Research Article Route Choice of the Shortest Travel Time

Research ArticleRoute Choice of the Shortest Travel Time Based onFloating Car Data

Jingwei Shen1 and Yifang Ban2

1School of Geographical Sciences Southwest University Chongqing 400715 China2Division of Geoinformatics KTH Royal Institute of Technology Stockholm Sweden

Correspondence should be addressed to Jingwei Shen sjwgisswueducn

Received 30 April 2016 Revised 5 September 2016 Accepted 4 October 2016

Academic Editor Biswajeet Pradhan

Copyright copy 2016 J Shen and Y Ban This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Finding a routewith shortest travel time according to the traffic condition can help travelers tomake better route choice decisions Inthis paper the shortest travel time based on FCD (floating car data) which is used to assess overall traffic conditions is proposed Tobetter fit FCD and roadmap a newmapmatching algorithmwhich fully considers distance factor direction factor and accessibilityfactor is designed to map all GPS (Global Positioning System) points to roads A mixed graph structure is constructed and a routeanalysis algorithm of shortest travel time which considers the dynamic edge weight is designed By comparing with other mapmatching algorithms the proposed method has a higher accuracyThe comparison results show that the shortest travel time path islonger than the shortest distance path but it costs less traveling timeThe implementation of the route choice based on the shortesttravel time method can be used to guide peoplersquos travel by selecting the space-time dependent optimal path

1 Introduction

There is an urgent need to obtain the traffic dynamics in a cityfor traffic guidance By providing effective traffic informationit can help travelers to make better route choice decisionsQueries of the type ldquohow do we get traffic informationrdquo andldquowhich path is the shortest distance between two vertices in agraphrdquo are widely addressed while queries of the type ldquohowdo we get traffic information efficiently and economicallyrdquoand ldquowhich path is the shortest travel time between twovertices in a graphrdquo need further analysis

Although traffic information on road networks can becollected by induction loops or visual systems it is difficultto obtain an accurate estimation of the instantaneous traveltime from the local traffic speed and flow data [1] The spa-tiotemporal distribution of traffic congestions demonstratesa multinuclear structure in urban road networks [2] Withthe availability of inexpensive positioning technology it ispossible to use historical navigation data to model the trafficflow at different times on a particular day

In recent years an increasing number of cars havebeen equipped with GPS (Global Positioning System) FCD

(floating car data) collects traffic information including real-time position direction speed and other information If thisFCD system achieves more than 15 of penetration rate [3]the service quality in urban traffic would be good enoughThe results from a large-scale freeway and arterial experimenthave highlighted the significance of FCD for traffic man-agement [4] So far there are abundant researches about thefloating car and its applications such as detecting hot spots[5ndash7] road networks updating [8 9] traffic prediction [10 11]experiential optimal paths [12] and spatiotemporal patterns[13] Having large amounts of vehicles collecting data for anurban area it will create an accurate picture of the trafficcondition in time and space [14] Nowadays it is possible tostudy the spatiotemporal characteristics of the traffic flow byanalyzing the FCD

In comparison to fixed traffic sensors FCD is capable ofproviding a robust overview of current road traffic conditionsat significantly less cost [15] A new operational system basedon information from a cellular phone service provider formeasuring traffic speeds and travel times was conducted [16]The main finding is that there is a good match between FCDmeasurements and dual magnetic loop detectors

Hindawi Publishing CorporationJournal of SensorsVolume 2016 Article ID 7041653 11 pageshttpdxdoiorg10115520167041653

2 Journal of Sensors

Pfoser et al showcased a system which facilitates the col-lection of FCD produces dynamic travel time informationand provides value-added services based on the dynamictravel times [14] However a basic problem was the limitedvehicle penetration and insufficient data coverage Kestingand Treiber considered a vehicle-based approach to collecttraffic data and used the data to estimate the upstreamand downstream fronts of a traffic jam [17] However thisestimation did not allow predicting travel timewhich becamerelevant when no probe vehicle passed the roadside units fora while

Because of GPS measurement errors and road geometricerrors in digital maps the GPS locations of probe vehiclesmay not appear on network links [18] Therefore it isnecessary not only to match the GPS points to the roadnetworks but also to get the route of the consecutive GPSpoints There are a number of works that propose methodsfor map matching An incremental algorithm that matchesconsecutive portions of the trajectory to the roadnetwork andtwo global algorithms that compared the entire trajectory tocandidate paths in the road network were proposed [19] Dueto limitations in the tracking data and the road network ofglobal algorithms the matching results need to be evaluatedto discard portions of bad matches Adaptive Clipping algo-rithm which takes tracking error estimates into account wasintroduced to solve this map matching task [20] Howeverthe quality of this map matching algorithm was not assessedThe procedures and algorithms for the computation andmapmatching of road segment velocities to a digital road networkwere presented [21] Because lots of adjacent GPS pointsbelong to the different roads the consideration of directionand distance factors only is not enough for map matching

Analysis studies of traffic conditions based on FCD werebecoming more prominent Mean link travel time basedon the classification for the traffic flow offset control andmoving direction at downstream signalized intersections inurban traffic networks was studied [22] The mean originand destination (OD) travel time was evaluated by summingup the mean travel time of each link in traffic networksTraffic state was detected with FCD [23] A statistical analysisshowed the high quality of the reconstruction of the actualtravel times in the net with only 15 equipped with FCDvehicles The probe-car system was used to predict trafficcongestion in the immediate future [24] A basic model forpredicting traffic congestion in the immediate future usingpheromone was developed Traffic quality was provided bythe aggregation and evaluation of FCD with a commonevaluation scheme [25] GPS traffic-related data for trafficmonitoring and control was presented and the scope oftraffic information was illustrated [26] However this study islimited in analyzing the road situation and does not providethe accurate traveling time

