e+007 186000e+0072010 4809e+006 457571e+006 19619e+007 187390e+0072011 4983e+006 528216e+006 20186e+007 188790e+0072012 5200e+006 560956e+006 20693e+007 190200e+0072013 5437e+006 577509e+006 21148e+007 191621e+0072014 5591e+006 584424e+006 21516e+007 193053e+0072015 5619e+006 591422e+006 21705e+007 194495e+007

sequence and its simulation value sequence were respec-tively calculated as follows

119883119894 =[[[[[[[[[[

119909119894 (1)119909119894 (2)119909119894 (3)

119909119894 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

4019119890 + 0064809119890 + 0064983119890 + 0065200119890 + 0065437119890 + 0065591119890 + 0065619119890 + 006

]]]]]]]]]]]]]]]

119883119895 =[[[[[[[[[[

119909119895 (1)119909119895 (2)119909119895 (3)

119909119895 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

401900119890 + 006457571119890 + 006528216119890 + 006560956119890 + 006577509119890 + 006584424119890 + 006591422119890 + 006

]]]]]]]]]]]]]]]

(36)

TheGAID andGRIDwere respectively calculated as follows

120585119894119895 asymp 09235119903119894119895 asymp 09390 (37)

Hence when exist1205760 = 09 and 120579 = 05120576119894119895 = 120579120585119894119895 + (1 minus 120579) 119903119894119895 = 09313 gt 09 = 1205760 (38)

Therefore according to Definition 3 and Table 5 thismodel verified the degree of grey incidence and exhibited anaccuracy belonging to grade 1

34 Policy Simulation Analysis and Discussion

341 Horizontal Analysis According to the horizontal anal-ysis the curves exhibited different changes with time Thespecific analysis results are presented as follows

Following the adoption of the low charge policy egAPCF = 5 yuandaysdotvehicle the AMVT (curve 1) exhibiteda decrease since about 2014 as exhibited in Figure 6(a)Although the growth rates of ANOG and APMG exhibited adecrease the total emissions maintained an increasing trendthereby resulting in high DAP levels (curve 4) The analysisresults indicate the inability of the low charge policy toeffectively reduce the DAP

According to Figure 6(f) curve 1 first exhibited aslow rise (before 2013) and a subsequent sharp descentfollowing the adoption of the high charge policy (APCF= 50 yuandaylowastvehicle) As a result the AMVT valuesdescended until 2013 wherein its descending range continu-ously increased Curve 3 terminated its previously continuousrise and instead descended slowly Similarly the rising rate

Discrete Dynamics in Nature and Society 13

0

2

4

6

8

10

12

14

16

18A

MV

T (

)

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

(a) AMVT

0

2

4

6

8

10

12

14

APM

G (

)

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

(b) APMG

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

0

2

4

6

8

10

12

AN

OG

()

(c) ANOG

AMVT ()APMG ()ANOG ()

0

2

4

6

8

10

12

14

16

18

5 20 8010 50 60 7030 9040 100

(d) Trend comparison

Figure 5 Development trends of the change rates of the main variables (a) AMVT (b) APMG (c) ANOG (d) Trend comparison

Table 10 The comparison of different policies

Variable APCF (yuandaylowastvehicle) Trend Variation ()5 50

AMVT (vehicle) 345229e+006 238178e+006 darr -3101APMG (t) 161737e+005 118839e+005 darr -2652ANOG (t) 154899e+005 121928e+005 darr -2129DAP 06 0525 darr -1250

of curve 2 slowed down relatively These results indicatethe effective control on the increase of APMG and ANOGafter which the values began to descend slowly Curve 4exhibited three phases specifically a rapid rise between 2011and 2014 a slow rise in rate between 2014 and 2018 and a slowdescent after 2018These results indicate the presence of DAPimprovements which exhibited gradual descent after 2018

The analysis results in Figures 6(b)ndash6(e) were similar tothose presented above

342 Vertical Analysis According to Figures 6(a)ndash6(f) theAPCF exhibited a continuous increase thereby generating achange in the rules of all the curves as follows

(i) AMVT (curve 1)TheAMVT exhibited a continuousdecrease Within a certain range the increase inAPCF aided in the descent of the AMVT therebyfurther alleviating the traffic pressures

(ii) APMG (curve 3) and ANOG (curve 2) A charge ofmore than 30 (Figures 6(d)ndash6(f)) generated a slowdescent in APMGMeanwhile the increase in ANOGalso exhibited effective restraint

(iii) DAP (curve 4)TheDAP exhibited an overall declineespecially following the implementation of a highcharge policy (APCF isin [40 50]) A subsequentdescending trend was later observed in the period ofanalogue simulation as presented in Figures 6(e) and6(f)

343 Comparison of Policies According to Table 10 in thepresence of a low charge policy (APCF=5) the AMVTAPMG ANOG and DAP under a high charge pol-icy exhibited an obvious decrease which indicates thatthe implementation of a high charge policy effectivelyreduced motor vehicle exhaust emissions to restrain the

14 Discrete Dynamics in Nature and Society

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

083 M

10000004

2 M00

2011 2013 2015 2017 20192009Time (year)

AMVT APCF=5ANOG APCF=5APMG APCF=5DAP APCF=5

vehicletontonDmnl

(a)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=10ANOG APCF=10APMG APCF=10DAP APCF=10

vehicletontonDmnl

(b)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=20ANOG APCF=20APMG APCF=20DAP APCF=20

vehicletontonDmnl

(c)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=30ANOG APCF=30APMG APCF=30DAP APCF=30

vehicletontonDmnl

(d)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=40ANOG APCF=40APMG APCF=40DAP APCF=40

vehicletontonDmnl

(e)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=50ANOG APCF=50APMG APCF=50DAP APCF=50

vehicletontonDmnl

(f)

Figure 6 Policy simulation (a) APCF=5 (b) APCF=10 (c) APCF=20 (d) APCF=30 (e) APCF=40 (f) APCF=50

intensification of ldquohazerdquo pollution degree in Beijing Specif-ically the gap between curves 1 and 2 exhibited a continuouswidening as presented in Figure 7(a) After 2013 curve 2exhibited an obvious descent Therefore the APCF policyeffectively reduced the AMVT and enabled an about 3101decrease in 2020

The results in Figures 7(b)ndash7(d) were similarly analyzed

In conclusion the adoption of a low charge policygenerated increasing APMG and ANOG trends as presentedin Figures 6(a) and 6(b) thereby suggesting the inabilityof the low charge policy to effectively reduce the DAP Anincrease of the fee to a certain extent especially followingthe implementation of a high charge policy (Figures 6(e) and6(f)) not only reduced the AMVT and alleviated traffic jams

Discrete Dynamics in Nature and Society 15

APCF=5

APCF=50

x 106

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 20202009Time (year)

2

25

3

35ve

hicle

(a) AMVT

APCF=5

APCF=50

x 105

20182017 2019 20202015 2016201420122011 201320102009Time (year)

11

12

13

14

15

16

17

ton

(b) APMG

APCF=5

APCF=50

x 105

08

09

1

11

12

13

14

15

16

ton

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 20202009Time (year)

(c) ANOG

02

APCF=5

APCF=50

2009 2011 20122010 20142013 2016 2017 20182015 20202019Time (year)

025

03

035

04

045

05

055D

mnl

(d) DAP

Figure 7 Comparison of the policies (a) AVT (b) APMG (c) ANOG (d) DAP

in cities but also effectively reduced the APMG and ANOGthereby reducing the DAP

According to a comparison on the different schemes atthe end of the analogue simulation period the high chargepolicy functioned as follows in terms of the emission reduc-tion of the motor vehicle exhaust the APMG and ANOGexhibited reductions of 2652 and 2129 respectively interms of alleviating traffic jams the AMVT exhibited a 3101decrease and in terms of reducing the degree of air pollutionthe DAP exhibited a 1250 decrease

4 Conclusions

41 Main Conclusions To resolve the air pollution problemsgenerated by motor vehicle exhaust emission the presentstudy introduced the charging mechanism and built a motorvehicle exhaust emission reduction strategy managementmodel using economic means and the SD-GM approach to

generate the following conclusions based on tests validationof the models and the simulation analysis of policies

(1)Within a certain range the reduction effects of APMGandANOGexhibited continuous enhancements following anincrease in APCF However the APCF did not always followthe principle ldquobigger means betterrdquo because the emissionreduction effect which was generated by an increase inthe APCF exhibited a marginal decreasing effect Accord-ing to the sensitivity analysis a pollution charge of 30ndash50yuandaysdotvehicle for the motor vehicles in Beijing was withinthe relatively reasonable range

(2) Three high charge policy functions were generatedbased on a comparison of the simulation results of thedifferent charging schemes the implementation of highcharge policies not only reduced the AMVT and alleviatedtraffic jams (Figures 6(e) 6(f) and 7(a) Table 10) but alsoeffectively reduced the APMG andANOG (Figures 6(e) 6(f)7(b) and 7(c) Tables 5 and 10) thereby further reducing theDAP (Figures 6(e) 6(f) and 7(d) Table 10) According to the

16 Discrete Dynamics in Nature and Society

contrastive analysis the DAP exhibited a decrease of about1250

(3) However the following problems were encounteredfollowing the implementation of the APCF policy (a) Theimplementation of the APCF policy increased the cost ofmotor vehicle trips and urged part-time drivers to take publictransportation which increased the burden of public trans-portation The subsidy policy and other applicable policiesmust be introduced to improve the public transport supplylevel and service quality Otherwise the trip demands ofpassengers will be difficult to satisfy which will influencethe implementation of the APCF policy (b) In the earlyperiods of APCF policy implementation an increase in thecost of motor vehicle trips due to the insufficient publicunderstanding and utilization of the APCF policy loweredits public support rate The government must strengthenits public relations work especially regarding the purposeand significance of its implementation to improve publicawareness and acknowledgment (c) The purpose of thesepolicies must be supervised and managed to gather APCFincome and improve public transportation infrastructures

42 Deficiencies and Future Work The present study consid-ered NOx and PMx as the principal motor vehicle emissionpollutants Future research must fully consider other com-ponents such as SO2 airborne particles hydrocarbons COand CO2 Secondly the implementation of a single chargingmeasure can reduce the supply level of public transportationFuture research should consider a subsidy mechanism toimprove the service quality Thirdly the function and effectof a single policy are limited Future work must considerthe integration of multiple policies to improve the emissionreduction effect For example future work may focus priorityon public transportation improvement of fuel quality vigor-ous promotion of new energy vehicles and improvements inemission standards

Appendix

A

See Table 11

B

Summary of the major variables and equations(1) Cost of motor vehicle trips = Air pollution charging

feelowast (1+ Air pollution control)(2) Amount ofNOx generation = INTEG (NOx emissions

- Annual dissipation of NOx 80380)(3) NOx emissions = Per vehicle annual of NOx

emissionslowast Amount of motor vehicle tripslowast Contributionrate of NOx from vehicle

(4) Contribution rate of NOx from vehicle = 05(5) Dissipation rate of NOx = 02(6) Annual dissipation of NOx = Amount of NOx

generationlowast Dissipation rate of NOx(7) Per vehicle annual of NOx emissions = 002

(8) Amount of PMx generation = INTEG (PMxemissions- Annual dissipation of PMx 160760)

(9) PMx emissions = Amount of motor vehicle tripslowastContribution rate of PMx from vehiclelowast Per vehicle annualof PMx emissions

(10) Contribution rate of PMx from vehicle = 05(11) Per vehicle annual of PMx emissions = 004(12) Annual dissipation of PMx = Amount of PMx

generationlowast Dissipation and control rate of PMx(13) Dissipation and control rate of PMx = 05(14) Pollution degree of NOx = IF THEN ELSE (Amount

of NOx generationgt= 11182e+005 09 IF THEN ELSE(Amount of NOx generationgt= 10874e+005 08 IF THENELSE (Amount of NOx generationgt= 10400e+005 07 IFTHEN ELSE (Amount of NOx generationgt= 9966e+00406 IF THEN ELSE (Amount of NOx generationgt=9618e+004 05 IF THEN ELSE (Amount of NOxgenerationgt= 8038e+004 03 IF THEN ELSE (Amountof NOx generationgt= 7008e+004 025 IF THEN ELSE(Amount of NOx generationgt= 6144e+004 02 IF THENELSE (Amount of NOx generationgt= 5508e+004 015 01)))))))))

(15) Pollution degree of PMx = IF THEN ELSE (Amountof PMx generationgt= 22364e+005 09 IF THEN ELSE(Amount of PMx generationgt= 21748e+005 08 IF THENELSE (Amount of PMx generationgt= 20800e+005 07 IFTHEN ELSE (Amount of PMx generationgt= 19932e+00506 IF THEN ELSE (Amount of PMx generationgt=19236e+005 05 IF THEN ELSE (Amount of PMxgenerationgt= 16076e+005 03 IF THEN ELSE (Amountof PMx generationgt= 14016e+005 025 IF THEN ELSE(Amount of PMx generationgt= 12288e+005 02 IF THENELSE (Amount of PMx generationgt= 11016e+005 015 01)))))))))

(16) Ratio of motor vehicle trips = 055(17) Amount of motor vehicle trips = Amount of motor

vehicleslowast Ratio of motor vehicle trips(18) Degree of air pollution = Weight ratio of NOxlowast

Pollution degree of NOx+ Weight ratio of PMxlowast Pollutiondegree of PMx

(19) Weight ratio of PMx = 05(20) Weight ratio of NOx = 05(21) Air pollution control = IF THEN ELSE (Degree of air

pollutiongt= 07 1 IF THEN ELSE (Degree of air pollutiongt=06 08 IF THEN ELSE (Degree of air pollutiongt= 05 07IF THEN ELSE (Degree of air pollutiongt= 04 06 IF THENELSE (Degree of air pollutiongt= 03 05 IF THEN ELSE(Degree of air pollutiongt= 025 045 IF THENELSE (Degreeof air pollutiongt= 02 04 IF THEN ELSE (Degree of airpollutiongt= 015 035 03))))))))

(22) Attraction degree of the growth of vehicles= (1-Airpollution control)lowast 055+ Attraction degree of vehicle tripslowast045

(23) Per capita annual income = Amount of GDPAmount of population

(24) Amount of population = INTEG (Growth of popu-lation+ Net migration- Population reduction 186e+007)

(25) Birth rate = Adjustment coefficient of birth ratelowastPredictive value of birth rate

Discrete Dynamics in Nature and Society 17

Table 11 Description of main variables in stock flow diagram

Signicant variable Unit Variable type Data sourceAir pollution charging fee yuandaysdotvehicle ConstantAir pollution control Dmnl Auxiliary variable M1+M3Amount of GDP yuan Level M1Amount of motor vehicles vehicle Level M1Amount of motor vehicle trips vehicle Auxiliary variableAmount of NOx (PMx) generation ton Level M1Amount of population person Level M1Annual dissipation of NOx (PMx) tonyear FlowAnnual scrapped vehicleyear FlowAttraction degree of city Constant M2Attraction degree of the growth of vehicles Auxiliary variable M1+M3Attraction degree of vehicle trips Auxiliary variable M1+M3Birth rate 1year Constant M3Contribution rate of NOx (PMx) from vehicle Constant M2Cost of motor vehicle trips yuandaysdotvehicle Auxiliary variable M3Death rate 1year Constant M3Degree of air pollution Dmnl Auxiliary variable M3Dissipation and control rate of NOx (PMx) 1year Constant M2Graphical function of the growth of GDP Dmnl Auxiliary variable M3Growth of GDP yuanyear FlowGrowth rate of motor vehicles 1year Auxiliary variable M1+M3Growth of motor vehicles vehicleyear FlowGrowth of population personyear FlowGrowth rate of vehicle ownership Dmnl Auxiliary variable M1+M3Impact factor of policy Dmnl Constant M3Net migration personyear FlowNet migration rate 1year Constant M1+M3NOx (PMx) emissions tonyear FlowPer capita annual income yuanperson Auxiliary variablePer vehicle annual of NOx (PMx) emissions tonyearsdotvehicle Constant M2Pollution degree of NOx (PMx) Dmnl Auxiliary variable M1+M3Population reduction personyear FlowRatio of motor vehicle trips Constant M2Scrap rate 1year Constant M2The average of net migration rate 1year Constant M1Weight ratio of PMx (NOx) Auxiliary variable M3

(26) Predictive value of birth rate = 000925(27) Death rate = Adjustment coefficient of death ratelowast

Predictive value of death rate(28) Predictive value of death rate = 000494(29) Net migration = Amount of populationlowastNet migra-

tion rate(30) Net migration rate = The average of net migration

ratelowast Attraction degree of cityand(Impact factor of policy)(31) Impact factor of policy = 15(32) The average of net migration rate = 000531(33) Attraction degree of city = 07056(34) Amount of GDP = INTEG (Growth of GDP