In this paper there are two important problems to beaddressed in order to better guide the route choice The firstis the acquisition of the road traffic situation from FCD Thesecond is to find a route with the shortest travel time bydesigning an optimal route analysis algorithm

The two main contributions of this paper are the follow-ing

(1) A newmapmatching algorithmwhich fully considersthe distance factor direction factor and accessibilityfactor is proposed This algorithm can be used toacquire the road traffic situation

(2) A shortest travel time algorithm is designed Animproved Dijkstra algorithm is proposed and traveltime is assigned to edges as the dynamic weight of theroad

The paper is organized as follows In Section 2 FCDare presented and two algorithms including map matchingalgorithmand the shortest travel time algorithmare designedIn Section 3 experiments are implemented to verify theproposed methods In Section 4 map matching algorithmand the average driving speed of roads based on historicalFCD are discussed Lastly Section 5 presents the conclusionsand points to the future work

2 Materials and Methods

21 Data Description The original FCD is collected fromover 11 thousand taxicabs fromWuhan in September 2009 atregular intervals (average 20ndash60 seconds) during the coursesof six days Wuhan is the capital of Hubei province ChinaIt is located in the eastern Jianghan Plain at the intersectionof the middle reaches of the Yangtze and Han Rivers It is amajor transportation hub with dozens of railways roads andexpressways passing through the city It has a population of91000000 people in 2009 [27]The number of cars inWuhanis about 556 thousand in 2008 [28]

The FCD samples achieve a sufficient penetration ratewith 19 to calculate the traffic informationThere are morethan 85 million records in total (over 14 million per day)with attributes of timestamp CarID 119883 119884 speed and angleA timestamp is a sequence of characters usually giving theaccurate date and time of day CarID is a unique identificationof a taxicab 119883 and 119884 are longitude and latitude respectivelyrecording the location of the taxicab Speed is the instantspeed of the taxicab at a given time Angle is defined as ahorizontal angle measured clockwise from a north base lineBrockfeld et al concluded that the Taxi-FCD system is able todeliver valuable travel time information for mobility servicesand the average travel times can be detected and calculatedreliably [29] Table 1 shows some typical FCD records

22 Methodology

221 Map Matching Algorithm Because of the GPS error ordigital map measurement error the deviation phenomenonbetween FCD and map often exists The objective of thissection is to develop a map matching algorithm for FCD toassess the traffic condition The core of this map matchingalgorithm proceeds as follows (Figure 1) The original GPSpoints and roads are showed in Figure 1(a) Then location isdetermined for eachGPSpoint GPSpoints aremapmatchingto the corresponding position of the road in Figure 1(b)Furthermore the route of the adjacent points is determinedA route is given to describe the path of the points inFigure 1(c)

Journal of Sensors 3

Table 1 Samples of typical FCD records

Timestamp CarID 119883 119884 Speed Angle1236441601 124410 114311215 30610151 16511 124381236441601 123259 114305106 30613588 1016 124991236441701 117247 11429426 30619716 10653 29987

GPS pointsRoad

(a)

GPS pointsMatching points

(b)RouteMatching points

(c)

Figure 1 The process of the map matching algorithm

In the location determination phase a comprehensivemodel (formula (1)) which includes the distance factordirection factor and accessibility factor is fully consideredDistance factor denotes the vertical distance between GPSpoint and road Direction factor is the angle of the car drivingdirection and the road azimuth Accessibility factor is thespatial accessibility of adjacent GPS points in timeMoreover

119891 (MM) = 119892 (Dis) + ℎ (Dir) + 119897 (Acc) (1)

119892 (Dis) = 119882dis timesMaxdis minus Dis

Maxdis (2)

ℎ (Dir) = 119882dir timesMaxdir minus Dir

Maxdir (3)

119897 (Acc) = 119882acc timesMaxacc minus Dispp

Maxacc (4)

where 119891(MM) is the comprehensive result of distancedirection and accessibility factors and map matching isabbreviated as MM The parameters of 119892(Dis) ℎ(Dir) and119897(Acc) are distance factor direction factor and accessibilityfactor respectively Distance direction and accessibility areabbreviated as Dis Dir and Acc respectively 119882dis 119882dirand 119882acc are the weight of distance factor direction factorand accessibility factor respectively The sum of the 119882dis119882dir and 119882acc is 1 Dis and Maxdis represent the distanceto the road and the maximum distance of the road bufferrespectively Dir denotes the angle between driving directionand road azimuth Maxdir is the maximum angle betweendriving direction and road azimuth Dispp and Maxacc arethe distance of the adjacent points and themaximumdistanceof the car within a certain time According to formula (1) acomprehensive maximum value of the road is selected

The shortest path algorithm is to find a path betweentwo vertices in a graph such that the sum of the weights ofits constituent edges is minimized Dijkstrarsquos algorithm [30]Floyd-Warshall algorithm [31] 119860

lowast search algorithm [32]

and their improved algorithms were widely used to find theshortest paths Onemerit of Dijkstrarsquos algorithm is to stop thealgorithm once the shortest path to the destination node hasbeen determined In the route determination phase Dijkstrarsquosalgorithm is designed to implement the route analysis Dueto large amount of the data the shortest path algorithm istime consuming Quadtree index is introduced to acceleratethe speed of the shortest path algorithm The framework ofthe proposed algorithm consists of three steps initializationsearching and the shortest path calculation