12153e+012)

(35) Graphical function of the growth of GDP = WITHLOOKUP (Amount of GDP ([(8e+011 0)- (3e+ 012 03)](81178e+011 01648) (98468e+011 0213) (11115e+01201288) (12153e+012 00934) (141136e+012 01613)(162519e+012 01515) (178794e+012 01001) (198008e+01201075) (213308e+012 00773) (230146e+012 00789)(235396e+012 002281) (240162e+012 00203) (245025e+012 002025) (249987e+012 002024) (255049e+0120020249)))

(36) Growth rate of GDP = Graphical function of thegrowth of GDPlowast Impact factor of the growth of GDP

(37) Amount of motor vehicles = INTEG (Growth ofmotor vehicles- Annual scrapped 4019e+006)

18 Discrete Dynamics in Nature and Society

(38) Annual scrapped = Amount of motor vehicleslowastScrap rate

(39) Scrap rate = 0067

Conflicts of Interest

The author declares no conflicts of interest

Acknowledgments

This work has been partially supported by the NationalNatural Science Foundation of China (71571119) ShanghaiFirst-Class Academic Discipline Project (S1201YLXK) andChina Postdoctoral Science Foundation (2018M630404)Theauthor would like to thank LetPub (httpwwwletpubcom)for providing linguistic assistance during the preparation ofthis manuscript

References

[1] X Liu S Ma J Tian N Jia and G Li ldquoA system dynamicsapproach to scenario analysis for urban passenger transportenergy consumption and CO2 emissions A case study ofBeijingrdquo Energy Policy vol 85 pp 253ndash270 2015

[2] B Xu L Luo and B Lin ldquoA dynamic analysis of air pollutionemissions in China Evidence from nonparametric additiveregression modelsrdquo Ecological Indicators vol 63 pp 346ndash3582016

[3] S Leinert H Daly B Hyde and B O Gallachoir ldquoCo-benefitsNot always Quantifying the negative effect of a CO2-reducingcar taxation policy on NOx emissionsrdquo Energy Policy vol 63pp 1151ndash1159 2013

[4] Z Cheng L Li and J Liu ldquoIdentifying the spatial effects anddriving factors of urban PM25 pollution in Chinardquo EcologicalIndicators vol 82 pp 61ndash75 2017

[5] N Kaida and K Kaida ldquoSpillover effect of congestion chargingon pro-environmental behaviorrdquo Environment Developmentand Sustainability vol 17 no 3 pp 409ndash421 2015

[6] R Penabaena-Niebles V Cantillo and J L Moura ldquoImpactof transition between signal timing plans in social cost basedin delay fuel consumption and air emissionsrdquo TransportationResearch Part D Transport and Environment vol 41 pp 445ndash456 2015

[7] DDing andB Shuai ldquoA traffic restriction scheme for enhancingcarpoolingrdquoDiscreteDynamics inNature and Society Article ID9626938 9 pages 2017

[8] D Kong X Guo B Yang and D Wu ldquoAnalyzing the Impactof Trucks on Traffic Flow Based on an Improved CellularAutomaton Modelrdquo Discrete Dynamics in Nature and Societyvol 2016 pp 1ndash14 2016

[9] S Cakmak C Hebbern J D Cakmak and J Vanos ldquoThemodifying effect of socioeconomic status on the relationshipbetween traffic air pollution and respiratory health in elemen-tary schoolchildrenrdquo Journal of Environmental Managementvol 177 pp 1ndash8 2016

[10] L Song H Song J Lin et al ldquoPM25 emissions from differenttypes of heavy-duty truck a case study and meta-analysis ofthe Beijing-Tianjin-Hebei regionrdquo Environmental Science andPollution Research vol 24 no 12 pp 11206ndash11214 2017

[11] Z Hu S Kang C Li et al ldquoLight absorption of biomassburning and vehicle emission-sourced carbonaceous aerosolsof the Tibetan Plateaurdquo Environmental Science and PollutionResearch vol 24 no 18 pp 15369ndash15378 2017

[12] X Cen H K Lo and L Li ldquoA framework for estimating trafficemissions The development of Passenger Car Emission UnitrdquoTransportation Research Part D Transport and Environmentvol 44 pp 78ndash92 2016

[13] S Wang X Liu C Zhou J Hu and J Ou ldquoExamining theimpacts of socioeconomic factors urban form and transporta-tion networks on CO2 emissions in Chinarsquos megacitiesrdquoAppliedEnergy vol 185 pp 189ndash200 2017

[14] Q Wang K Hubacek K Feng Y-M Wei and Q-M LiangldquoDistributional effects of carbon taxationrdquo Applied Energy vol184 pp 1123ndash1131 2016

[15] C Johansson L Burman and B Forsberg ldquoThe effects ofcongestions tax on air quality and healthrdquo Atmospheric Envi-ronment vol 43 no 31 pp 4843ndash4854 2009

[16] A Rakowska K C Wong T Townsend et al ldquoImpact of trafficvolume and composition on the air quality and pedestrianexposure in urban street canyonrdquo Atmospheric Environmentvol 98 pp 260ndash270 2014

[17] S Batterman R Ganguly and P Harbin ldquoHigh resolutionspatial and temporal mapping of traffic-related air pollutantsrdquoInternational Journal of Environmental Research and PublicHealth vol 12 no 4 pp 3646ndash3666 2015

[18] J Eliasson M Borjesson D van Amelsfort K Brundell-Freijand L Engelson ldquoAccuracy of congestion pricing forecastsrdquoTransportation Research Part A Policy and Practice vol 52 pp34ndash46 2013

[19] J Eliasson ldquoThe role of attitude structures direct experienceand reframing for the success of congestion pricingrdquo Trans-portation Research Part A Policy and Practice vol 67 pp 81ndash952014

[20] H X Yang J D Li H Zhang and S Q Liu ldquoResearch on thegovernance of urban traffic jam based on system dynamicsrdquoSystems EngineeringTheory and Practice vol 34 no 8 pp 2135ndash2143 2014 (Chinese)

[21] M H Zhu Research on Socio-Economic Impact of UrbanTrafficCongestion [PhD thesis] Beijing JiaotongUniversity 2013(Chinese)

[22] B Zeng Research on Modeling Technologies of Grey Prediction[PhD thesis] Nanjing University of Aeronautics and Astronau-tics 2011 (Chinese)

[23] S F Liu Y J Yang and L F Wu Grey System Theory andApplication Science Press Beijing China 2017

[24] S W Jia K Yang J J Zhao and G L Yan ldquoThe traffic-congestion charging fee management model based on thesystem dynamics approachrdquo Mathematical Problems in Engi-neering vol 2017 Article ID 3024898 13 pages 2017

12 Discrete Dynamics in Nature and Society

Table 8 The effects of different APCFs on AMVT APNG and ANOG

APCF AMVT Trend Variation APMG Trend Variation ANOG Trend Variation() () ()

5 345229e+006 -- -- 161737 -- -- 154899 -- --10 287697e+006 darr -166649 139146 darr -139677 137782 darr -11050420 257473e+006 darr -105055 126743 darr -89137 128122 darr -7011130 248435e+006 darr -35103 123126 darr -28538 125306 darr -2197940 242246e+006 darr -24912 120542 darr -20987 123272 darr -1623250 238178e+006 darr -16793 118839 darr -14128 121928 darr -1090360 235237e+006 darr -12348 117604 darr -10392 120952 darr -0800570 232979e+006 darr -09599 116655 darr -08069 120202 darr -0620180 231171e+006 darr -07760 115894 darr -06524 119599 darr -0501790 229680e+006 darr -06450 115265 darr -05427 119101 darr -04164100 228421e+006 darr -05482 114734 darr -04607 118680 darr -03535

Table 9 Historical data and their simulation values (2009-2015)

Time Amount of motor vehicles (vehicle) Amount of population (person)Actual value Simulation value Actual value Simulation value

2009 4019e+006 401900e+006 18600e+007 186000e+0072010 4809e+006 457571e+006 19619e+007 187390e+0072011 4983e+006 528216e+006 20186e+007 188790e+0072012 5200e+006 560956e+006 20693e+007 190200e+0072013 5437e+006 577509e+006 21148e+007 191621e+0072014 5591e+006 584424e+006 21516e+007 193053e+0072015 5619e+006 591422e+006 21705e+007 194495e+007

sequence and its simulation value sequence were respec-tively calculated as follows

119883119894 =[[[[[[[[[[

119909119894 (1)119909119894 (2)119909119894 (3)

119909119894 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

4019119890 + 0064809119890 + 0064983119890 + 0065200119890 + 0065437119890 + 0065591119890 + 0065619119890 + 006

]]]]]]]]]]]]]]]

119883119895 =[[[[[[[[[[

119909119895 (1)119909119895 (2)119909119895 (3)

119909119895 (7)

]]]]]]]]]]

=

[[[[[[[[[[[[[[[

401900119890 + 006457571119890 + 006528216119890 + 006560956119890 + 006577509119890 + 006584424119890 + 006591422119890 + 006

]]]]]]]]]]]]]]]

(36)

TheGAID andGRIDwere respectively calculated as follows

120585119894119895 asymp 09235119903119894119895 asymp 09390 (37)

Hence when exist1205760 = 09 and 120579 = 05120576119894119895 = 120579120585119894119895 + (1 minus 120579) 119903119894119895 = 09313 gt 09 = 1205760 (38)

Therefore according to Definition 3 and Table 5 thismodel verified the degree of grey incidence and exhibited anaccuracy belonging to grade 1

34 Policy Simulation Analysis and Discussion

341 Horizontal Analysis According to the horizontal anal-ysis the curves exhibited different changes with time Thespecific analysis results are presented as follows

Following the adoption of the low charge policy egAPCF = 5 yuandaysdotvehicle the AMVT (curve 1) exhibiteda decrease since about 2014 as exhibited in Figure 6(a)Although the growth rates of ANOG and APMG exhibited adecrease the total emissions maintained an increasing trendthereby resulting in high DAP levels (curve 4) The analysisresults indicate the inability of the low charge policy toeffectively reduce the DAP

According to Figure 6(f) curve 1 first exhibited aslow rise (before 2013) and a subsequent sharp descentfollowing the adoption of the high charge policy (APCF= 50 yuandaylowastvehicle) As a result the AMVT valuesdescended until 2013 wherein its descending range continu-ously increased Curve 3 terminated its previously continuousrise and instead descended slowly Similarly the rising rate

Discrete Dynamics in Nature and Society 13

0

2

4

6

8

10

12

14

16

18A

MV

T (

)

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

(a) AMVT

0

2

4

6

8

10

12

14

APM

G (

)

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

(b) APMG

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

0

2

4

6

8

10

12

AN

OG

()

(c) ANOG

AMVT ()APMG ()ANOG ()

0

2

4

6

8

10

12

14

16

18

5 20 8010 50 60 7030 9040 100

(d) Trend comparison

Figure 5 Development trends of the change rates of the main variables (a) AMVT (b) APMG (c) ANOG (d) Trend comparison

Table 10 The comparison of different policies

Variable APCF (yuandaylowastvehicle) Trend Variation ()5 50

AMVT (vehicle) 345229e+006 238178e+006 darr -3101APMG (t) 161737e+005 118839e+005 darr -2652ANOG (t) 154899e+005 121928e+005 darr -2129DAP 06 0525 darr -1250

of curve 2 slowed down relatively These results indicatethe effective control on the increase of APMG and ANOGafter which the values began to descend slowly Curve 4exhibited three phases specifically a rapid rise between 2011and 2014 a slow rise in rate between 2014 and 2018 and a slowdescent after 2018These results indicate the presence of DAPimprovements which exhibited gradual descent after 2018

The analysis results in Figures 6(b)ndash6(e) were similar tothose presented above

342 Vertical Analysis According to Figures 6(a)ndash6(f) theAPCF exhibited a continuous increase thereby generating achange in the rules of all the curves as follows

(i) AMVT (curve 1)TheAMVT exhibited a continuousdecrease Within a certain range the increase inAPCF aided in the descent of the AMVT therebyfurther alleviating the traffic pressures

(ii) APMG (curve 3) and ANOG (curve 2) A charge ofmore than 30 (Figures 6(d)ndash6(f)) generated a slowdescent in APMGMeanwhile the increase in ANOGalso exhibited effective restraint

(iii) DAP (curve 4)TheDAP exhibited an overall declineespecially following the implementation of a highcharge policy (APCF isin [40 50]) A subsequentdescending trend was later observed in the period ofanalogue simulation as presented in Figures 6(e) and6(f)

343 Comparison of Policies According to Table 10 in thepresence of a low charge policy (APCF=5) the AMVTAPMG ANOG and DAP under a high charge pol-icy exhibited an obvious decrease which indicates thatthe implementation of a high charge policy effectivelyreduced motor vehicle exhaust emissions to restrain the

14 Discrete Dynamics in Nature and Society

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

083 M

10000004

2 M00

2011 2013 2015 2017 20192009Time (year)

AMVT APCF=5ANOG APCF=5APMG APCF=5DAP APCF=5

vehicletontonDmnl

(a)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=10ANOG APCF=10APMG APCF=10DAP APCF=10

vehicletontonDmnl

(b)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=20ANOG APCF=20APMG APCF=20DAP APCF=20

vehicletontonDmnl

(c)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=30ANOG APCF=30APMG APCF=30DAP APCF=30

vehicletontonDmnl

(d)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=40ANOG APCF=40APMG APCF=40DAP APCF=40

vehicletontonDmnl

(e)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=50ANOG APCF=50APMG APCF=50DAP APCF=50

vehicletontonDmnl

(f)

Figure 6 Policy simulation (a) APCF=5 (b) APCF=10 (c) APCF=20 (d) APCF=30 (e) APCF=40 (f) APCF=50

intensification of ldquohazerdquo pollution degree in Beijing Specif-ically the gap between curves 1 and 2 exhibited a continuouswidening as presented in Figure 7(a) After 2013 curve 2exhibited an obvious descent Therefore the APCF policyeffectively reduced the AMVT and enabled an about 3101decrease in 2020

The results in Figures 7(b)ndash7(d) were similarly analyzed

In conclusion the adoption of a low charge policygenerated increasing APMG and ANOG trends as presentedin Figures 6(a) and 6(b) thereby suggesting the inabilityof the low charge policy to effectively reduce the DAP Anincrease of the fee to a certain extent especially followingthe implementation of a high charge policy (Figures 6(e) and6(f)) not only reduced the AMVT and alleviated traffic jams

Discrete Dynamics in Nature and Society 15

APCF=5

APCF=50

x 106

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 20202009Time (year)

2

25

3

35ve

hicle

(a) AMVT

APCF=5

APCF=50

x 105

20182017 2019 20202015 2016201420122011 201320102009Time (year)

11

12

13

14

15

16

17

ton

(b) APMG

APCF=5

APCF=50

x 105

08

09

1

11

12

13

14

15

16

ton

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 20202009Time (year)

(c) ANOG

02

APCF=5

APCF=50

2009 2011 20122010 20142013 2016 2017 20182015 20202019Time (year)

025

03

035

04

045

05

055D

mnl

(d) DAP

Figure 7 Comparison of the policies (a) AVT (b) APMG (c) ANOG (d) DAP

in cities but also effectively reduced the APMG and ANOGthereby reducing the DAP

According to a comparison on the different schemes atthe end of the analogue simulation period the high chargepolicy functioned as follows in terms of the emission reduc-tion of the motor vehicle exhaust the APMG and ANOGexhibited reductions of 2652 and 2129 respectively interms of alleviating traffic jams the AMVT exhibited a 3101decrease and in terms of reducing the degree of air pollutionthe DAP exhibited a 1250 decrease

4 Conclusions

41 Main Conclusions To resolve the air pollution problemsgenerated by motor vehicle exhaust emission the presentstudy introduced the charging mechanism and built a motorvehicle exhaust emission reduction strategy managementmodel using economic means and the SD-GM approach to

generate the following conclusions based on tests validationof the models and the simulation analysis of policies

(1)Within a certain range the reduction effects of APMGandANOGexhibited continuous enhancements following anincrease in APCF However the APCF did not always followthe principle ldquobigger means betterrdquo because the emissionreduction effect which was generated by an increase inthe APCF exhibited a marginal decreasing effect Accord-ing to the sensitivity analysis a pollution charge of 30ndash50yuandaysdotvehicle for the motor vehicles in Beijing was withinthe relatively reasonable range

(2) Three high charge policy functions were generatedbased on a comparison of the simulation results of thedifferent charging schemes the implementation of highcharge policies not only reduced the AMVT and alleviatedtraffic jams (Figures 6(e) 6(f) and 7(a) Table 10) but alsoeffectively reduced the APMG andANOG (Figures 6(e) 6(f)7(b) and 7(c) Tables 5 and 10) thereby further reducing theDAP (Figures 6(e) 6(f) and 7(d) Table 10) According to the