In Step 1 (initialization) road networks data is preloadedinto memory in order to search the shortest path Quadtreeindex is constructed in order to facilitate the spatial queryin the road network Each road segment is constructed as arectangle which is inserted into the Quadtree

In Step 2 (searching) searching rectangle is constructedto index the related roads Two adjacent GPS points areintroduced to construct the bounding boxThere is a distancelimitation in a given time period for a taxicab So themaximum distance in a given time is applied to extend thesearching area After construction of the searching area therelated roads to calculate the shortest path can be selected

In Step 3 (shortest path calculation) Dijkstrarsquos algorithmis designed to solve the shortest path problem Because theroad networks can be viewed as a sparse graph list structureis defined to accelerate the route searching By connecting allthe adjacent points the taxicab route can be acquired

222 Route Analysis The shortest path problem is to finda path between two vertices (or nodes) in a graph suchthat the sum of the edge weights is minimized Routechoice of the shortest travel time can also be taken as theshortest path problem The edge weight is the travel timeThe difference from the traditional shortest path problemis that the edge weight is dynamically changed over timeThis section introduces the calculation method for the routechoice of the shortest time


E1 E2

E5

E7E6

E3 E4

A1 A3

A8A5 A7

A2 A4

A6 A9

A10 A12

A11 A13

Figure 2 Analysis of a mixed graph

Graph

Node2

Node1

Nodelist

Node1

NodeID

Edge2

Edge1

EdgeList

Edge1

Length

EdgeID

bSingleWay

StartID

EndID

Time1 rate1

htTimeRate

Time rate

Time2 rate2

Weight

Node2 Edge2middot middot middot

middot middot middot



Edge

Edge

Node

Node

Figure 3 Hierarchical relationship of Graph Node and Edge Classes

Road network is constructed to conduct the route anal-ysis Node Information and Edge Information are createdfirstly from road segments for further analysis The NodeInformation includes three parts PointID Lon and LatPointID is the identification of the point Lon represents thelongitude of the point Lat denotes the latitude of the pointA new data table named Node Information is created to storethe above information Edge Information records the startand end point identifications of the edge Meanwhile twocolumns named StartID and EndID are added to the attributetable of road segment StartID and EndID are the foreign keysthat are consistent with the PointID of the Node Informationtable

According to the Node Information and Edge Informa-tion the network can be constructed Because some roadsegments are single way sharing a common node does notmean that the two segments can have access to each other Inthe following section single way and two-way road segmentsare further discussed

Road network is a typical mixed graph (Figure 2) Someof the road segments are one-way and others are two-wayEach undirected road segment as two-directed edge with theopposite directions is reset in Figure 2

Three classes including Node Edge and Graph aredesigned for the route analysis The hierarchical relationshipof those three classes can be depicted in Figure 3 The road

network can be taken as a sparse graph so the adjacent liststructure is used to store the relation of the Node and EdgeGraphClass contains the node collectionNodeClass includesnode identification and edge collection from this nodeEdge Class contains the edge identification edge lengthbSingleWay StartID EndID Weight and htTimeRate wherebSingleWay represents whether the edge is one-way or notand htTimeRate is a hash table that records the driving speedof roads at different TimeSlice

Based on Figure 3 route analysis of shortest travel timeis designed Traditionally the road segment weight is a staticvariable In this study the edge weight changes with timeto solve dynamic edge weight problem Figure 4 is takenas a case to explain the process of the shortest travel timeand the results of every step are listed in Table 2 Theminimum cost edge is selected and the corresponding pointis placed into a set named 119878 every step in Table 2 Firstlyoriginal point destination point and departure time are setup In Figure 4 119873

5 1198734 and 800 are the original point

destination point and departure time respectively Secondlythe minimum time cost of edge (⟨119873

5 1198736⟩ is the minimum

time cost of edge because it takes 10 minutes from 1198735to 1198736

and 810 is less than arriving time from 1198735to other points)

from original point (1198735in Figure 4) is selected Following

steps show the calculation process of travel time for eachedge


800

Start point

End point

Road

N5

N6N7 N8

N4N3N2

N1

Figure 4 A case study for the shortest travel time

(a) CurRate that is the average driving speed at Current-Time on the road is acquired from htTimeRate CurrentTimeis the driving time of the vehicle

(b) Remainingtime that is the rest time of the TimeSliceis calculated by formula (5) TimeSlice is the smallest unit oftime period for statistics information of the driving speed ofroads INTmeans that the integer part of the floating numberis acquired

(c) If the Remainingtime of this TimeSlice with this ratecan complete this road segment then the edge weight iscalculated by formula (6) eLength and eWeight are thelength and the weight of the road segment respectively

(d) If in the Remainingtime of this TimeSlice with thisrate the car cannot pass through this road segment then usethe next TimeSlice and its rate to compute the driving lengthuntil the car can finish the road segments in the TimeSlice Ifthis road segment has been traveled through then assign theweight to this edge

119877119890119898119886119894119899119894119899119892119879119894119898119890

= (119868119873119879 (119862119906119903119903119890119899119905119879119894119898119890 divide 119879119894119898119890119878119897119894119888119890) + 1)

times 119879119894119898119890119878119897119894119888119890 minus 119862119906119903119903119890119899119905119879119894119898119890

(5)

119890119882119890119894119892ℎ119905 = 119890119871119890119899119892119905ℎ divide 119862119906119903119877119886119905119890 (6)

Thirdly theminimumweight of the edge relating to otherpoints which is named 119873

7in Figure 4 is marked It means

that this node has been searched andwill not be considered inthe following steps Fourthly loop to update the edges weightif path passes 119873

7and nearer to the original point Fifthly

continue to select next minimum weight edge and add thepoint until the destination point is found Lastly the path ofshortest travel time from the original point to the destinationpoint is acquired The path of ⟨119873

5 1198736 1198737 1198733 1198734⟩ is short

travel time from1198735to1198734in Figure 4

Because road length is not equal to road weight whichis dynamically changed over time edges cannot be sortedby length This algorithm runs in 119874(|119881|

2

) (where |119881| is thenumber of vertices)

3 Results

31 Map Matching Result Continuous trajectory of the taxi-cabs can be acquired by the proposedmapmatchingmethod

Firstly GPS points are projected to roads Then the shortestpath algorithm is used to acquire the path of the adjacentpoints Finally the spatiotemporal position of taxicabs isobtained (Figure 5) Figure 5 shows the map matchingresult of FCD Figure 5(a) is the random five taxicabs inFCD database in 24 hours The primary GPS points arediscrete points in space Figure 5(b) displays the result of thetrajectory of the five taxicabs By the proposedmapmatchingcontinuous trajectory of the taxicabs is well acquired

32 Spatiotemporal Rate of the Road The weekend andweekday have different patterns in traffic [7] Therefore theweekday and weekend are separated to study the road trafficsituation The taxicabs in the study area are continuouslydriven for more pickups to maximum profits The taxicabsspeed of all 24 hours can be acquired The driving speed ofroads is calculated in every TimeSlice TimeSlice cannot betoo long or short Too short time will lead to inadequaterecords and too long time will result in low time accuracyVarious studies indicated that the minimum informationrate should be between 10 minutes and 3 minutes [33 34]After consideration of various factors TimeSlice calculationformula is represented as follows

119879119894119898119890119878119897119894119888119890 = 119879119886119909119894119873119890119890119889 divide119879119886119909119894119873119906119898

119877119900119886119889119878119890119892119873119906119898

times119877119900119886119889119871119890119899119860V119892119878119901119890119890119889119860V119892

(7)

where TaxiNeed is the minimal number of taxis to calculatethe average speed TaxiNum denotes the total number oftaxicabs in study area RoadSegNum is the total numberof the road segments 119879119886119909119894119873119906119898 divide 119877119900119886119889119878119890119892119873119906119898 repre-sents the average number of taxicabs every instantaneousmoment RoadLenAvg represents the average length of theroad segments SpeedAvg denotes the average speeds of all thetaxicabs and 119877119900119886119889119871119890119899119860V119892 divide 119878119901119890119890119889119860V119892 means the averagedriving time of the car on the road segments In this studythe result of TimeSlice is 23804 seconds In order to calculateconveniently the integer of TimeSlice as 240 seconds is takenGPS points are selected to compute the average speed of theroad for every slice Most of the taxicabs are concentrated inthe city center and nearby If the road has no GPS points thelimit speed of the road is taken as themean speed of this road

Three roads are selected randomly to calculate the averagedriving speed of every weekday fromFCD that is DingziqiaoRoad (in the lower right corner of Figure 6(a)) WuhanYangtze River Bridge (in the middle of Figure 6(a)) andXinhua Road (in the upper left corner of Figure 6(a)) Themean speeds of the Dingziqiao Road Wuhan Yangtze RiverBridge and Xinhua Road are presented in Figures 6(b) 6(c)and 6(d) respectively

The four weekdays in the same road present a similarpattern in Figures 6(b)ndash6(d) Generally speaking all of thethree roads have two rush hours and the rush hours appeararound 800 and 1800 An obvious decline period from 000to 400 and an obvious rising period from 400 to 800 areshowed


Table2Th

eprocessof

thes

hortesttraveltim

efor

Figure

4

Destin

ation

Thep

athandthea

rrivaltim

efrom

1198735to

othern

odes

1198731

infininfin

infin850

⟨1198735119873611987321198731⟩

850

⟨1198735119873611987321198731⟩

850

⟨1198735119873611987321198731⟩

1198732

infin830

⟨119873511987361198732⟩

830

⟨119873511987361198732⟩

mdashmdash

mdash1198733

infininfin

830

⟨1198735119873611987371198733⟩

830

⟨1198735119873611987371198733⟩

mdashmdash

1198734

infininfin

infininfin

840

⟨11987351198736119873711987331198734⟩

840

⟨11987351198736119873711987331198734⟩

1198736

810

⟨11987351198736⟩

mdashmdash

mdashmdash

mdash1198737

infin820

⟨119873511987361198737⟩

mdashmdash

mdashmdash

1198738

infininfin

835

⟨1198735119873611987371198738⟩

835

⟨1198735119873611987371198738⟩

835

⟨1198735119873611987371198738⟩

mdash119878

11987351198736

119873511987361198737

1198735119873611987371198732

11987351198736119873711987321198733

119873511987361198737119873211987331198738

1198735119873611987371198732119873311987381198734


(a) (b)