16 Discrete Dynamics in Nature and Society

contrastive analysis the DAP exhibited a decrease of about1250

(3) However the following problems were encounteredfollowing the implementation of the APCF policy (a) Theimplementation of the APCF policy increased the cost ofmotor vehicle trips and urged part-time drivers to take publictransportation which increased the burden of public trans-portation The subsidy policy and other applicable policiesmust be introduced to improve the public transport supplylevel and service quality Otherwise the trip demands ofpassengers will be difficult to satisfy which will influencethe implementation of the APCF policy (b) In the earlyperiods of APCF policy implementation an increase in thecost of motor vehicle trips due to the insufficient publicunderstanding and utilization of the APCF policy loweredits public support rate The government must strengthenits public relations work especially regarding the purposeand significance of its implementation to improve publicawareness and acknowledgment (c) The purpose of thesepolicies must be supervised and managed to gather APCFincome and improve public transportation infrastructures

42 Deficiencies and Future Work The present study consid-ered NOx and PMx as the principal motor vehicle emissionpollutants Future research must fully consider other com-ponents such as SO2 airborne particles hydrocarbons COand CO2 Secondly the implementation of a single chargingmeasure can reduce the supply level of public transportationFuture research should consider a subsidy mechanism toimprove the service quality Thirdly the function and effectof a single policy are limited Future work must considerthe integration of multiple policies to improve the emissionreduction effect For example future work may focus priorityon public transportation improvement of fuel quality vigor-ous promotion of new energy vehicles and improvements inemission standards

Appendix

A

See Table 11

B

Summary of the major variables and equations(1) Cost of motor vehicle trips = Air pollution charging

feelowast (1+ Air pollution control)(2) Amount ofNOx generation = INTEG (NOx emissions

- Annual dissipation of NOx 80380)(3) NOx emissions = Per vehicle annual of NOx

emissionslowast Amount of motor vehicle tripslowast Contributionrate of NOx from vehicle

(4) Contribution rate of NOx from vehicle = 05(5) Dissipation rate of NOx = 02(6) Annual dissipation of NOx = Amount of NOx

generationlowast Dissipation rate of NOx(7) Per vehicle annual of NOx emissions = 002

(8) Amount of PMx generation = INTEG (PMxemissions- Annual dissipation of PMx 160760)

(9) PMx emissions = Amount of motor vehicle tripslowastContribution rate of PMx from vehiclelowast Per vehicle annualof PMx emissions

(10) Contribution rate of PMx from vehicle = 05(11) Per vehicle annual of PMx emissions = 004(12) Annual dissipation of PMx = Amount of PMx

generationlowast Dissipation and control rate of PMx(13) Dissipation and control rate of PMx = 05(14) Pollution degree of NOx = IF THEN ELSE (Amount

of NOx generationgt= 11182e+005 09 IF THEN ELSE(Amount of NOx generationgt= 10874e+005 08 IF THENELSE (Amount of NOx generationgt= 10400e+005 07 IFTHEN ELSE (Amount of NOx generationgt= 9966e+00406 IF THEN ELSE (Amount of NOx generationgt=9618e+004 05 IF THEN ELSE (Amount of NOxgenerationgt= 8038e+004 03 IF THEN ELSE (Amountof NOx generationgt= 7008e+004 025 IF THEN ELSE(Amount of NOx generationgt= 6144e+004 02 IF THENELSE (Amount of NOx generationgt= 5508e+004 015 01)))))))))

(15) Pollution degree of PMx = IF THEN ELSE (Amountof PMx generationgt= 22364e+005 09 IF THEN ELSE(Amount of PMx generationgt= 21748e+005 08 IF THENELSE (Amount of PMx generationgt= 20800e+005 07 IFTHEN ELSE (Amount of PMx generationgt= 19932e+00506 IF THEN ELSE (Amount of PMx generationgt=19236e+005 05 IF THEN ELSE (Amount of PMxgenerationgt= 16076e+005 03 IF THEN ELSE (Amountof PMx generationgt= 14016e+005 025 IF THEN ELSE(Amount of PMx generationgt= 12288e+005 02 IF THENELSE (Amount of PMx generationgt= 11016e+005 015 01)))))))))

(16) Ratio of motor vehicle trips = 055(17) Amount of motor vehicle trips = Amount of motor

vehicleslowast Ratio of motor vehicle trips(18) Degree of air pollution = Weight ratio of NOxlowast

Pollution degree of NOx+ Weight ratio of PMxlowast Pollutiondegree of PMx

(19) Weight ratio of PMx = 05(20) Weight ratio of NOx = 05(21) Air pollution control = IF THEN ELSE (Degree of air

pollutiongt= 07 1 IF THEN ELSE (Degree of air pollutiongt=06 08 IF THEN ELSE (Degree of air pollutiongt= 05 07IF THEN ELSE (Degree of air pollutiongt= 04 06 IF THENELSE (Degree of air pollutiongt= 03 05 IF THEN ELSE(Degree of air pollutiongt= 025 045 IF THENELSE (Degreeof air pollutiongt= 02 04 IF THEN ELSE (Degree of airpollutiongt= 015 035 03))))))))

(22) Attraction degree of the growth of vehicles= (1-Airpollution control)lowast 055+ Attraction degree of vehicle tripslowast045

(23) Per capita annual income = Amount of GDPAmount of population

(24) Amount of population = INTEG (Growth of popu-lation+ Net migration- Population reduction 186e+007)

(25) Birth rate = Adjustment coefficient of birth ratelowastPredictive value of birth rate

Discrete Dynamics in Nature and Society 17

Table 11 Description of main variables in stock flow diagram

Signicant variable Unit Variable type Data sourceAir pollution charging fee yuandaysdotvehicle ConstantAir pollution control Dmnl Auxiliary variable M1+M3Amount of GDP yuan Level M1Amount of motor vehicles vehicle Level M1Amount of motor vehicle trips vehicle Auxiliary variableAmount of NOx (PMx) generation ton Level M1Amount of population person Level M1Annual dissipation of NOx (PMx) tonyear FlowAnnual scrapped vehicleyear FlowAttraction degree of city Constant M2Attraction degree of the growth of vehicles Auxiliary variable M1+M3Attraction degree of vehicle trips Auxiliary variable M1+M3Birth rate 1year Constant M3Contribution rate of NOx (PMx) from vehicle Constant M2Cost of motor vehicle trips yuandaysdotvehicle Auxiliary variable M3Death rate 1year Constant M3Degree of air pollution Dmnl Auxiliary variable M3Dissipation and control rate of NOx (PMx) 1year Constant M2Graphical function of the growth of GDP Dmnl Auxiliary variable M3Growth of GDP yuanyear FlowGrowth rate of motor vehicles 1year Auxiliary variable M1+M3Growth of motor vehicles vehicleyear FlowGrowth of population personyear FlowGrowth rate of vehicle ownership Dmnl Auxiliary variable M1+M3Impact factor of policy Dmnl Constant M3Net migration personyear FlowNet migration rate 1year Constant M1+M3NOx (PMx) emissions tonyear FlowPer capita annual income yuanperson Auxiliary variablePer vehicle annual of NOx (PMx) emissions tonyearsdotvehicle Constant M2Pollution degree of NOx (PMx) Dmnl Auxiliary variable M1+M3Population reduction personyear FlowRatio of motor vehicle trips Constant M2Scrap rate 1year Constant M2The average of net migration rate 1year Constant M1Weight ratio of PMx (NOx) Auxiliary variable M3

(26) Predictive value of birth rate = 000925(27) Death rate = Adjustment coefficient of death ratelowast

Predictive value of death rate(28) Predictive value of death rate = 000494(29) Net migration = Amount of populationlowastNet migra-

tion rate(30) Net migration rate = The average of net migration

ratelowast Attraction degree of cityand(Impact factor of policy)(31) Impact factor of policy = 15(32) The average of net migration rate = 000531(33) Attraction degree of city = 07056(34) Amount of GDP = INTEG (Growth of GDP

12153e+012)

(35) Graphical function of the growth of GDP = WITHLOOKUP (Amount of GDP ([(8e+011 0)- (3e+ 012 03)](81178e+011 01648) (98468e+011 0213) (11115e+01201288) (12153e+012 00934) (141136e+012 01613)(162519e+012 01515) (178794e+012 01001) (198008e+01201075) (213308e+012 00773) (230146e+012 00789)(235396e+012 002281) (240162e+012 00203) (245025e+012 002025) (249987e+012 002024) (255049e+0120020249)))

(36) Growth rate of GDP = Graphical function of thegrowth of GDPlowast Impact factor of the growth of GDP

(37) Amount of motor vehicles = INTEG (Growth ofmotor vehicles- Annual scrapped 4019e+006)

18 Discrete Dynamics in Nature and Society

(38) Annual scrapped = Amount of motor vehicleslowastScrap rate

(39) Scrap rate = 0067

Conflicts of Interest

The author declares no conflicts of interest

Acknowledgments

This work has been partially supported by the NationalNatural Science Foundation of China (71571119) ShanghaiFirst-Class Academic Discipline Project (S1201YLXK) andChina Postdoctoral Science Foundation (2018M630404)Theauthor would like to thank LetPub (httpwwwletpubcom)for providing linguistic assistance during the preparation ofthis manuscript

References

[1] X Liu S Ma J Tian N Jia and G Li ldquoA system dynamicsapproach to scenario analysis for urban passenger transportenergy consumption and CO2 emissions A case study ofBeijingrdquo Energy Policy vol 85 pp 253ndash270 2015

[2] B Xu L Luo and B Lin ldquoA dynamic analysis of air pollutionemissions in China Evidence from nonparametric additiveregression modelsrdquo Ecological Indicators vol 63 pp 346ndash3582016

[3] S Leinert H Daly B Hyde and B O Gallachoir ldquoCo-benefitsNot always Quantifying the negative effect of a CO2-reducingcar taxation policy on NOx emissionsrdquo Energy Policy vol 63pp 1151ndash1159 2013

[4] Z Cheng L Li and J Liu ldquoIdentifying the spatial effects anddriving factors of urban PM25 pollution in Chinardquo EcologicalIndicators vol 82 pp 61ndash75 2017

[5] N Kaida and K Kaida ldquoSpillover effect of congestion chargingon pro-environmental behaviorrdquo Environment Developmentand Sustainability vol 17 no 3 pp 409ndash421 2015

[6] R Penabaena-Niebles V Cantillo and J L Moura ldquoImpactof transition between signal timing plans in social cost basedin delay fuel consumption and air emissionsrdquo TransportationResearch Part D Transport and Environment vol 41 pp 445ndash456 2015

[7] DDing andB Shuai ldquoA traffic restriction scheme for enhancingcarpoolingrdquoDiscreteDynamics inNature and Society Article ID9626938 9 pages 2017

[8] D Kong X Guo B Yang and D Wu ldquoAnalyzing the Impactof Trucks on Traffic Flow Based on an Improved CellularAutomaton Modelrdquo Discrete Dynamics in Nature and Societyvol 2016 pp 1ndash14 2016

[9] S Cakmak C Hebbern J D Cakmak and J Vanos ldquoThemodifying effect of socioeconomic status on the relationshipbetween traffic air pollution and respiratory health in elemen-tary schoolchildrenrdquo Journal of Environmental Managementvol 177 pp 1ndash8 2016

[10] L Song H Song J Lin et al ldquoPM25 emissions from differenttypes of heavy-duty truck a case study and meta-analysis ofthe Beijing-Tianjin-Hebei regionrdquo Environmental Science andPollution Research vol 24 no 12 pp 11206ndash11214 2017

[11] Z Hu S Kang C Li et al ldquoLight absorption of biomassburning and vehicle emission-sourced carbonaceous aerosolsof the Tibetan Plateaurdquo Environmental Science and PollutionResearch vol 24 no 18 pp 15369ndash15378 2017

[12] X Cen H K Lo and L Li ldquoA framework for estimating trafficemissions The development of Passenger Car Emission UnitrdquoTransportation Research Part D Transport and Environmentvol 44 pp 78ndash92 2016

[13] S Wang X Liu C Zhou J Hu and J Ou ldquoExamining theimpacts of socioeconomic factors urban form and transporta-tion networks on CO2 emissions in Chinarsquos megacitiesrdquoAppliedEnergy vol 185 pp 189ndash200 2017

[14] Q Wang K Hubacek K Feng Y-M Wei and Q-M LiangldquoDistributional effects of carbon taxationrdquo Applied Energy vol184 pp 1123ndash1131 2016

[15] C Johansson L Burman and B Forsberg ldquoThe effects ofcongestions tax on air quality and healthrdquo Atmospheric Envi-ronment vol 43 no 31 pp 4843ndash4854 2009

[16] A Rakowska K C Wong T Townsend et al ldquoImpact of trafficvolume and composition on the air quality and pedestrianexposure in urban street canyonrdquo Atmospheric Environmentvol 98 pp 260ndash270 2014

[17] S Batterman R Ganguly and P Harbin ldquoHigh resolutionspatial and temporal mapping of traffic-related air pollutantsrdquoInternational Journal of Environmental Research and PublicHealth vol 12 no 4 pp 3646ndash3666 2015

[18] J Eliasson M Borjesson D van Amelsfort K Brundell-Freijand L Engelson ldquoAccuracy of congestion pricing forecastsrdquoTransportation Research Part A Policy and Practice vol 52 pp34ndash46 2013

[19] J Eliasson ldquoThe role of attitude structures direct experienceand reframing for the success of congestion pricingrdquo Trans-portation Research Part A Policy and Practice vol 67 pp 81ndash952014

[20] H X Yang J D Li H Zhang and S Q Liu ldquoResearch on thegovernance of urban traffic jam based on system dynamicsrdquoSystems EngineeringTheory and Practice vol 34 no 8 pp 2135ndash2143 2014 (Chinese)

[21] M H Zhu Research on Socio-Economic Impact of UrbanTrafficCongestion [PhD thesis] Beijing JiaotongUniversity 2013(Chinese)

[22] B Zeng Research on Modeling Technologies of Grey Prediction[PhD thesis] Nanjing University of Aeronautics and Astronau-tics 2011 (Chinese)

[23] S F Liu Y J Yang and L F Wu Grey System Theory andApplication Science Press Beijing China 2017

[24] S W Jia K Yang J J Zhao and G L Yan ldquoThe traffic-congestion charging fee management model based on thesystem dynamics approachrdquo Mathematical Problems in Engi-neering vol 2017 Article ID 3024898 13 pages 2017

Discrete Dynamics in Nature and Society 13

0

2

4

6

8

10

12

14

16

18A

MV

T (

)

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

(a) AMVT

0

2

4

6

8

10

12

14

APM

G (

)

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

(b) APMG

5 20 8010 50 60 7030 9040 100

APCF (yuandaylowastvehicle)

0

2

4

6

8

10

12

AN

OG

()

(c) ANOG

AMVT ()APMG ()ANOG ()

0

2

4

6

8

10

12

14

16

18

5 20 8010 50 60 7030 9040 100

(d) Trend comparison

Figure 5 Development trends of the change rates of the main variables (a) AMVT (b) APMG (c) ANOG (d) Trend comparison

Table 10 The comparison of different policies

Variable APCF (yuandaylowastvehicle) Trend Variation ()5 50

AMVT (vehicle) 345229e+006 238178e+006 darr -3101APMG (t) 161737e+005 118839e+005 darr -2652ANOG (t) 154899e+005 121928e+005 darr -2129DAP 06 0525 darr -1250

of curve 2 slowed down relatively These results indicatethe effective control on the increase of APMG and ANOGafter which the values began to descend slowly Curve 4exhibited three phases specifically a rapid rise between 2011and 2014 a slow rise in rate between 2014 and 2018 and a slowdescent after 2018These results indicate the presence of DAPimprovements which exhibited gradual descent after 2018

The analysis results in Figures 6(b)ndash6(e) were similar tothose presented above

342 Vertical Analysis According to Figures 6(a)ndash6(f) theAPCF exhibited a continuous increase thereby generating achange in the rules of all the curves as follows

(i) AMVT (curve 1)TheAMVT exhibited a continuousdecrease Within a certain range the increase inAPCF aided in the descent of the AMVT therebyfurther alleviating the traffic pressures

(ii) APMG (curve 3) and ANOG (curve 2) A charge ofmore than 30 (Figures 6(d)ndash6(f)) generated a slowdescent in APMGMeanwhile the increase in ANOGalso exhibited effective restraint

(iii) DAP (curve 4)TheDAP exhibited an overall declineespecially following the implementation of a highcharge policy (APCF isin [40 50]) A subsequentdescending trend was later observed in the period ofanalogue simulation as presented in Figures 6(e) and6(f)