Figure 5 Map matching of FCD (a) FCD of the five taxicabs (b) Trajectory of the taxicabs after map matching

(a)

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14 16 18 20 22 24

March 09 (Monday)March 10 (Tuesday)

March 12 (Thursday)March 13 (Friday)

Mea

n sp

eed

(ms

)

Time of day (hour)

(b)



Mea

n sp

eed

(ms

)

Time of day (hour)

02468

101214161820

0 2 4 6 8 10 12 14 16 18 20 22 24

(c)



Mea

n sp

eed

(ms

)

Time of day (hour)

0

2

4

6

8

10

12

14

16

18

0 2 4 6 8 10 12 14 16 18 20 22 24

(d)

Figure 6The position of the roads and the mean speed (a) Position of roads inWuhan (b) Mean speed of Dingziqiao Road (c) Mean speedof Wuhan Yangtze River Bridge (d) Mean speed of Xinhua Road

Since the average speed of roads can reflect the trafficinformation of roads the spatiotemporal distribution of theroad speed at every slice is investigated Figure 7 shows themean speed of roads about four weekdays at two typicalinstantaneous moments

Following conclusions can be drawn from Figure 7Generally the driving speed of all roads changes over timeSpecifically the driving speed of roads in the rush hour(0800) is lower than that in other hours (0600) The averagedriving speed of roads at the centers of the city or nearby is


0600plusmn

0ndash5

5ndash10

10ndash1

515

ndash20

20ndash2

5

(a)

0ndash5

5ndash10

10ndash1

515

ndash20

20ndash2

5

0800 plusmn

(b)

Figure 7 Illustration of spatiotemporal distribution of the average road speed (weekdays) (a) Average road speed at six AM (b) Averageroad speed at eight AM

(a) (b)

(c)

Figure 8 Prototype of the route choice (a)The shortest distance path (b)The shortest travel time path (departure time six AM weekdays)(c) The shortest travel time path (departure time eight AM weekdays)

lower than that at the suburb whereas the change of drivingspeed of roads at the centers of the city or nearby is greaterthan that at the suburb

33 The Shortest Travel Time Path Experiment According tothe improved Dijkstra algorithm the route choice prototypeis developed Both the shortest distance path and the shortesttravel time path function are implemented Since they mayproduce different results the same starting point and endpoint are chosen for route analysis in the following threeexperiments The experimental results show the differentcharacteristics (Figure 8) Figure 8(a) shows the shortestdistance path In Figure 8(b) the departure time is set to60000 and the shortest travel time path is illustrated InFigure 8(c) the departure time is set to 80000 and theshortest travel time path is illustrated

4 Discussion

41 Analysis of the Map Matching Algorithm The accuracyof map matching algorithm has a significant impact on theacquirement of road situation Therefore the accuracy is animportant factor in the experiment All FCD within a day(over 14 million records) are selected to verify the proposedalgorithm

Seven sets of values are assigned to the parameters informula (1) to evaluate the accuracy of the proposed mapmatching algorithm In experiment 1 the values of119882dis119882dirand 119882acc are assigned to 1 0 and 0 respectively The abovevalues mean that only distance factor is considered and theaccuracy rate is 817 In experiment 2 the values of 119882dis119882dir and 119882acc are assigned to 0 1 and 0 respectively Theabove values mean that only direction factor is consideredand the accuracy rate is 763 In experiment 3 the values of


0005

01015

02025

03035

0 2 4 6 8 10 12 14 16 18 20 22 24Time of day (hour)

CV

(a)

0005

01015

02025

03035

04

0 2 4 6 8 10 12 14 16 18 20 22 24Time of day (hour)

CV

(b)

0005

01015

02025

03035

04

0 2 4 6 8 10 12 14 16 18 20 22 24

CV

Time of day (hour)

(c)

Figure 9 CV of the driving speed about Dingziqiao RoadWuhan Yangtze River Bridge and Xinhua Road respectively (a) CV of the drivingspeed about Dingziqiao Road (b) CV of the driving speed about Wuhan Yangtze River Bridge (c) CV of the driving speed about XinhuaRoad

119882dis 119882dir and 119882acc are assigned to 0 0 and 1 respectivelyThe above values mean that only accessibility factor isconsidered and the accuracy rate is 708 In experiment 4the values of119882dis119882dir and119882acc are assigned to 12 12 and0 respectively The above values mean that distance factorand direction factor are considered and the accuracy rate is899 In experiment 5 the values of119882dis119882dir and119882acc areassigned to 12 0 and 12 respectivelyThe above valuesmeanthat distance factor and accessibility factor are consideredand the accuracy rate is 876 In experiment 6 the values of119882dis119882dir and119882acc are assigned to 0 12 and 12 respectivelyThe above values mean that direction factor and accessibilityfactor are considered and the accuracy rate is 851 Inexperiment 7 the values of 119882dis 119882dir and 119882acc are assignedto 13 13 and 13 respectively The above values mean thatdistance factor direction factor and accessibility factor areconsidered and the accuracy rate is 949 The accuracy ofproposed method which includes distance direction andaccessibility factors is better than traditional map matchingalgorithms that include distance and direction factors

Therefore the values of 119882dis 119882dir and 119882acc are assignedto 13 13 and 13 in this research Most of the GPS pointshave been matched to the correct road in Figure 5 Based onthe proposed map matching algorithm the driving speed ofroads can be well acquired

42 Average Driving Speed of Roads Based on HistoricalFCD The average speed of historical FCD for a certain timemay reflect road traffic conditions at a particular moment