343 Comparison of Policies According to Table 10 in thepresence of a low charge policy (APCF=5) the AMVTAPMG ANOG and DAP under a high charge pol-icy exhibited an obvious decrease which indicates thatthe implementation of a high charge policy effectivelyreduced motor vehicle exhaust emissions to restrain the

14 Discrete Dynamics in Nature and Society

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

083 M

10000004

2 M00

2011 2013 2015 2017 20192009Time (year)

AMVT APCF=5ANOG APCF=5APMG APCF=5DAP APCF=5

vehicletontonDmnl

(a)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=10ANOG APCF=10APMG APCF=10DAP APCF=10

vehicletontonDmnl

(b)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=20ANOG APCF=20APMG APCF=20DAP APCF=20

vehicletontonDmnl

(c)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=30ANOG APCF=30APMG APCF=30DAP APCF=30

vehicletontonDmnl

(d)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=40ANOG APCF=40APMG APCF=40DAP APCF=40

vehicletontonDmnl

(e)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=50ANOG APCF=50APMG APCF=50DAP APCF=50

vehicletontonDmnl

(f)

Figure 6 Policy simulation (a) APCF=5 (b) APCF=10 (c) APCF=20 (d) APCF=30 (e) APCF=40 (f) APCF=50

intensification of ldquohazerdquo pollution degree in Beijing Specif-ically the gap between curves 1 and 2 exhibited a continuouswidening as presented in Figure 7(a) After 2013 curve 2exhibited an obvious descent Therefore the APCF policyeffectively reduced the AMVT and enabled an about 3101decrease in 2020

The results in Figures 7(b)ndash7(d) were similarly analyzed

In conclusion the adoption of a low charge policygenerated increasing APMG and ANOG trends as presentedin Figures 6(a) and 6(b) thereby suggesting the inabilityof the low charge policy to effectively reduce the DAP Anincrease of the fee to a certain extent especially followingthe implementation of a high charge policy (Figures 6(e) and6(f)) not only reduced the AMVT and alleviated traffic jams

Discrete Dynamics in Nature and Society 15

APCF=5

APCF=50

x 106

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 20202009Time (year)

2

25

3

35ve

hicle

(a) AMVT

APCF=5

APCF=50

x 105

20182017 2019 20202015 2016201420122011 201320102009Time (year)

11

12

13

14

15

16

17

ton

(b) APMG

APCF=5

APCF=50

x 105

08

09

1

11

12

13

14

15

16

ton

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 20202009Time (year)

(c) ANOG

02

APCF=5

APCF=50

2009 2011 20122010 20142013 2016 2017 20182015 20202019Time (year)

025

03

035

04

045

05

055D

mnl

(d) DAP

Figure 7 Comparison of the policies (a) AVT (b) APMG (c) ANOG (d) DAP

in cities but also effectively reduced the APMG and ANOGthereby reducing the DAP

According to a comparison on the different schemes atthe end of the analogue simulation period the high chargepolicy functioned as follows in terms of the emission reduc-tion of the motor vehicle exhaust the APMG and ANOGexhibited reductions of 2652 and 2129 respectively interms of alleviating traffic jams the AMVT exhibited a 3101decrease and in terms of reducing the degree of air pollutionthe DAP exhibited a 1250 decrease

4 Conclusions

41 Main Conclusions To resolve the air pollution problemsgenerated by motor vehicle exhaust emission the presentstudy introduced the charging mechanism and built a motorvehicle exhaust emission reduction strategy managementmodel using economic means and the SD-GM approach to

generate the following conclusions based on tests validationof the models and the simulation analysis of policies

(1)Within a certain range the reduction effects of APMGandANOGexhibited continuous enhancements following anincrease in APCF However the APCF did not always followthe principle ldquobigger means betterrdquo because the emissionreduction effect which was generated by an increase inthe APCF exhibited a marginal decreasing effect Accord-ing to the sensitivity analysis a pollution charge of 30ndash50yuandaysdotvehicle for the motor vehicles in Beijing was withinthe relatively reasonable range

(2) Three high charge policy functions were generatedbased on a comparison of the simulation results of thedifferent charging schemes the implementation of highcharge policies not only reduced the AMVT and alleviatedtraffic jams (Figures 6(e) 6(f) and 7(a) Table 10) but alsoeffectively reduced the APMG andANOG (Figures 6(e) 6(f)7(b) and 7(c) Tables 5 and 10) thereby further reducing theDAP (Figures 6(e) 6(f) and 7(d) Table 10) According to the

16 Discrete Dynamics in Nature and Society

contrastive analysis the DAP exhibited a decrease of about1250

(3) However the following problems were encounteredfollowing the implementation of the APCF policy (a) Theimplementation of the APCF policy increased the cost ofmotor vehicle trips and urged part-time drivers to take publictransportation which increased the burden of public trans-portation The subsidy policy and other applicable policiesmust be introduced to improve the public transport supplylevel and service quality Otherwise the trip demands ofpassengers will be difficult to satisfy which will influencethe implementation of the APCF policy (b) In the earlyperiods of APCF policy implementation an increase in thecost of motor vehicle trips due to the insufficient publicunderstanding and utilization of the APCF policy loweredits public support rate The government must strengthenits public relations work especially regarding the purposeand significance of its implementation to improve publicawareness and acknowledgment (c) The purpose of thesepolicies must be supervised and managed to gather APCFincome and improve public transportation infrastructures

42 Deficiencies and Future Work The present study consid-ered NOx and PMx as the principal motor vehicle emissionpollutants Future research must fully consider other com-ponents such as SO2 airborne particles hydrocarbons COand CO2 Secondly the implementation of a single chargingmeasure can reduce the supply level of public transportationFuture research should consider a subsidy mechanism toimprove the service quality Thirdly the function and effectof a single policy are limited Future work must considerthe integration of multiple policies to improve the emissionreduction effect For example future work may focus priorityon public transportation improvement of fuel quality vigor-ous promotion of new energy vehicles and improvements inemission standards

Appendix

A

See Table 11

B

Summary of the major variables and equations(1) Cost of motor vehicle trips = Air pollution charging

feelowast (1+ Air pollution control)(2) Amount ofNOx generation = INTEG (NOx emissions

- Annual dissipation of NOx 80380)(3) NOx emissions = Per vehicle annual of NOx

emissionslowast Amount of motor vehicle tripslowast Contributionrate of NOx from vehicle

(4) Contribution rate of NOx from vehicle = 05(5) Dissipation rate of NOx = 02(6) Annual dissipation of NOx = Amount of NOx

generationlowast Dissipation rate of NOx(7) Per vehicle annual of NOx emissions = 002

(8) Amount of PMx generation = INTEG (PMxemissions- Annual dissipation of PMx 160760)

(9) PMx emissions = Amount of motor vehicle tripslowastContribution rate of PMx from vehiclelowast Per vehicle annualof PMx emissions

(10) Contribution rate of PMx from vehicle = 05(11) Per vehicle annual of PMx emissions = 004(12) Annual dissipation of PMx = Amount of PMx

generationlowast Dissipation and control rate of PMx(13) Dissipation and control rate of PMx = 05(14) Pollution degree of NOx = IF THEN ELSE (Amount

of NOx generationgt= 11182e+005 09 IF THEN ELSE(Amount of NOx generationgt= 10874e+005 08 IF THENELSE (Amount of NOx generationgt= 10400e+005 07 IFTHEN ELSE (Amount of NOx generationgt= 9966e+00406 IF THEN ELSE (Amount of NOx generationgt=9618e+004 05 IF THEN ELSE (Amount of NOxgenerationgt= 8038e+004 03 IF THEN ELSE (Amountof NOx generationgt= 7008e+004 025 IF THEN ELSE(Amount of NOx generationgt= 6144e+004 02 IF THENELSE (Amount of NOx generationgt= 5508e+004 015 01)))))))))

(15) Pollution degree of PMx = IF THEN ELSE (Amountof PMx generationgt= 22364e+005 09 IF THEN ELSE(Amount of PMx generationgt= 21748e+005 08 IF THENELSE (Amount of PMx generationgt= 20800e+005 07 IFTHEN ELSE (Amount of PMx generationgt= 19932e+00506 IF THEN ELSE (Amount of PMx generationgt=19236e+005 05 IF THEN ELSE (Amount of PMxgenerationgt= 16076e+005 03 IF THEN ELSE (Amountof PMx generationgt= 14016e+005 025 IF THEN ELSE(Amount of PMx generationgt= 12288e+005 02 IF THENELSE (Amount of PMx generationgt= 11016e+005 015 01)))))))))

(16) Ratio of motor vehicle trips = 055(17) Amount of motor vehicle trips = Amount of motor

vehicleslowast Ratio of motor vehicle trips(18) Degree of air pollution = Weight ratio of NOxlowast

Pollution degree of NOx+ Weight ratio of PMxlowast Pollutiondegree of PMx

(19) Weight ratio of PMx = 05(20) Weight ratio of NOx = 05(21) Air pollution control = IF THEN ELSE (Degree of air

pollutiongt= 07 1 IF THEN ELSE (Degree of air pollutiongt=06 08 IF THEN ELSE (Degree of air pollutiongt= 05 07IF THEN ELSE (Degree of air pollutiongt= 04 06 IF THENELSE (Degree of air pollutiongt= 03 05 IF THEN ELSE(Degree of air pollutiongt= 025 045 IF THENELSE (Degreeof air pollutiongt= 02 04 IF THEN ELSE (Degree of airpollutiongt= 015 035 03))))))))

(22) Attraction degree of the growth of vehicles= (1-Airpollution control)lowast 055+ Attraction degree of vehicle tripslowast045

(23) Per capita annual income = Amount of GDPAmount of population

(24) Amount of population = INTEG (Growth of popu-lation+ Net migration- Population reduction 186e+007)

(25) Birth rate = Adjustment coefficient of birth ratelowastPredictive value of birth rate

Discrete Dynamics in Nature and Society 17

Table 11 Description of main variables in stock flow diagram

Signicant variable Unit Variable type Data sourceAir pollution charging fee yuandaysdotvehicle ConstantAir pollution control Dmnl Auxiliary variable M1+M3Amount of GDP yuan Level M1Amount of motor vehicles vehicle Level M1Amount of motor vehicle trips vehicle Auxiliary variableAmount of NOx (PMx) generation ton Level M1Amount of population person Level M1Annual dissipation of NOx (PMx) tonyear FlowAnnual scrapped vehicleyear FlowAttraction degree of city Constant M2Attraction degree of the growth of vehicles Auxiliary variable M1+M3Attraction degree of vehicle trips Auxiliary variable M1+M3Birth rate 1year Constant M3Contribution rate of NOx (PMx) from vehicle Constant M2Cost of motor vehicle trips yuandaysdotvehicle Auxiliary variable M3Death rate 1year Constant M3Degree of air pollution Dmnl Auxiliary variable M3Dissipation and control rate of NOx (PMx) 1year Constant M2Graphical function of the growth of GDP Dmnl Auxiliary variable M3Growth of GDP yuanyear FlowGrowth rate of motor vehicles 1year Auxiliary variable M1+M3Growth of motor vehicles vehicleyear FlowGrowth of population personyear FlowGrowth rate of vehicle ownership Dmnl Auxiliary variable M1+M3Impact factor of policy Dmnl Constant M3Net migration personyear FlowNet migration rate 1year Constant M1+M3NOx (PMx) emissions tonyear FlowPer capita annual income yuanperson Auxiliary variablePer vehicle annual of NOx (PMx) emissions tonyearsdotvehicle Constant M2Pollution degree of NOx (PMx) Dmnl Auxiliary variable M1+M3Population reduction personyear FlowRatio of motor vehicle trips Constant M2Scrap rate 1year Constant M2The average of net migration rate 1year Constant M1Weight ratio of PMx (NOx) Auxiliary variable M3

(26) Predictive value of birth rate = 000925(27) Death rate = Adjustment coefficient of death ratelowast

Predictive value of death rate(28) Predictive value of death rate = 000494(29) Net migration = Amount of populationlowastNet migra-

tion rate(30) Net migration rate = The average of net migration

ratelowast Attraction degree of cityand(Impact factor of policy)(31) Impact factor of policy = 15(32) The average of net migration rate = 000531(33) Attraction degree of city = 07056(34) Amount of GDP = INTEG (Growth of GDP

12153e+012)

(35) Graphical function of the growth of GDP = WITHLOOKUP (Amount of GDP ([(8e+011 0)- (3e+ 012 03)](81178e+011 01648) (98468e+011 0213) (11115e+01201288) (12153e+012 00934) (141136e+012 01613)(162519e+012 01515) (178794e+012 01001) (198008e+01201075) (213308e+012 00773) (230146e+012 00789)(235396e+012 002281) (240162e+012 00203) (245025e+012 002025) (249987e+012 002024) (255049e+0120020249)))

(36) Growth rate of GDP = Graphical function of thegrowth of GDPlowast Impact factor of the growth of GDP

(37) Amount of motor vehicles = INTEG (Growth ofmotor vehicles- Annual scrapped 4019e+006)

18 Discrete Dynamics in Nature and Society

(38) Annual scrapped = Amount of motor vehicleslowastScrap rate

(39) Scrap rate = 0067

Conflicts of Interest

The author declares no conflicts of interest

Acknowledgments

This work has been partially supported by the NationalNatural Science Foundation of China (71571119) ShanghaiFirst-Class Academic Discipline Project (S1201YLXK) andChina Postdoctoral Science Foundation (2018M630404)Theauthor would like to thank LetPub (httpwwwletpubcom)for providing linguistic assistance during the preparation ofthis manuscript

References

[1] X Liu S Ma J Tian N Jia and G Li ldquoA system dynamicsapproach to scenario analysis for urban passenger transportenergy consumption and CO2 emissions A case study ofBeijingrdquo Energy Policy vol 85 pp 253ndash270 2015

[2] B Xu L Luo and B Lin ldquoA dynamic analysis of air pollutionemissions in China Evidence from nonparametric additiveregression modelsrdquo Ecological Indicators vol 63 pp 346ndash3582016

[3] S Leinert H Daly B Hyde and B O Gallachoir ldquoCo-benefitsNot always Quantifying the negative effect of a CO2-reducingcar taxation policy on NOx emissionsrdquo Energy Policy vol 63pp 1151ndash1159 2013

[4] Z Cheng L Li and J Liu ldquoIdentifying the spatial effects anddriving factors of urban PM25 pollution in Chinardquo EcologicalIndicators vol 82 pp 61ndash75 2017

[5] N Kaida and K Kaida ldquoSpillover effect of congestion chargingon pro-environmental behaviorrdquo Environment Developmentand Sustainability vol 17 no 3 pp 409ndash421 2015

[6] R Penabaena-Niebles V Cantillo and J L Moura ldquoImpactof transition between signal timing plans in social cost basedin delay fuel consumption and air emissionsrdquo TransportationResearch Part D Transport and Environment vol 41 pp 445ndash456 2015

[7] DDing andB Shuai ldquoA traffic restriction scheme for enhancingcarpoolingrdquoDiscreteDynamics inNature and Society Article ID9626938 9 pages 2017

[8] D Kong X Guo B Yang and D Wu ldquoAnalyzing the Impactof Trucks on Traffic Flow Based on an Improved CellularAutomaton Modelrdquo Discrete Dynamics in Nature and Societyvol 2016 pp 1ndash14 2016

[9] S Cakmak C Hebbern J D Cakmak and J Vanos ldquoThemodifying effect of socioeconomic status on the relationshipbetween traffic air pollution and respiratory health in elemen-tary schoolchildrenrdquo Journal of Environmental Managementvol 177 pp 1ndash8 2016

[10] L Song H Song J Lin et al ldquoPM25 emissions from differenttypes of heavy-duty truck a case study and meta-analysis ofthe Beijing-Tianjin-Hebei regionrdquo Environmental Science andPollution Research vol 24 no 12 pp 11206ndash11214 2017

[11] Z Hu S Kang C Li et al ldquoLight absorption of biomassburning and vehicle emission-sourced carbonaceous aerosolsof the Tibetan Plateaurdquo Environmental Science and PollutionResearch vol 24 no 18 pp 15369ndash15378 2017

[12] X Cen H K Lo and L Li ldquoA framework for estimating trafficemissions The development of Passenger Car Emission UnitrdquoTransportation Research Part D Transport and Environmentvol 44 pp 78ndash92 2016

[13] S Wang X Liu C Zhou J Hu and J Ou ldquoExamining theimpacts of socioeconomic factors urban form and transporta-tion networks on CO2 emissions in Chinarsquos megacitiesrdquoAppliedEnergy vol 185 pp 189ndash200 2017

[14] Q Wang K Hubacek K Feng Y-M Wei and Q-M LiangldquoDistributional effects of carbon taxationrdquo Applied Energy vol184 pp 1123ndash1131 2016

[15] C Johansson L Burman and B Forsberg ldquoThe effects ofcongestions tax on air quality and healthrdquo Atmospheric Envi-ronment vol 43 no 31 pp 4843ndash4854 2009

[16] A Rakowska K C Wong T Townsend et al ldquoImpact of trafficvolume and composition on the air quality and pedestrianexposure in urban street canyonrdquo Atmospheric Environmentvol 98 pp 260ndash270 2014

[17] S Batterman R Ganguly and P Harbin ldquoHigh resolutionspatial and temporal mapping of traffic-related air pollutantsrdquoInternational Journal of Environmental Research and PublicHealth vol 12 no 4 pp 3646ndash3666 2015

[18] J Eliasson M Borjesson D van Amelsfort K Brundell-Freijand L Engelson ldquoAccuracy of congestion pricing forecastsrdquoTransportation Research Part A Policy and Practice vol 52 pp34ndash46 2013

[19] J Eliasson ldquoThe role of attitude structures direct experienceand reframing for the success of congestion pricingrdquo Trans-portation Research Part A Policy and Practice vol 67 pp 81ndash952014

[20] H X Yang J D Li H Zhang and S Q Liu ldquoResearch on thegovernance of urban traffic jam based on system dynamicsrdquoSystems EngineeringTheory and Practice vol 34 no 8 pp 2135ndash2143 2014 (Chinese)

[21] M H Zhu Research on Socio-Economic Impact of UrbanTrafficCongestion [PhD thesis] Beijing JiaotongUniversity 2013(Chinese)

[22] B Zeng Research on Modeling Technologies of Grey Prediction[PhD thesis] Nanjing University of Aeronautics and Astronau-tics 2011 (Chinese)

[23] S F Liu Y J Yang and L F Wu Grey System Theory andApplication Science Press Beijing China 2017

[24] S W Jia K Yang J J Zhao and G L Yan ldquoThe traffic-congestion charging fee management model based on thesystem dynamics approachrdquo Mathematical Problems in Engi-neering vol 2017 Article ID 3024898 13 pages 2017

14 Discrete Dynamics in Nature and Society

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

083 M

10000004

2 M00

2011 2013 2015 2017 20192009Time (year)

AMVT APCF=5ANOG APCF=5APMG APCF=5DAP APCF=5

vehicletontonDmnl

(a)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=10ANOG APCF=10APMG APCF=10DAP APCF=10

vehicletontonDmnl

(b)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=20ANOG APCF=20APMG APCF=20DAP APCF=20

vehicletontonDmnl

(c)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=30ANOG APCF=30APMG APCF=30DAP APCF=30

vehicletontonDmnl

(d)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=40ANOG APCF=40APMG APCF=40DAP APCF=40

vehicletontonDmnl

(e)

Selected VariablesvehicletonDmnlvehicletonDmnlvehicletonDmnl

4 M200000

063 M

14000003

2 M80000

02011 2013 2015 2017 20192009

Time (year)

AMVT APCF=50ANOG APCF=50APMG APCF=50DAP APCF=50

vehicletontonDmnl

(f)

Figure 6 Policy simulation (a) APCF=5 (b) APCF=10 (c) APCF=20 (d) APCF=30 (e) APCF=40 (f) APCF=50

intensification of ldquohazerdquo pollution degree in Beijing Specif-ically the gap between curves 1 and 2 exhibited a continuouswidening as presented in Figure 7(a) After 2013 curve 2exhibited an obvious descent Therefore the APCF policyeffectively reduced the AMVT and enabled an about 3101decrease in 2020

The results in Figures 7(b)ndash7(d) were similarly analyzed

In conclusion the adoption of a low charge policygenerated increasing APMG and ANOG trends as presentedin Figures 6(a) and 6(b) thereby suggesting the inabilityof the low charge policy to effectively reduce the DAP Anincrease of the fee to a certain extent especially followingthe implementation of a high charge policy (Figures 6(e) and6(f)) not only reduced the AMVT and alleviated traffic jams

Discrete Dynamics in Nature and Society 15

APCF=5

APCF=50

x 106

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 20202009Time (year)

2

25

3

35ve

hicle

(a) AMVT

APCF=5

APCF=50

x 105

20182017 2019 20202015 2016201420122011 201320102009Time (year)

11

12

13

14

15

16

17

ton

(b) APMG

APCF=5

APCF=50

x 105

08

09

1

11

12

13

14

15

16

ton

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 20202009Time (year)

(c) ANOG

02

APCF=5

APCF=50

2009 2011 20122010 20142013 2016 2017 20182015 20202019Time (year)

025

03

035

04

045

05

055D

mnl

(d) DAP

Figure 7 Comparison of the policies (a) AVT (b) APMG (c) ANOG (d) DAP

in cities but also effectively reduced the APMG and ANOGthereby reducing the DAP

According to a comparison on the different schemes atthe end of the analogue simulation period the high chargepolicy functioned as follows in terms of the emission reduc-tion of the motor vehicle exhaust the APMG and ANOGexhibited reductions of 2652 and 2129 respectively interms of alleviating traffic jams the AMVT exhibited a 3101decrease and in terms of reducing the degree of air pollutionthe DAP exhibited a 1250 decrease

4 Conclusions

41 Main Conclusions To resolve the air pollution problemsgenerated by motor vehicle exhaust emission the presentstudy introduced the charging mechanism and built a motorvehicle exhaust emission reduction strategy managementmodel using economic means and the SD-GM approach to

generate the following conclusions based on tests validationof the models and the simulation analysis of policies

(1)Within a certain range the reduction effects of APMGandANOGexhibited continuous enhancements following anincrease in APCF However the APCF did not always followthe principle ldquobigger means betterrdquo because the emissionreduction effect which was generated by an increase inthe APCF exhibited a marginal decreasing effect Accord-ing to the sensitivity analysis a pollution charge of 30ndash50yuandaysdotvehicle for the motor vehicles in Beijing was withinthe relatively reasonable range

(2) Three high charge policy functions were generatedbased on a comparison of the simulation results of thedifferent charging schemes the implementation of highcharge policies not only reduced the AMVT and alleviatedtraffic jams (Figures 6(e) 6(f) and 7(a) Table 10) but alsoeffectively reduced the APMG andANOG (Figures 6(e) 6(f)7(b) and 7(c) Tables 5 and 10) thereby further reducing theDAP (Figures 6(e) 6(f) and 7(d) Table 10) According to the

16 Discrete Dynamics in Nature and Society

contrastive analysis the DAP exhibited a decrease of about1250

(3) However the following problems were encounteredfollowing the implementation of the APCF policy (a) Theimplementation of the APCF policy increased the cost ofmotor vehicle trips and urged part-time drivers to take publictransportation which increased the burden of public trans-portation The subsidy policy and other applicable policiesmust be introduced to improve the public transport supplylevel and service quality Otherwise the trip demands ofpassengers will be difficult to satisfy which will influencethe implementation of the APCF policy (b) In the earlyperiods of APCF policy implementation an increase in thecost of motor vehicle trips due to the insufficient publicunderstanding and utilization of the APCF policy loweredits public support rate The government must strengthenits public relations work especially regarding the purposeand significance of its implementation to improve publicawareness and acknowledgment (c) The purpose of thesepolicies must be supervised and managed to gather APCFincome and improve public transportation infrastructures

42 Deficiencies and Future Work The present study consid-ered NOx and PMx as the principal motor vehicle emissionpollutants Future research must fully consider other com-ponents such as SO2 airborne particles hydrocarbons COand CO2 Secondly the implementation of a single chargingmeasure can reduce the supply level of public transportationFuture research should consider a subsidy mechanism toimprove the service quality Thirdly the function and effectof a single policy are limited Future work must considerthe integration of multiple policies to improve the emissionreduction effect For example future work may focus priorityon public transportation improvement of fuel quality vigor-ous promotion of new energy vehicles and improvements inemission standards

Appendix

A

See Table 11

B

Summary of the major variables and equations(1) Cost of motor vehicle trips = Air pollution charging

feelowast (1+ Air pollution control)(2) Amount ofNOx generation = INTEG (NOx emissions

- Annual dissipation of NOx 80380)(3) NOx emissions = Per vehicle annual of NOx

emissionslowast Amount of motor vehicle tripslowast Contributionrate of NOx from vehicle

(4) Contribution rate of NOx from vehicle = 05(5) Dissipation rate of NOx = 02(6) Annual dissipation of NOx = Amount of NOx

generationlowast Dissipation rate of NOx(7) Per vehicle annual of NOx emissions = 002

(8) Amount of PMx generation = INTEG (PMxemissions- Annual dissipation of PMx 160760)

(9) PMx emissions = Amount of motor vehicle tripslowastContribution rate of PMx from vehiclelowast Per vehicle annualof PMx emissions

(10) Contribution rate of PMx from vehicle = 05(11) Per vehicle annual of PMx emissions = 004(12) Annual dissipation of PMx = Amount of PMx

generationlowast Dissipation and control rate of PMx(13) Dissipation and control rate of PMx = 05(14) Pollution degree of NOx = IF THEN ELSE (Amount

of NOx generationgt= 11182e+005 09 IF THEN ELSE(Amount of NOx generationgt= 10874e+005 08 IF THENELSE (Amount of NOx generationgt= 10400e+005 07 IFTHEN ELSE (Amount of NOx generationgt= 9966e+00406 IF THEN ELSE (Amount of NOx generationgt=9618e+004 05 IF THEN ELSE (Amount of NOxgenerationgt= 8038e+004 03 IF THEN ELSE (Amountof NOx generationgt= 7008e+004 025 IF THEN ELSE(Amount of NOx generationgt= 6144e+004 02 IF THENELSE (Amount of NOx generationgt= 5508e+004 015 01)))))))))

(15) Pollution degree of PMx = IF THEN ELSE (Amountof PMx generationgt= 22364e+005 09 IF THEN ELSE(Amount of PMx generationgt= 21748e+005 08 IF THENELSE (Amount of PMx generationgt= 20800e+005 07 IFTHEN ELSE (Amount of PMx generationgt= 19932e+00506 IF THEN ELSE (Amount of PMx generationgt=19236e+005 05 IF THEN ELSE (Amount of PMxgenerationgt= 16076e+005 03 IF THEN ELSE (Amountof PMx generationgt= 14016e+005 025 IF THEN ELSE(Amount of PMx generationgt= 12288e+005 02 IF THENELSE (Amount of PMx generationgt= 11016e+005 015 01)))))))))

(16) Ratio of motor vehicle trips = 055(17) Amount of motor vehicle trips = Amount of motor

vehicleslowast Ratio of motor vehicle trips(18) Degree of air pollution = Weight ratio of NOxlowast

Pollution degree of NOx+ Weight ratio of PMxlowast Pollutiondegree of PMx

(19) Weight ratio of PMx = 05(20) Weight ratio of NOx = 05(21) Air pollution control = IF THEN ELSE (Degree of air

pollutiongt= 07 1 IF THEN ELSE (Degree of air pollutiongt=06 08 IF THEN ELSE (Degree of air pollutiongt= 05 07IF THEN ELSE (Degree of air pollutiongt= 04 06 IF THENELSE (Degree of air pollutiongt= 03 05 IF THEN ELSE(Degree of air pollutiongt= 025 045 IF THENELSE (Degreeof air pollutiongt= 02 04 IF THEN ELSE (Degree of airpollutiongt= 015 035 03))))))))

(22) Attraction degree of the growth of vehicles= (1-Airpollution control)lowast 055+ Attraction degree of vehicle tripslowast045

(23) Per capita annual income = Amount of GDPAmount of population

(24) Amount of population = INTEG (Growth of popu-lation+ Net migration- Population reduction 186e+007)

(25) Birth rate = Adjustment coefficient of birth ratelowastPredictive value of birth rate

Discrete Dynamics in Nature and Society 17

Table 11 Description of main variables in stock flow diagram

Signicant variable Unit Variable type Data sourceAir pollution charging fee yuandaysdotvehicle ConstantAir pollution control Dmnl Auxiliary variable M1+M3Amount of GDP yuan Level M1Amount of motor vehicles vehicle Level M1Amount of motor vehicle trips vehicle Auxiliary variableAmount of NOx (PMx) generation ton Level M1Amount of population person Level M1Annual dissipation of NOx (PMx) tonyear FlowAnnual scrapped vehicleyear FlowAttraction degree of city Constant M2Attraction degree of the growth of vehicles Auxiliary variable M1+M3Attraction degree of vehicle trips Auxiliary variable M1+M3Birth rate 1year Constant M3Contribution rate of NOx (PMx) from vehicle Constant M2Cost of motor vehicle trips yuandaysdotvehicle Auxiliary variable M3Death rate 1year Constant M3Degree of air pollution Dmnl Auxiliary variable M3Dissipation and control rate of NOx (PMx) 1year Constant M2Graphical function of the growth of GDP Dmnl Auxiliary variable M3Growth of GDP yuanyear FlowGrowth rate of motor vehicles 1year Auxiliary variable M1+M3Growth of motor vehicles vehicleyear FlowGrowth of population personyear FlowGrowth rate of vehicle ownership Dmnl Auxiliary variable M1+M3Impact factor of policy Dmnl Constant M3Net migration personyear FlowNet migration rate 1year Constant M1+M3NOx (PMx) emissions tonyear FlowPer capita annual income yuanperson Auxiliary variablePer vehicle annual of NOx (PMx) emissions tonyearsdotvehicle Constant M2Pollution degree of NOx (PMx) Dmnl Auxiliary variable M1+M3Population reduction personyear FlowRatio of motor vehicle trips Constant M2Scrap rate 1year Constant M2The average of net migration rate 1year Constant M1Weight ratio of PMx (NOx) Auxiliary variable M3

(26) Predictive value of birth rate = 000925(27) Death rate = Adjustment coefficient of death ratelowast

Predictive value of death rate(28) Predictive value of death rate = 000494(29) Net migration = Amount of populationlowastNet migra-

tion rate(30) Net migration rate = The average of net migration

ratelowast Attraction degree of cityand(Impact factor of policy)(31) Impact factor of policy = 15(32) The average of net migration rate = 000531(33) Attraction degree of city = 07056(34) Amount of GDP = INTEG (Growth of GDP

12153e+012)

(35) Graphical function of the growth of GDP = WITHLOOKUP (Amount of GDP ([(8e+011 0)- (3e+ 012 03)](81178e+011 01648) (98468e+011 0213) (11115e+01201288) (12153e+012 00934) (141136e+012 01613)(162519e+012 01515) (178794e+012 01001) (198008e+01201075) (213308e+012 00773) (230146e+012 00789)(235396e+012 002281) (240162e+012 00203) (245025e+012 002025) (249987e+012 002024) (255049e+0120020249)))

(36) Growth rate of GDP = Graphical function of thegrowth of GDPlowast Impact factor of the growth of GDP

(37) Amount of motor vehicles = INTEG (Growth ofmotor vehicles- Annual scrapped 4019e+006)

18 Discrete Dynamics in Nature and Society

(38) Annual scrapped = Amount of motor vehicleslowastScrap rate

(39) Scrap rate = 0067

Conflicts of Interest

The author declares no conflicts of interest

Acknowledgments

This work has been partially supported by the NationalNatural Science Foundation of China (71571119) ShanghaiFirst-Class Academic Discipline Project (S1201YLXK) andChina Postdoctoral Science Foundation (2018M630404)Theauthor would like to thank LetPub (httpwwwletpubcom)for providing linguistic assistance during the preparation ofthis manuscript

References

[1] X Liu S Ma J Tian N Jia and G Li ldquoA system dynamicsapproach to scenario analysis for urban passenger transportenergy consumption and CO2 emissions A case study ofBeijingrdquo Energy Policy vol 85 pp 253ndash270 2015

[2] B Xu L Luo and B Lin ldquoA dynamic analysis of air pollutionemissions in China Evidence from nonparametric additiveregression modelsrdquo Ecological Indicators vol 63 pp 346ndash3582016

[3] S Leinert H Daly B Hyde and B O Gallachoir ldquoCo-benefitsNot always Quantifying the negative effect of a CO2-reducingcar taxation policy on NOx emissionsrdquo Energy Policy vol 63pp 1151ndash1159 2013

[4] Z Cheng L Li and J Liu ldquoIdentifying the spatial effects anddriving factors of urban PM25 pollution in Chinardquo EcologicalIndicators vol 82 pp 61ndash75 2017

[5] N Kaida and K Kaida ldquoSpillover effect of congestion chargingon pro-environmental behaviorrdquo Environment Developmentand Sustainability vol 17 no 3 pp 409ndash421 2015