CV (coefficient of variation) is introduced to express thedispersion degree of the driving speed of roads

CV =

10038161003816100381610038161003816V minus 119881

10038161003816100381610038161003816

119881

(8)

where V is the average daily speed of the weekday and 119881

represents the average speed of the four weekdaysCV of the driving speed about three roads (Figure 6(a)) is

shown in Figure 9 The CV mean values of the three roadsare 0099244701 0079581216 and 0110617283 separatelyAccording to the statistical analysis the percentages of theDingziqiao Roadrsquos CV that are less than 01 015 and 02 are5512 8393 and 9723 respectively Similarly the per-centages of the Wuhan Yangtze River Bridge Roadrsquos CV thatare less than 01 015 and 02 are 7396 8255 and 9224respectively The percentages of the Xinhua Roadrsquos CV thatare less than 01 015 and 02 are 4903 7673 and 9363respectively Obviously the percentages less than thresholdsof 02 are absolutemajorities for three roadsWe can concludethat the average speed of historical FCD can approximate tothe mean speed of the road at a particular moment

43 Analysis of Shortest Travel Time Path Distance factor andtime factor are used to evaluate the proposed shortest traveltime algorithm The distance and time cost of the planningpaths in Figures 8(a) 8(b) and 8(c) are listed in Table 3 Theunits of the distance and time cost are separately measured inmeters and seconds


Table 3 The distance and time cost of planning paths in Figure 8

Planningpath in

Figure 8(a)

Planningpath in

Figure 8(b)

Planningpath in

Figure 8(c)Distance 1243279 1342416 1805825Time Null 109426 116066

If the traffic condition is good the planning paths (theshortest distance path and the shortest travel time path) maybe close in spatiality and partly overlap (Figures 8(a) and8(b)) The difference in distance of paths in Figures 8(a) and8(b) is small (Table 3) However the shortest travel timepath (Figure 8(b)) usually contains more primary roads Onthe contrary the shortest distance path (Figure 8(a)) usuallycontains more secondary roads

If traffic jams have occurred in some roads of the citycenter there is usually a big difference between the shortesttravel time path and the shortest distance path since thetraffic condition of highway is usually better than that ofother roads For example the shortest travel time path inFigure 8(c) contains more highways Although the planningpath distance in Figure 8(c) is longer than the planning pathdistance in Figure 8(a) it costs less travel time

The planning paths in different time are also differentalthough they apply the same algorithm The road trafficcondition varies over time so the shortest travel time pathsare totally different in different departure time (Figures 8(b)and 8(c))

5 Conclusions

In this study an effective map matching algorithm is pro-posed and the results show that the proposed method has ahigher accuracy Based on the results of three roadsrsquo CV weconclude that traffic distribution in four weekdays for eachroad has a similar pattern By comparing with routes of theshortest travel time and the shortest distance the results showthat the shortest travel time paths cost less traveling time thanthe shortest distance path

Although more than 85 million records are collectedand analyzed traffic conditions may be influenced by otherfactors such as weather and holiday However we have notconsidered the influence of these factors on traffic in thisstudy For the proposed map matching algorithm becausesomemapmatching algorithms are not open source we havenot computed the accuracy of these algorithms

Clearly the research in this article can be regarded as aninitial step in the application of FCD Because FCD has thecharacteristic of big data future research is planned to applydistributed computing technology to speed up the analysisrate of large-scale GPS records In addition multisource datawill be used to analyze the traffic condition in the futurework

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work is sponsored by the National Natural ScienceFoundation of China (no 41301417) State-Sponsored Schol-arship Program the Chongqing Natural Science Foundation(no cstc2014jcyjA20017) the Fundamental Research Fundsfor the Central Universities (no XDJK2015B022) and OpenResearch Fund by Sichuan Engineering Research Center forEmergencyMapping amp Disaster Reduction (no K2015B015)

References

[1] X Liu S Chien and K Kim ldquoEvaluation of floating car tech-nologies for travel time estimationrdquo Journal of Modern Trans-portation vol 20 no 1 pp 49ndash56 2012

[2] B Jiang and X Liu ldquoScaling of geographic space from theperspective of city and field blocks and using volunteeredgeographic informationrdquo International Journal of GeographicalInformation Science vol 26 no 2 pp 215ndash229 2011

[3] R Quintero A Llamazares D F Llorca et al ldquoExtended float-ing car data system-experimental studyrdquo in Proceedings of theIEEE Intelligent Vehicles Symposium (IV) pp 631ndash636 BadenGermany June 2011

[4] D Work and A Bayen ldquoImpacts of the mobile internet ontransportation cyberphysical systems traffic monitoring usingsmartphonesrdquo in Proceedings of the National Workshop forResearch onHigh-Confidence TransportationCyber-Physical Sys-tems Automotive Aviation and Rail pp 1ndash3 Washington DCUSA November 2008

[5] H-W Chang Y-C Tai and Y-J J Hsu ldquoContext-aware taxidemand hotspots predictionrdquo International Journal of BusinessIntelligence and Data Mining vol 5 no 1 pp 3ndash18 2010

[6] U Feuerhake C Kuntzsch and M Sester ldquoFinding interestingplaces and characteristic patterns in spatio-temporal trajec-toriesrdquo in Proceedings of the 8th International Symposium onLocation-Based Services (LBS rsquo11) pp 1ndash18 Vienna AustriaNovember 2011