[6] R Penabaena-Niebles V Cantillo and J L Moura ldquoImpactof transition between signal timing plans in social cost basedin delay fuel consumption and air emissionsrdquo TransportationResearch Part D Transport and Environment vol 41 pp 445ndash456 2015

[7] DDing andB Shuai ldquoA traffic restriction scheme for enhancingcarpoolingrdquoDiscreteDynamics inNature and Society Article ID9626938 9 pages 2017

[8] D Kong X Guo B Yang and D Wu ldquoAnalyzing the Impactof Trucks on Traffic Flow Based on an Improved CellularAutomaton Modelrdquo Discrete Dynamics in Nature and Societyvol 2016 pp 1ndash14 2016

[9] S Cakmak C Hebbern J D Cakmak and J Vanos ldquoThemodifying effect of socioeconomic status on the relationshipbetween traffic air pollution and respiratory health in elemen-tary schoolchildrenrdquo Journal of Environmental Managementvol 177 pp 1ndash8 2016

[10] L Song H Song J Lin et al ldquoPM25 emissions from differenttypes of heavy-duty truck a case study and meta-analysis ofthe Beijing-Tianjin-Hebei regionrdquo Environmental Science andPollution Research vol 24 no 12 pp 11206ndash11214 2017

[11] Z Hu S Kang C Li et al ldquoLight absorption of biomassburning and vehicle emission-sourced carbonaceous aerosolsof the Tibetan Plateaurdquo Environmental Science and PollutionResearch vol 24 no 18 pp 15369ndash15378 2017

[12] X Cen H K Lo and L Li ldquoA framework for estimating trafficemissions The development of Passenger Car Emission UnitrdquoTransportation Research Part D Transport and Environmentvol 44 pp 78ndash92 2016

[13] S Wang X Liu C Zhou J Hu and J Ou ldquoExamining theimpacts of socioeconomic factors urban form and transporta-tion networks on CO2 emissions in Chinarsquos megacitiesrdquoAppliedEnergy vol 185 pp 189ndash200 2017

[14] Q Wang K Hubacek K Feng Y-M Wei and Q-M LiangldquoDistributional effects of carbon taxationrdquo Applied Energy vol184 pp 1123ndash1131 2016

[15] C Johansson L Burman and B Forsberg ldquoThe effects ofcongestions tax on air quality and healthrdquo Atmospheric Envi-ronment vol 43 no 31 pp 4843ndash4854 2009

[16] A Rakowska K C Wong T Townsend et al ldquoImpact of trafficvolume and composition on the air quality and pedestrianexposure in urban street canyonrdquo Atmospheric Environmentvol 98 pp 260ndash270 2014

[17] S Batterman R Ganguly and P Harbin ldquoHigh resolutionspatial and temporal mapping of traffic-related air pollutantsrdquoInternational Journal of Environmental Research and PublicHealth vol 12 no 4 pp 3646ndash3666 2015

[18] J Eliasson M Borjesson D van Amelsfort K Brundell-Freijand L Engelson ldquoAccuracy of congestion pricing forecastsrdquoTransportation Research Part A Policy and Practice vol 52 pp34ndash46 2013

[19] J Eliasson ldquoThe role of attitude structures direct experienceand reframing for the success of congestion pricingrdquo Trans-portation Research Part A Policy and Practice vol 67 pp 81ndash952014

[20] H X Yang J D Li H Zhang and S Q Liu ldquoResearch on thegovernance of urban traffic jam based on system dynamicsrdquoSystems EngineeringTheory and Practice vol 34 no 8 pp 2135ndash2143 2014 (Chinese)

[21] M H Zhu Research on Socio-Economic Impact of UrbanTrafficCongestion [PhD thesis] Beijing JiaotongUniversity 2013(Chinese)

[22] B Zeng Research on Modeling Technologies of Grey Prediction[PhD thesis] Nanjing University of Aeronautics and Astronau-tics 2011 (Chinese)

[23] S F Liu Y J Yang and L F Wu Grey System Theory andApplication Science Press Beijing China 2017

[24] S W Jia K Yang J J Zhao and G L Yan ldquoThe traffic-congestion charging fee management model based on thesystem dynamics approachrdquo Mathematical Problems in Engi-neering vol 2017 Article ID 3024898 13 pages 2017

Discrete Dynamics in Nature and Society 15

APCF=5

APCF=50

x 106

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 20202009Time (year)

2

25

3

35ve

hicle

(a) AMVT

APCF=5

APCF=50

x 105

20182017 2019 20202015 2016201420122011 201320102009Time (year)

11

12

13

14

15

16

17

ton

(b) APMG

APCF=5

APCF=50

x 105

08

09

1

11

12

13

14

15

16

ton

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 20202009Time (year)

(c) ANOG

02

APCF=5

APCF=50

2009 2011 20122010 20142013 2016 2017 20182015 20202019Time (year)

025

03

035

04

045

05

055D

mnl

(d) DAP

Figure 7 Comparison of the policies (a) AVT (b) APMG (c) ANOG (d) DAP

in cities but also effectively reduced the APMG and ANOGthereby reducing the DAP

According to a comparison on the different schemes atthe end of the analogue simulation period the high chargepolicy functioned as follows in terms of the emission reduc-tion of the motor vehicle exhaust the APMG and ANOGexhibited reductions of 2652 and 2129 respectively interms of alleviating traffic jams the AMVT exhibited a 3101decrease and in terms of reducing the degree of air pollutionthe DAP exhibited a 1250 decrease

4 Conclusions

41 Main Conclusions To resolve the air pollution problemsgenerated by motor vehicle exhaust emission the presentstudy introduced the charging mechanism and built a motorvehicle exhaust emission reduction strategy managementmodel using economic means and the SD-GM approach to

generate the following conclusions based on tests validationof the models and the simulation analysis of policies

(1)Within a certain range the reduction effects of APMGandANOGexhibited continuous enhancements following anincrease in APCF However the APCF did not always followthe principle ldquobigger means betterrdquo because the emissionreduction effect which was generated by an increase inthe APCF exhibited a marginal decreasing effect Accord-ing to the sensitivity analysis a pollution charge of 30ndash50yuandaysdotvehicle for the motor vehicles in Beijing was withinthe relatively reasonable range

(2) Three high charge policy functions were generatedbased on a comparison of the simulation results of thedifferent charging schemes the implementation of highcharge policies not only reduced the AMVT and alleviatedtraffic jams (Figures 6(e) 6(f) and 7(a) Table 10) but alsoeffectively reduced the APMG andANOG (Figures 6(e) 6(f)7(b) and 7(c) Tables 5 and 10) thereby further reducing theDAP (Figures 6(e) 6(f) and 7(d) Table 10) According to the

16 Discrete Dynamics in Nature and Society

contrastive analysis the DAP exhibited a decrease of about1250

(3) However the following problems were encounteredfollowing the implementation of the APCF policy (a) Theimplementation of the APCF policy increased the cost ofmotor vehicle trips and urged part-time drivers to take publictransportation which increased the burden of public trans-portation The subsidy policy and other applicable policiesmust be introduced to improve the public transport supplylevel and service quality Otherwise the trip demands ofpassengers will be difficult to satisfy which will influencethe implementation of the APCF policy (b) In the earlyperiods of APCF policy implementation an increase in thecost of motor vehicle trips due to the insufficient publicunderstanding and utilization of the APCF policy loweredits public support rate The government must strengthenits public relations work especially regarding the purposeand significance of its implementation to improve publicawareness and acknowledgment (c) The purpose of thesepolicies must be supervised and managed to gather APCFincome and improve public transportation infrastructures

42 Deficiencies and Future Work The present study consid-ered NOx and PMx as the principal motor vehicle emissionpollutants Future research must fully consider other com-ponents such as SO2 airborne particles hydrocarbons COand CO2 Secondly the implementation of a single chargingmeasure can reduce the supply level of public transportationFuture research should consider a subsidy mechanism toimprove the service quality Thirdly the function and effectof a single policy are limited Future work must considerthe integration of multiple policies to improve the emissionreduction effect For example future work may focus priorityon public transportation improvement of fuel quality vigor-ous promotion of new energy vehicles and improvements inemission standards

Appendix

A

See Table 11

B

Summary of the major variables and equations(1) Cost of motor vehicle trips = Air pollution charging

feelowast (1+ Air pollution control)(2) Amount ofNOx generation = INTEG (NOx emissions

- Annual dissipation of NOx 80380)(3) NOx emissions = Per vehicle annual of NOx

emissionslowast Amount of motor vehicle tripslowast Contributionrate of NOx from vehicle

(4) Contribution rate of NOx from vehicle = 05(5) Dissipation rate of NOx = 02(6) Annual dissipation of NOx = Amount of NOx

generationlowast Dissipation rate of NOx(7) Per vehicle annual of NOx emissions = 002

(8) Amount of PMx generation = INTEG (PMxemissions- Annual dissipation of PMx 160760)

(9) PMx emissions = Amount of motor vehicle tripslowastContribution rate of PMx from vehiclelowast Per vehicle annualof PMx emissions

(10) Contribution rate of PMx from vehicle = 05(11) Per vehicle annual of PMx emissions = 004(12) Annual dissipation of PMx = Amount of PMx

generationlowast Dissipation and control rate of PMx(13) Dissipation and control rate of PMx = 05(14) Pollution degree of NOx = IF THEN ELSE (Amount

of NOx generationgt= 11182e+005 09 IF THEN ELSE(Amount of NOx generationgt= 10874e+005 08 IF THENELSE (Amount of NOx generationgt= 10400e+005 07 IFTHEN ELSE (Amount of NOx generationgt= 9966e+00406 IF THEN ELSE (Amount of NOx generationgt=9618e+004 05 IF THEN ELSE (Amount of NOxgenerationgt= 8038e+004 03 IF THEN ELSE (Amountof NOx generationgt= 7008e+004 025 IF THEN ELSE(Amount of NOx generationgt= 6144e+004 02 IF THENELSE (Amount of NOx generationgt= 5508e+004 015 01)))))))))

(15) Pollution degree of PMx = IF THEN ELSE (Amountof PMx generationgt= 22364e+005 09 IF THEN ELSE(Amount of PMx generationgt= 21748e+005 08 IF THENELSE (Amount of PMx generationgt= 20800e+005 07 IFTHEN ELSE (Amount of PMx generationgt= 19932e+00506 IF THEN ELSE (Amount of PMx generationgt=19236e+005 05 IF THEN ELSE (Amount of PMxgenerationgt= 16076e+005 03 IF THEN ELSE (Amountof PMx generationgt= 14016e+005 025 IF THEN ELSE(Amount of PMx generationgt= 12288e+005 02 IF THENELSE (Amount of PMx generationgt= 11016e+005 015 01)))))))))

(16) Ratio of motor vehicle trips = 055(17) Amount of motor vehicle trips = Amount of motor

vehicleslowast Ratio of motor vehicle trips(18) Degree of air pollution = Weight ratio of NOxlowast

Pollution degree of NOx+ Weight ratio of PMxlowast Pollutiondegree of PMx

(19) Weight ratio of PMx = 05(20) Weight ratio of NOx = 05(21) Air pollution control = IF THEN ELSE (Degree of air

pollutiongt= 07 1 IF THEN ELSE (Degree of air pollutiongt=06 08 IF THEN ELSE (Degree of air pollutiongt= 05 07IF THEN ELSE (Degree of air pollutiongt= 04 06 IF THENELSE (Degree of air pollutiongt= 03 05 IF THEN ELSE(Degree of air pollutiongt= 025 045 IF THENELSE (Degreeof air pollutiongt= 02 04 IF THEN ELSE (Degree of airpollutiongt= 015 035 03))))))))

(22) Attraction degree of the growth of vehicles= (1-Airpollution control)lowast 055+ Attraction degree of vehicle tripslowast045

(23) Per capita annual income = Amount of GDPAmount of population

(24) Amount of population = INTEG (Growth of popu-lation+ Net migration- Population reduction 186e+007)

(25) Birth rate = Adjustment coefficient of birth ratelowastPredictive value of birth rate

Discrete Dynamics in Nature and Society 17

Table 11 Description of main variables in stock flow diagram

Signicant variable Unit Variable type Data sourceAir pollution charging fee yuandaysdotvehicle ConstantAir pollution control Dmnl Auxiliary variable M1+M3Amount of GDP yuan Level M1Amount of motor vehicles vehicle Level M1Amount of motor vehicle trips vehicle Auxiliary variableAmount of NOx (PMx) generation ton Level M1Amount of population person Level M1Annual dissipation of NOx (PMx) tonyear FlowAnnual scrapped vehicleyear FlowAttraction degree of city Constant M2Attraction degree of the growth of vehicles Auxiliary variable M1+M3Attraction degree of vehicle trips Auxiliary variable M1+M3Birth rate 1year Constant M3Contribution rate of NOx (PMx) from vehicle Constant M2Cost of motor vehicle trips yuandaysdotvehicle Auxiliary variable M3Death rate 1year Constant M3Degree of air pollution Dmnl Auxiliary variable M3Dissipation and control rate of NOx (PMx) 1year Constant M2Graphical function of the growth of GDP Dmnl Auxiliary variable M3Growth of GDP yuanyear FlowGrowth rate of motor vehicles 1year Auxiliary variable M1+M3Growth of motor vehicles vehicleyear FlowGrowth of population personyear FlowGrowth rate of vehicle ownership Dmnl Auxiliary variable M1+M3Impact factor of policy Dmnl Constant M3Net migration personyear FlowNet migration rate 1year Constant M1+M3NOx (PMx) emissions tonyear FlowPer capita annual income yuanperson Auxiliary variablePer vehicle annual of NOx (PMx) emissions tonyearsdotvehicle Constant M2Pollution degree of NOx (PMx) Dmnl Auxiliary variable M1+M3Population reduction personyear FlowRatio of motor vehicle trips Constant M2Scrap rate 1year Constant M2The average of net migration rate 1year Constant M1Weight ratio of PMx (NOx) Auxiliary variable M3

(26) Predictive value of birth rate = 000925(27) Death rate = Adjustment coefficient of death ratelowast

Predictive value of death rate(28) Predictive value of death rate = 000494(29) Net migration = Amount of populationlowastNet migra-

tion rate(30) Net migration rate = The average of net migration

ratelowast Attraction degree of cityand(Impact factor of policy)(31) Impact factor of policy = 15(32) The average of net migration rate = 000531(33) Attraction degree of city = 07056(34) Amount of GDP = INTEG (Growth of GDP

12153e+012)

(35) Graphical function of the growth of GDP = WITHLOOKUP (Amount of GDP ([(8e+011 0)- (3e+ 012 03)](81178e+011 01648) (98468e+011 0213) (11115e+01201288) (12153e+012 00934) (141136e+012 01613)(162519e+012 01515) (178794e+012 01001) (198008e+01201075) (213308e+012 00773) (230146e+012 00789)(235396e+012 002281) (240162e+012 00203) (245025e+012 002025) (249987e+012 002024) (255049e+0120020249)))

(36) Growth rate of GDP = Graphical function of thegrowth of GDPlowast Impact factor of the growth of GDP

(37) Amount of motor vehicles = INTEG (Growth ofmotor vehicles- Annual scrapped 4019e+006)

18 Discrete Dynamics in Nature and Society

(38) Annual scrapped = Amount of motor vehicleslowastScrap rate

(39) Scrap rate = 0067

Conflicts of Interest

The author declares no conflicts of interest

Acknowledgments

This work has been partially supported by the NationalNatural Science Foundation of China (71571119) ShanghaiFirst-Class Academic Discipline Project (S1201YLXK) andChina Postdoctoral Science Foundation (2018M630404)Theauthor would like to thank LetPub (httpwwwletpubcom)for providing linguistic assistance during the preparation ofthis manuscript

References

[1] X Liu S Ma J Tian N Jia and G Li ldquoA system dynamicsapproach to scenario analysis for urban passenger transportenergy consumption and CO2 emissions A case study ofBeijingrdquo Energy Policy vol 85 pp 253ndash270 2015

[2] B Xu L Luo and B Lin ldquoA dynamic analysis of air pollutionemissions in China Evidence from nonparametric additiveregression modelsrdquo Ecological Indicators vol 63 pp 346ndash3582016

[3] S Leinert H Daly B Hyde and B O Gallachoir ldquoCo-benefitsNot always Quantifying the negative effect of a CO2-reducingcar taxation policy on NOx emissionsrdquo Energy Policy vol 63pp 1151ndash1159 2013

[4] Z Cheng L Li and J Liu ldquoIdentifying the spatial effects anddriving factors of urban PM25 pollution in Chinardquo EcologicalIndicators vol 82 pp 61ndash75 2017

[5] N Kaida and K Kaida ldquoSpillover effect of congestion chargingon pro-environmental behaviorrdquo Environment Developmentand Sustainability vol 17 no 3 pp 409ndash421 2015