[7] X Liu andY Ban ldquoUncovering Spatio-temporal cluster patternsusing massive floating car datardquo ISPRS International Journal ofGeo-Information vol 2 no 2 pp 371ndash384 2013

[8] Y Zhao J Liu R Chen et al ldquoA new method of road networkupdating based on floating car datardquo in Proceedings of the 2011IEEE International Geoscience and Remote Sensing Symposium(IGARSS rsquo11) pp 1878ndash1881 Melbourne Australia July 2011

[9] J Li Q Qin C Xie and Y Zhao ldquoIntegrated use of spatial andsemantic relationships for extracting road networks from float-ing car datardquo International Journal of Applied Earth Observationand Geoinformation vol 19 no 1 pp 238ndash247 2012

[10] A Simroth and H Zahle ldquoTravel time prediction using floatingcar data applied to logistics planningrdquo IEEE Transactions onIntelligent Transportation Systems vol 12 no 1 pp 243ndash2532011

[11] P S Castro D Zhang and S Li ldquoUrban traffic modelling andprediction using large scale taxi GPS tracesrdquo in Pervasive Com-puting 10th International Conference Pervasive 2012 NewcastleUK June 18ndash22 2012 Proceedings vol 7319 of Lecture Notes inComputer Science pp 57ndash72 Springer Berlin Germany 2012

[12] Q Li Z Zeng T Zhang J Li and ZWu ldquoPath-finding throughflexible hierarchical road networks an experiential approachusing taxi trajectory datardquo International Journal of Applied EarthObservation and Geoinformation vol 13 no 1 pp 110ndash119 2011


[13] F Mao M Ji and T Liu ldquoMining spatiotemporal patterns ofurban dwellers from taxi trajectory datardquo Frontiers of EarthScience vol 10 no 2 pp 205ndash221 2015

[14] D Pfoser S Brakatsoulas P Brosch M Umlauft N Tryfonaand G Tsironis ldquoDynamic travel time provision for road net-worksrdquo in Proceedings of the 16th ACM SIGSPATIAL Inter-national Conference on Advances in Geographic InformationSystems (ACM GIS rsquo08) pp 475ndash478 Irvine Calif USANovember 2008

[15] H Lahrmann ldquoFloating car data for traffic monitoringrdquo in Pro-ceedings of the i2TERN Conference pp 1ndash4 Aalborg DenmarkJune 2007

[16] H Bar-Gera ldquoEvaluation of a cellular phone-based systemfor measurements of traffic speeds and travel times a casestudy from Israelrdquo Transportation Research Part C EmergingTechnologies vol 15 no 6 pp 380ndash391 2007

[17] A Kesting andM Treiber ldquoOnline traffic state estimation basedon floating car datardquo in Proceedings of the Traffic and GranularFlow (TGF rsquo09) pp 1ndash11 Shanghai China June 2009

[18] B Y Chen H Yuan Q LiWH K Lam S-L Shaw andK YanldquoMap-matching algorithm for large-scale low-frequency float-ing car datardquo International Journal of Geographical InformationScience vol 28 no 1 pp 22ndash38 2014

[19] S Brakatsoulas D Pfoser R Salas and C Wenk ldquoOn map-matching vehicle tracking datardquo in Proceedings of the 31stInternational Conference on Very Large Data Bases (VLDB rsquo05)pp 853ndash864 Trondheim Norway September 2005

[20] CWenk R Salas and D Pfoser ldquoAddressing the need for map-matching speed localizing global curve-matching algorithmsrdquoin Proceedings of the 18th International Conference on Scientificand Statistical Database Management (SSDBM rsquo06) pp 379ndash388 IEEE Vienna Austria July 2006

[21] C Liu X Meng and Y Fan ldquoDetermination of routing velocitywith GPS floating car data and webGIS-based instantaneoustraffic information disseminationrdquo The Journal of Navigationvol 61 no 2 pp 337ndash353 2008

[22] H Shimizu M Kobayashi and Y Yonezawa ldquoAnalysis of meanlink travel time for urban traffic networksrdquo in Proceedings ofthe 51st Vehicular Technology Conference (VTC rsquo00) pp 318ndash322Tokyo Japan May 2000

[23] B S Kerner C Demir R G Herrtwich et al ldquoTraffic statedetection with floating car data in road networksrdquo in Proceed-ings of the 8th International IEEE Conference on IntelligentTransportation Systems pp 700ndash705 Vienna Austria Septem-ber 2005

[24] Y Ando O Fukazawa O Masutani et al ldquoPerformance ofpheromonemodel for predicting traffic congestionrdquo in Proceed-ings of the 5th International Joint Conference on AutonomousAgents and Multiagent Systems pp 73ndash80 Hakodate JapanMay 2006

[25] J F Ehmke S Meise and D C Mattfeld ldquoFloating car databased analysis of urban travel times for the provision of trafficqualityrdquo International Series in Operations Research amp Manage-ment Science vol 144 pp 129ndash149 2010

[26] M Rahmani H N Koutsopoulos and A RanganathanldquoRequirements and potential of GPS-based floating car datafor traffic management stockholm case studyrdquo in Proceedingsof the 13th International IEEE Annual Conference on IntelligentTransportation Systems (ITSC rsquo10) pp 730ndash735 IEEE FunchalPortugal September 2010

[27] Wuhan Statistics Bureau Wuhan Statistical Yearbook 2010China Statistics Press Beijing China 2010