[6] R Penabaena-Niebles V Cantillo and J L Moura ldquoImpactof transition between signal timing plans in social cost basedin delay fuel consumption and air emissionsrdquo TransportationResearch Part D Transport and Environment vol 41 pp 445ndash456 2015

[7] DDing andB Shuai ldquoA traffic restriction scheme for enhancingcarpoolingrdquoDiscreteDynamics inNature and Society Article ID9626938 9 pages 2017

[8] D Kong X Guo B Yang and D Wu ldquoAnalyzing the Impactof Trucks on Traffic Flow Based on an Improved CellularAutomaton Modelrdquo Discrete Dynamics in Nature and Societyvol 2016 pp 1ndash14 2016

[9] S Cakmak C Hebbern J D Cakmak and J Vanos ldquoThemodifying effect of socioeconomic status on the relationshipbetween traffic air pollution and respiratory health in elemen-tary schoolchildrenrdquo Journal of Environmental Managementvol 177 pp 1ndash8 2016

[10] L Song H Song J Lin et al ldquoPM25 emissions from differenttypes of heavy-duty truck a case study and meta-analysis ofthe Beijing-Tianjin-Hebei regionrdquo Environmental Science andPollution Research vol 24 no 12 pp 11206ndash11214 2017

[11] Z Hu S Kang C Li et al ldquoLight absorption of biomassburning and vehicle emission-sourced carbonaceous aerosolsof the Tibetan Plateaurdquo Environmental Science and PollutionResearch vol 24 no 18 pp 15369ndash15378 2017

[12] X Cen H K Lo and L Li ldquoA framework for estimating trafficemissions The development of Passenger Car Emission UnitrdquoTransportation Research Part D Transport and Environmentvol 44 pp 78ndash92 2016

[13] S Wang X Liu C Zhou J Hu and J Ou ldquoExamining theimpacts of socioeconomic factors urban form and transporta-tion networks on CO2 emissions in Chinarsquos megacitiesrdquoAppliedEnergy vol 185 pp 189ndash200 2017

[14] Q Wang K Hubacek K Feng Y-M Wei and Q-M LiangldquoDistributional effects of carbon taxationrdquo Applied Energy vol184 pp 1123ndash1131 2016

[15] C Johansson L Burman and B Forsberg ldquoThe effects ofcongestions tax on air quality and healthrdquo Atmospheric Envi-ronment vol 43 no 31 pp 4843ndash4854 2009

[16] A Rakowska K C Wong T Townsend et al ldquoImpact of trafficvolume and composition on the air quality and pedestrianexposure in urban street canyonrdquo Atmospheric Environmentvol 98 pp 260ndash270 2014

[17] S Batterman R Ganguly and P Harbin ldquoHigh resolutionspatial and temporal mapping of traffic-related air pollutantsrdquoInternational Journal of Environmental Research and PublicHealth vol 12 no 4 pp 3646ndash3666 2015

[18] J Eliasson M Borjesson D van Amelsfort K Brundell-Freijand L Engelson ldquoAccuracy of congestion pricing forecastsrdquoTransportation Research Part A Policy and Practice vol 52 pp34ndash46 2013

[19] J Eliasson ldquoThe role of attitude structures direct experienceand reframing for the success of congestion pricingrdquo Trans-portation Research Part A Policy and Practice vol 67 pp 81ndash952014

[20] H X Yang J D Li H Zhang and S Q Liu ldquoResearch on thegovernance of urban traffic jam based on system dynamicsrdquoSystems EngineeringTheory and Practice vol 34 no 8 pp 2135ndash2143 2014 (Chinese)

[21] M H Zhu Research on Socio-Economic Impact of UrbanTrafficCongestion [PhD thesis] Beijing JiaotongUniversity 2013(Chinese)

[22] B Zeng Research on Modeling Technologies of Grey Prediction[PhD thesis] Nanjing University of Aeronautics and Astronau-tics 2011 (Chinese)

[23] S F Liu Y J Yang and L F Wu Grey System Theory andApplication Science Press Beijing China 2017

[24] S W Jia K Yang J J Zhao and G L Yan ldquoThe traffic-congestion charging fee management model based on thesystem dynamics approachrdquo Mathematical Problems in Engi-neering vol 2017 Article ID 3024898 13 pages 2017

16 Discrete Dynamics in Nature and Society

contrastive analysis the DAP exhibited a decrease of about1250

(3) However the following problems were encounteredfollowing the implementation of the APCF policy (a) Theimplementation of the APCF policy increased the cost ofmotor vehicle trips and urged part-time drivers to take publictransportation which increased the burden of public trans-portation The subsidy policy and other applicable policiesmust be introduced to improve the public transport supplylevel and service quality Otherwise the trip demands ofpassengers will be difficult to satisfy which will influencethe implementation of the APCF policy (b) In the earlyperiods of APCF policy implementation an increase in thecost of motor vehicle trips due to the insufficient publicunderstanding and utilization of the APCF policy loweredits public support rate The government must strengthenits public relations work especially regarding the purposeand significance of its implementation to improve publicawareness and acknowledgment (c) The purpose of thesepolicies must be supervised and managed to gather APCFincome and improve public transportation infrastructures

42 Deficiencies and Future Work The present study consid-ered NOx and PMx as the principal motor vehicle emissionpollutants Future research must fully consider other com-ponents such as SO2 airborne particles hydrocarbons COand CO2 Secondly the implementation of a single chargingmeasure can reduce the supply level of public transportationFuture research should consider a subsidy mechanism toimprove the service quality Thirdly the function and effectof a single policy are limited Future work must considerthe integration of multiple policies to improve the emissionreduction effect For example future work may focus priorityon public transportation improvement of fuel quality vigor-ous promotion of new energy vehicles and improvements inemission standards

Appendix

A

See Table 11

B

Summary of the major variables and equations(1) Cost of motor vehicle trips = Air pollution charging

feelowast (1+ Air pollution control)(2) Amount ofNOx generation = INTEG (NOx emissions

- Annual dissipation of NOx 80380)(3) NOx emissions = Per vehicle annual of NOx

emissionslowast Amount of motor vehicle tripslowast Contributionrate of NOx from vehicle

(4) Contribution rate of NOx from vehicle = 05(5) Dissipation rate of NOx = 02(6) Annual dissipation of NOx = Amount of NOx

generationlowast Dissipation rate of NOx(7) Per vehicle annual of NOx emissions = 002

(8) Amount of PMx generation = INTEG (PMxemissions- Annual dissipation of PMx 160760)

(9) PMx emissions = Amount of motor vehicle tripslowastContribution rate of PMx from vehiclelowast Per vehicle annualof PMx emissions

(10) Contribution rate of PMx from vehicle = 05(11) Per vehicle annual of PMx emissions = 004(12) Annual dissipation of PMx = Amount of PMx

generationlowast Dissipation and control rate of PMx(13) Dissipation and control rate of PMx = 05(14) Pollution degree of NOx = IF THEN ELSE (Amount

of NOx generationgt= 11182e+005 09 IF THEN ELSE(Amount of NOx generationgt= 10874e+005 08 IF THENELSE (Amount of NOx generationgt= 10400e+005 07 IFTHEN ELSE (Amount of NOx generationgt= 9966e+00406 IF THEN ELSE (Amount of NOx generationgt=9618e+004 05 IF THEN ELSE (Amount of NOxgenerationgt= 8038e+004 03 IF THEN ELSE (Amountof NOx generationgt= 7008e+004 025 IF THEN ELSE(Amount of NOx generationgt= 6144e+004 02 IF THENELSE (Amount of NOx generationgt= 5508e+004 015 01)))))))))

(15) Pollution degree of PMx = IF THEN ELSE (Amountof PMx generationgt= 22364e+005 09 IF THEN ELSE(Amount of PMx generationgt= 21748e+005 08 IF THENELSE (Amount of PMx generationgt= 20800e+005 07 IFTHEN ELSE (Amount of PMx generationgt= 19932e+00506 IF THEN ELSE (Amount of PMx generationgt=19236e+005 05 IF THEN ELSE (Amount of PMxgenerationgt= 16076e+005 03 IF THEN ELSE (Amountof PMx generationgt= 14016e+005 025 IF THEN ELSE(Amount of PMx generationgt= 12288e+005 02 IF THENELSE (Amount of PMx generationgt= 11016e+005 015 01)))))))))

(16) Ratio of motor vehicle trips = 055(17) Amount of motor vehicle trips = Amount of motor

vehicleslowast Ratio of motor vehicle trips(18) Degree of air pollution = Weight ratio of NOxlowast

Pollution degree of NOx+ Weight ratio of PMxlowast Pollutiondegree of PMx

(19) Weight ratio of PMx = 05(20) Weight ratio of NOx = 05(21) Air pollution control = IF THEN ELSE (Degree of air

pollutiongt= 07 1 IF THEN ELSE (Degree of air pollutiongt=06 08 IF THEN ELSE (Degree of air pollutiongt= 05 07IF THEN ELSE (Degree of air pollutiongt= 04 06 IF THENELSE (Degree of air pollutiongt= 03 05 IF THEN ELSE(Degree of air pollutiongt= 025 045 IF THENELSE (Degreeof air pollutiongt= 02 04 IF THEN ELSE (Degree of airpollutiongt= 015 035 03))))))))

(22) Attraction degree of the growth of vehicles= (1-Airpollution control)lowast 055+ Attraction degree of vehicle tripslowast045

(23) Per capita annual income = Amount of GDPAmount of population

(24) Amount of population = INTEG (Growth of popu-lation+ Net migration- Population reduction 186e+007)

(25) Birth rate = Adjustment coefficient of birth ratelowastPredictive value of birth rate

Discrete Dynamics in Nature and Society 17

Table 11 Description of main variables in stock flow diagram

Signicant variable Unit Variable type Data sourceAir pollution charging fee yuandaysdotvehicle ConstantAir pollution control Dmnl Auxiliary variable M1+M3Amount of GDP yuan Level M1Amount of motor vehicles vehicle Level M1Amount of motor vehicle trips vehicle Auxiliary variableAmount of NOx (PMx) generation ton Level M1Amount of population person Level M1Annual dissipation of NOx (PMx) tonyear FlowAnnual scrapped vehicleyear FlowAttraction degree of city Constant M2Attraction degree of the growth of vehicles Auxiliary variable M1+M3Attraction degree of vehicle trips Auxiliary variable M1+M3Birth rate 1year Constant M3Contribution rate of NOx (PMx) from vehicle Constant M2Cost of motor vehicle trips yuandaysdotvehicle Auxiliary variable M3Death rate 1year Constant M3Degree of air pollution Dmnl Auxiliary variable M3Dissipation and control rate of NOx (PMx) 1year Constant M2Graphical function of the growth of GDP Dmnl Auxiliary variable M3Growth of GDP yuanyear FlowGrowth rate of motor vehicles 1year Auxiliary variable M1+M3Growth of motor vehicles vehicleyear FlowGrowth of population personyear FlowGrowth rate of vehicle ownership Dmnl Auxiliary variable M1+M3Impact factor of policy Dmnl Constant M3Net migration personyear FlowNet migration rate 1year Constant M1+M3NOx (PMx) emissions tonyear FlowPer capita annual income yuanperson Auxiliary variablePer vehicle annual of NOx (PMx) emissions tonyearsdotvehicle Constant M2Pollution degree of NOx (PMx) Dmnl Auxiliary variable M1+M3Population reduction personyear FlowRatio of motor vehicle trips Constant M2Scrap rate 1year Constant M2The average of net migration rate 1year Constant M1Weight ratio of PMx (NOx) Auxiliary variable M3

(26) Predictive value of birth rate = 000925(27) Death rate = Adjustment coefficient of death ratelowast

Predictive value of death rate(28) Predictive value of death rate = 000494(29) Net migration = Amount of populationlowastNet migra-

tion rate(30) Net migration rate = The average of net migration

ratelowast Attraction degree of cityand(Impact factor of policy)(31) Impact factor of policy = 15(32) The average of net migration rate = 000531(33) Attraction degree of city = 07056(34) Amount of GDP = INTEG (Growth of GDP

12153e+012)

(35) Graphical function of the growth of GDP = WITHLOOKUP (Amount of GDP ([(8e+011 0)- (3e+ 012 03)](81178e+011 01648) (98468e+011 0213) (11115e+01201288) (12153e+012 00934) (141136e+012 01613)(162519e+012 01515) (178794e+012 01001) (198008e+01201075) (213308e+012 00773) (230146e+012 00789)(235396e+012 002281) (240162e+012 00203) (245025e+012 002025) (249987e+012 002024) (255049e+0120020249)))

(36) Growth rate of GDP = Graphical function of thegrowth of GDPlowast Impact factor of the growth of GDP

(37) Amount of motor vehicles = INTEG (Growth ofmotor vehicles- Annual scrapped 4019e+006)

18 Discrete Dynamics in Nature and Society

(38) Annual scrapped = Amount of motor vehicleslowastScrap rate

(39) Scrap rate = 0067

Conflicts of Interest

The author declares no conflicts of interest

Acknowledgments

This work has been partially supported by the NationalNatural Science Foundation of China (71571119) ShanghaiFirst-Class Academic Discipline Project (S1201YLXK) andChina Postdoctoral Science Foundation (2018M630404)Theauthor would like to thank LetPub (httpwwwletpubcom)for providing linguistic assistance during the preparation ofthis manuscript

References

[1] X Liu S Ma J Tian N Jia and G Li ldquoA system dynamicsapproach to scenario analysis for urban passenger transportenergy consumption and CO2 emissions A case study ofBeijingrdquo Energy Policy vol 85 pp 253ndash270 2015

[2] B Xu L Luo and B Lin ldquoA dynamic analysis of air pollutionemissions in China Evidence from nonparametric additiveregression modelsrdquo Ecological Indicators vol 63 pp 346ndash3582016

[3] S Leinert H Daly B Hyde and B O Gallachoir ldquoCo-benefitsNot always Quantifying the negative effect of a CO2-reducingcar taxation policy on NOx emissionsrdquo Energy Policy vol 63pp 1151ndash1159 2013

[4] Z Cheng L Li and J Liu ldquoIdentifying the spatial effects anddriving factors of urban PM25 pollution in Chinardquo EcologicalIndicators vol 82 pp 61ndash75 2017

[5] N Kaida and K Kaida ldquoSpillover effect of congestion chargingon pro-environmental behaviorrdquo Environment Developmentand Sustainability vol 17 no 3 pp 409ndash421 2015

[6] R Penabaena-Niebles V Cantillo and J L Moura ldquoImpactof transition between signal timing plans in social cost basedin delay fuel consumption and air emissionsrdquo TransportationResearch Part D Transport and Environment vol 41 pp 445ndash456 2015

[7] DDing andB Shuai ldquoA traffic restriction scheme for enhancingcarpoolingrdquoDiscreteDynamics inNature and Society Article ID9626938 9 pages 2017

[8] D Kong X Guo B Yang and D Wu ldquoAnalyzing the Impactof Trucks on Traffic Flow Based on an Improved CellularAutomaton Modelrdquo Discrete Dynamics in Nature and Societyvol 2016 pp 1ndash14 2016

[9] S Cakmak C Hebbern J D Cakmak and J Vanos ldquoThemodifying effect of socioeconomic status on the relationshipbetween traffic air pollution and respiratory health in elemen-tary schoolchildrenrdquo Journal of Environmental Managementvol 177 pp 1ndash8 2016

[10] L Song H Song J Lin et al ldquoPM25 emissions from differenttypes of heavy-duty truck a case study and meta-analysis ofthe Beijing-Tianjin-Hebei regionrdquo Environmental Science andPollution Research vol 24 no 12 pp 11206ndash11214 2017

[11] Z Hu S Kang C Li et al ldquoLight absorption of biomassburning and vehicle emission-sourced carbonaceous aerosolsof the Tibetan Plateaurdquo Environmental Science and PollutionResearch vol 24 no 18 pp 15369ndash15378 2017

[12] X Cen H K Lo and L Li ldquoA framework for estimating trafficemissions The development of Passenger Car Emission UnitrdquoTransportation Research Part D Transport and Environmentvol 44 pp 78ndash92 2016

[13] S Wang X Liu C Zhou J Hu and J Ou ldquoExamining theimpacts of socioeconomic factors urban form and transporta-tion networks on CO2 emissions in Chinarsquos megacitiesrdquoAppliedEnergy vol 185 pp 189ndash200 2017

[14] Q Wang K Hubacek K Feng Y-M Wei and Q-M LiangldquoDistributional effects of carbon taxationrdquo Applied Energy vol184 pp 1123ndash1131 2016

[15] C Johansson L Burman and B Forsberg ldquoThe effects ofcongestions tax on air quality and healthrdquo Atmospheric Envi-ronment vol 43 no 31 pp 4843ndash4854 2009

[16] A Rakowska K C Wong T Townsend et al ldquoImpact of trafficvolume and composition on the air quality and pedestrianexposure in urban street canyonrdquo Atmospheric Environmentvol 98 pp 260ndash270 2014

[17] S Batterman R Ganguly and P Harbin ldquoHigh resolutionspatial and temporal mapping of traffic-related air pollutantsrdquoInternational Journal of Environmental Research and PublicHealth vol 12 no 4 pp 3646ndash3666 2015

[18] J Eliasson M Borjesson D van Amelsfort K Brundell-Freijand L Engelson ldquoAccuracy of congestion pricing forecastsrdquoTransportation Research Part A Policy and Practice vol 52 pp34ndash46 2013

[19] J Eliasson ldquoThe role of attitude structures direct experienceand reframing for the success of congestion pricingrdquo Trans-portation Research Part A Policy and Practice vol 67 pp 81ndash952014

[20] H X Yang J D Li H Zhang and S Q Liu ldquoResearch on thegovernance of urban traffic jam based on system dynamicsrdquoSystems EngineeringTheory and Practice vol 34 no 8 pp 2135ndash2143 2014 (Chinese)

[21] M H Zhu Research on Socio-Economic Impact of UrbanTrafficCongestion [PhD thesis] Beijing JiaotongUniversity 2013(Chinese)

[22] B Zeng Research on Modeling Technologies of Grey Prediction[PhD thesis] Nanjing University of Aeronautics and Astronau-tics 2011 (Chinese)

[23] S F Liu Y J Yang and L F Wu Grey System Theory andApplication Science Press Beijing China 2017

[24] S W Jia K Yang J J Zhao and G L Yan ldquoThe traffic-congestion charging fee management model based on thesystem dynamics approachrdquo Mathematical Problems in Engi-neering vol 2017 Article ID 3024898 13 pages 2017

Discrete Dynamics in Nature and Society 17

Table 11 Description of main variables in stock flow diagram

Signicant variable Unit Variable type Data sourceAir pollution charging fee yuandaysdotvehicle ConstantAir pollution control Dmnl Auxiliary variable M1+M3Amount of GDP yuan Level M1Amount of motor vehicles vehicle Level M1Amount of motor vehicle trips vehicle Auxiliary variableAmount of NOx (PMx) generation ton Level M1Amount of population person Level M1Annual dissipation of NOx (PMx) tonyear FlowAnnual scrapped vehicleyear FlowAttraction degree of city Constant M2Attraction degree of the growth of vehicles Auxiliary variable M1+M3Attraction degree of vehicle trips Auxiliary variable M1+M3Birth rate 1year Constant M3Contribution rate of NOx (PMx) from vehicle Constant M2Cost of motor vehicle trips yuandaysdotvehicle Auxiliary variable M3Death rate 1year Constant M3Degree of air pollution Dmnl Auxiliary variable M3Dissipation and control rate of NOx (PMx) 1year Constant M2Graphical function of the growth of GDP Dmnl Auxiliary variable M3Growth of GDP yuanyear FlowGrowth rate of motor vehicles 1year Auxiliary variable M1+M3Growth of motor vehicles vehicleyear FlowGrowth of population personyear FlowGrowth rate of vehicle ownership Dmnl Auxiliary variable M1+M3Impact factor of policy Dmnl Constant M3Net migration personyear FlowNet migration rate 1year Constant M1+M3NOx (PMx) emissions tonyear FlowPer capita annual income yuanperson Auxiliary variablePer vehicle annual of NOx (PMx) emissions tonyearsdotvehicle Constant M2Pollution degree of NOx (PMx) Dmnl Auxiliary variable M1+M3Population reduction personyear FlowRatio of motor vehicle trips Constant M2Scrap rate 1year Constant M2The average of net migration rate 1year Constant M1Weight ratio of PMx (NOx) Auxiliary variable M3

(26) Predictive value of birth rate = 000925(27) Death rate = Adjustment coefficient of death ratelowast

Predictive value of death rate(28) Predictive value of death rate = 000494(29) Net migration = Amount of populationlowastNet migra-

tion rate(30) Net migration rate = The average of net migration

ratelowast Attraction degree of cityand(Impact factor of policy)(31) Impact factor of policy = 15(32) The average of net migration rate = 000531(33) Attraction degree of city = 07056(34) Amount of GDP = INTEG (Growth of GDP

12153e+012)

(35) Graphical function of the growth of GDP = WITHLOOKUP (Amount of GDP ([(8e+011 0)- (3e+ 012 03)](81178e+011 01648) (98468e+011 0213) (11115e+01201288) (12153e+012 00934) (141136e+012 01613)(162519e+012 01515) (178794e+012 01001) (198008e+01201075) (213308e+012 00773) (230146e+012 00789)(235396e+012 002281) (240162e+012 00203) (245025e+012 002025) (249987e+012 002024) (255049e+0120020249)))

(36) Growth rate of GDP = Graphical function of thegrowth of GDPlowast Impact factor of the growth of GDP

(37) Amount of motor vehicles = INTEG (Growth ofmotor vehicles- Annual scrapped 4019e+006)

18 Discrete Dynamics in Nature and Society

(38) Annual scrapped = Amount of motor vehicleslowastScrap rate

(39) Scrap rate = 0067

Conflicts of Interest

The author declares no conflicts of interest

Acknowledgments

This work has been partially supported by the NationalNatural Science Foundation of China (71571119) ShanghaiFirst-Class Academic Discipline Project (S1201YLXK) andChina Postdoctoral Science Foundation (2018M630404)Theauthor would like to thank LetPub (httpwwwletpubcom)for providing linguistic assistance during the preparation ofthis manuscript

References

[1] X Liu S Ma J Tian N Jia and G Li ldquoA system dynamicsapproach to scenario analysis for urban passenger transportenergy consumption and CO2 emissions A case study ofBeijingrdquo Energy Policy vol 85 pp 253ndash270 2015

[2] B Xu L Luo and B Lin ldquoA dynamic analysis of air pollutionemissions in China Evidence from nonparametric additiveregression modelsrdquo Ecological Indicators vol 63 pp 346ndash3582016

[3] S Leinert H Daly B Hyde and B O Gallachoir ldquoCo-benefitsNot always Quantifying the negative effect of a CO2-reducingcar taxation policy on NOx emissionsrdquo Energy Policy vol 63pp 1151ndash1159 2013

[4] Z Cheng L Li and J Liu ldquoIdentifying the spatial effects anddriving factors of urban PM25 pollution in Chinardquo EcologicalIndicators vol 82 pp 61ndash75 2017

[5] N Kaida and K Kaida ldquoSpillover effect of congestion chargingon pro-environmental behaviorrdquo Environment Developmentand Sustainability vol 17 no 3 pp 409ndash421 2015

[6] R Penabaena-Niebles V Cantillo and J L Moura ldquoImpactof transition between signal timing plans in social cost basedin delay fuel consumption and air emissionsrdquo TransportationResearch Part D Transport and Environment vol 41 pp 445ndash456 2015

[7] DDing andB Shuai ldquoA traffic restriction scheme for enhancingcarpoolingrdquoDiscreteDynamics inNature and Society Article ID9626938 9 pages 2017

[8] D Kong X Guo B Yang and D Wu ldquoAnalyzing the Impactof Trucks on Traffic Flow Based on an Improved CellularAutomaton Modelrdquo Discrete Dynamics in Nature and Societyvol 2016 pp 1ndash14 2016

[9] S Cakmak C Hebbern J D Cakmak and J Vanos ldquoThemodifying effect of socioeconomic status on the relationshipbetween traffic air pollution and respiratory health in elemen-tary schoolchildrenrdquo Journal of Environmental Managementvol 177 pp 1ndash8 2016

[10] L Song H Song J Lin et al ldquoPM25 emissions from differenttypes of heavy-duty truck a case study and meta-analysis ofthe Beijing-Tianjin-Hebei regionrdquo Environmental Science andPollution Research vol 24 no 12 pp 11206ndash11214 2017

[11] Z Hu S Kang C Li et al ldquoLight absorption of biomassburning and vehicle emission-sourced carbonaceous aerosolsof the Tibetan Plateaurdquo Environmental Science and PollutionResearch vol 24 no 18 pp 15369ndash15378 2017

[12] X Cen H K Lo and L Li ldquoA framework for estimating trafficemissions The development of Passenger Car Emission UnitrdquoTransportation Research Part D Transport and Environmentvol 44 pp 78ndash92 2016

[13] S Wang X Liu C Zhou J Hu and J Ou ldquoExamining theimpacts of socioeconomic factors urban form and transporta-tion networks on CO2 emissions in Chinarsquos megacitiesrdquoAppliedEnergy vol 185 pp 189ndash200 2017

[14] Q Wang K Hubacek K Feng Y-M Wei and Q-M LiangldquoDistributional effects of carbon taxationrdquo Applied Energy vol184 pp 1123ndash1131 2016

[15] C Johansson L Burman and B Forsberg ldquoThe effects ofcongestions tax on air quality and healthrdquo Atmospheric Envi-ronment vol 43 no 31 pp 4843ndash4854 2009

[16] A Rakowska K C Wong T Townsend et al ldquoImpact of trafficvolume and composition on the air quality and pedestrianexposure in urban street canyonrdquo Atmospheric Environmentvol 98 pp 260ndash270 2014

[17] S Batterman R Ganguly and P Harbin ldquoHigh resolutionspatial and temporal mapping of traffic-related air pollutantsrdquoInternational Journal of Environmental Research and PublicHealth vol 12 no 4 pp 3646ndash3666 2015

[18] J Eliasson M Borjesson D van Amelsfort K Brundell-Freijand L Engelson ldquoAccuracy of congestion pricing forecastsrdquoTransportation Research Part A Policy and Practice vol 52 pp34ndash46 2013

[19] J Eliasson ldquoThe role of attitude structures direct experienceand reframing for the success of congestion pricingrdquo Trans-portation Research Part A Policy and Practice vol 67 pp 81ndash952014

[20] H X Yang J D Li H Zhang and S Q Liu ldquoResearch on thegovernance of urban traffic jam based on system dynamicsrdquoSystems EngineeringTheory and Practice vol 34 no 8 pp 2135ndash2143 2014 (Chinese)

[21] M H Zhu Research on Socio-Economic Impact of UrbanTrafficCongestion [PhD thesis] Beijing JiaotongUniversity 2013(Chinese)

[22] B Zeng Research on Modeling Technologies of Grey Prediction[PhD thesis] Nanjing University of Aeronautics and Astronau-tics 2011 (Chinese)

[23] S F Liu Y J Yang and L F Wu Grey System Theory andApplication Science Press Beijing China 2017

[24] S W Jia K Yang J J Zhao and G L Yan ldquoThe traffic-congestion charging fee management model based on thesystem dynamics approachrdquo Mathematical Problems in Engi-neering vol 2017 Article ID 3024898 13 pages 2017

18 Discrete Dynamics in Nature and Society

(38) Annual scrapped = Amount of motor vehicleslowastScrap rate

(39) Scrap rate = 0067

Conflicts of Interest

The author declares no conflicts of interest

Acknowledgments

This work has been partially supported by the NationalNatural Science Foundation of China (71571119) ShanghaiFirst-Class Academic Discipline Project (S1201YLXK) andChina Postdoctoral Science Foundation (2018M630404)Theauthor would like to thank LetPub (httpwwwletpubcom)for providing linguistic assistance during the preparation ofthis manuscript

References

[1] X Liu S Ma J Tian N Jia and G Li ldquoA system dynamicsapproach to scenario analysis for urban passenger transportenergy consumption and CO2 emissions A case study ofBeijingrdquo Energy Policy vol 85 pp 253ndash270 2015

[2] B Xu L Luo and B Lin ldquoA dynamic analysis of air pollutionemissions in China Evidence from nonparametric additiveregression modelsrdquo Ecological Indicators vol 63 pp 346ndash3582016

[3] S Leinert H Daly B Hyde and B O Gallachoir ldquoCo-benefitsNot always Quantifying the negative effect of a CO2-reducingcar taxation policy on NOx emissionsrdquo Energy Policy vol 63pp 1151ndash1159 2013

[4] Z Cheng L Li and J Liu ldquoIdentifying the spatial effects anddriving factors of urban PM25 pollution in Chinardquo EcologicalIndicators vol 82 pp 61ndash75 2017

[5] N Kaida and K Kaida ldquoSpillover effect of congestion chargingon pro-environmental behaviorrdquo Environment Developmentand Sustainability vol 17 no 3 pp 409ndash421 2015

[6] R Penabaena-Niebles V Cantillo and J L Moura ldquoImpactof transition between signal timing plans in social cost basedin delay fuel consumption and air emissionsrdquo TransportationResearch Part D Transport and Environment vol 41 pp 445ndash456 2015

[7] DDing andB Shuai ldquoA traffic restriction scheme for enhancingcarpoolingrdquoDiscreteDynamics inNature and Society Article ID9626938 9 pages 2017

[8] D Kong X Guo B Yang and D Wu ldquoAnalyzing the Impactof Trucks on Traffic Flow Based on an Improved CellularAutomaton Modelrdquo Discrete Dynamics in Nature and Societyvol 2016 pp 1ndash14 2016

[9] S Cakmak C Hebbern J D Cakmak and J Vanos ldquoThemodifying effect of socioeconomic status on the relationshipbetween traffic air pollution and respiratory health in elemen-tary schoolchildrenrdquo Journal of Environmental Managementvol 177 pp 1ndash8 2016

[10] L Song H Song J Lin et al ldquoPM25 emissions from differenttypes of heavy-duty truck a case study and meta-analysis ofthe Beijing-Tianjin-Hebei regionrdquo Environmental Science andPollution Research vol 24 no 12 pp 11206ndash11214 2017

[11] Z Hu S Kang C Li et al ldquoLight absorption of biomassburning and vehicle emission-sourced carbonaceous aerosolsof the Tibetan Plateaurdquo Environmental Science and PollutionResearch vol 24 no 18 pp 15369ndash15378 2017

[12] X Cen H K Lo and L Li ldquoA framework for estimating trafficemissions The development of Passenger Car Emission UnitrdquoTransportation Research Part D Transport and Environmentvol 44 pp 78ndash92 2016

[13] S Wang X Liu C Zhou J Hu and J Ou ldquoExamining theimpacts of socioeconomic factors urban form and transporta-tion networks on CO2 emissions in Chinarsquos megacitiesrdquoAppliedEnergy vol 185 pp 189ndash200 2017

[14] Q Wang K Hubacek K Feng Y-M Wei and Q-M LiangldquoDistributional effects of carbon taxationrdquo Applied Energy vol184 pp 1123ndash1131 2016

[15] C Johansson L Burman and B Forsberg ldquoThe effects ofcongestions tax on air quality and healthrdquo Atmospheric Envi-ronment vol 43 no 31 pp 4843ndash4854 2009

[16] A Rakowska K C Wong T Townsend et al ldquoImpact of trafficvolume and composition on the air quality and pedestrianexposure in urban street canyonrdquo Atmospheric Environmentvol 98 pp 260ndash270 2014

[17] S Batterman R Ganguly and P Harbin ldquoHigh resolutionspatial and temporal mapping of traffic-related air pollutantsrdquoInternational Journal of Environmental Research and PublicHealth vol 12 no 4 pp 3646ndash3666 2015

[18] J Eliasson M Borjesson D van Amelsfort K Brundell-Freijand L Engelson ldquoAccuracy of congestion pricing forecastsrdquoTransportation Research Part A Policy and Practice vol 52 pp34ndash46 2013

[19] J Eliasson ldquoThe role of attitude structures direct experienceand reframing for the success of congestion pricingrdquo Trans-portation Research Part A Policy and Practice vol 67 pp 81ndash952014

[20] H X Yang J D Li H Zhang and S Q Liu ldquoResearch on thegovernance of urban traffic jam based on system dynamicsrdquoSystems EngineeringTheory and Practice vol 34 no 8 pp 2135ndash2143 2014 (Chinese)

[21] M H Zhu Research on Socio-Economic Impact of UrbanTrafficCongestion [PhD thesis] Beijing JiaotongUniversity 2013(Chinese)

[22] B Zeng Research on Modeling Technologies of Grey Prediction[PhD thesis] Nanjing University of Aeronautics and Astronau-tics 2011 (Chinese)

[23] S F Liu Y J Yang and L F Wu Grey System Theory andApplication Science Press Beijing China 2017

[24] S W Jia K Yang J J Zhao and G L Yan ldquoThe traffic-congestion charging fee management model based on thesystem dynamics approachrdquo Mathematical Problems in Engi-neering vol 2017 Article ID 3024898 13 pages 2017

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