[29] E Brockfeld S Lorkowski P Mieth et al ldquoBenefits and limitsof recent FCD technologymdashan evaluation studyrdquo in Proceedingsof 11th WCTR Conference pp 1ndash14 Berkeley Calif USA June2007

[30] E W Dijkstra ldquoA note on two problems in connexion withgraphsrdquo Numerische Mathematik vol 1 pp 269ndash271 1959

[31] R W Floyd ldquoAlgorithm 97 shortest pathrdquo Communications ofthe ACM vol 5 no 6 p 345 1962

[32] P E Hart N J Nilsson and B Raphael ldquoA formal basis forthe heuristic determination of minimum cost pathsrdquo IEEETransactions on Systems Science and Cybernetics vol 4 no 2pp 100ndash107 1968

[33] S Messelodi C M Modena M Zanin et al ldquoIntelligentextended floating car data collectionrdquo Expert Systems withApplications vol 36 no 3 pp 4213ndash4227 2009

[34] J E Naranjo F Jimenez F J Serradilla and J G Zato ldquoFloatingcar data augmentation based on infrastructure sensors and neu-ral networksrdquo IEEE Transactions on Intelligent TransportationSystems vol 13 no 1 pp 107ndash114 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Pfoser et al showcased a system which facilitates the col-lection of FCD produces dynamic travel time informationand provides value-added services based on the dynamictravel times [14] However a basic problem was the limitedvehicle penetration and insufficient data coverage Kestingand Treiber considered a vehicle-based approach to collecttraffic data and used the data to estimate the upstreamand downstream fronts of a traffic jam [17] However thisestimation did not allow predicting travel timewhich becamerelevant when no probe vehicle passed the roadside units fora while

Because of GPS measurement errors and road geometricerrors in digital maps the GPS locations of probe vehiclesmay not appear on network links [18] Therefore it isnecessary not only to match the GPS points to the roadnetworks but also to get the route of the consecutive GPSpoints There are a number of works that propose methodsfor map matching An incremental algorithm that matchesconsecutive portions of the trajectory to the roadnetwork andtwo global algorithms that compared the entire trajectory tocandidate paths in the road network were proposed [19] Dueto limitations in the tracking data and the road network ofglobal algorithms the matching results need to be evaluatedto discard portions of bad matches Adaptive Clipping algo-rithm which takes tracking error estimates into account wasintroduced to solve this map matching task [20] Howeverthe quality of this map matching algorithm was not assessedThe procedures and algorithms for the computation andmapmatching of road segment velocities to a digital road networkwere presented [21] Because lots of adjacent GPS pointsbelong to the different roads the consideration of directionand distance factors only is not enough for map matching

Analysis studies of traffic conditions based on FCD werebecoming more prominent Mean link travel time basedon the classification for the traffic flow offset control andmoving direction at downstream signalized intersections inurban traffic networks was studied [22] The mean originand destination (OD) travel time was evaluated by summingup the mean travel time of each link in traffic networksTraffic state was detected with FCD [23] A statistical analysisshowed the high quality of the reconstruction of the actualtravel times in the net with only 15 equipped with FCDvehicles The probe-car system was used to predict trafficcongestion in the immediate future [24] A basic model forpredicting traffic congestion in the immediate future usingpheromone was developed Traffic quality was provided bythe aggregation and evaluation of FCD with a commonevaluation scheme [25] GPS traffic-related data for trafficmonitoring and control was presented and the scope oftraffic information was illustrated [26] However this study islimited in analyzing the road situation and does not providethe accurate traveling time

In this paper there are two important problems to beaddressed in order to better guide the route choice The firstis the acquisition of the road traffic situation from FCD Thesecond is to find a route with the shortest travel time bydesigning an optimal route analysis algorithm

The two main contributions of this paper are the follow-ing

(1) A newmapmatching algorithmwhich fully considersthe distance factor direction factor and accessibilityfactor is proposed This algorithm can be used toacquire the road traffic situation

(2) A shortest travel time algorithm is designed Animproved Dijkstra algorithm is proposed and traveltime is assigned to edges as the dynamic weight of theroad

The paper is organized as follows In Section 2 FCDare presented and two algorithms including map matchingalgorithmand the shortest travel time algorithmare designedIn Section 3 experiments are implemented to verify theproposed methods In Section 4 map matching algorithmand the average driving speed of roads based on historicalFCD are discussed Lastly Section 5 presents the conclusionsand points to the future work

2 Materials and Methods

21 Data Description The original FCD is collected fromover 11 thousand taxicabs fromWuhan in September 2009 atregular intervals (average 20ndash60 seconds) during the coursesof six days Wuhan is the capital of Hubei province ChinaIt is located in the eastern Jianghan Plain at the intersectionof the middle reaches of the Yangtze and Han Rivers It is amajor transportation hub with dozens of railways roads andexpressways passing through the city It has a population of91000000 people in 2009 [27]The number of cars inWuhanis about 556 thousand in 2008 [28]

The FCD samples achieve a sufficient penetration ratewith 19 to calculate the traffic informationThere are morethan 85 million records in total (over 14 million per day)with attributes of timestamp CarID 119883 119884 speed and angleA timestamp is a sequence of characters usually giving theaccurate date and time of day CarID is a unique identificationof a taxicab 119883 and 119884 are longitude and latitude respectivelyrecording the location of the taxicab Speed is the instantspeed of the taxicab at a given time Angle is defined as ahorizontal angle measured clockwise from a north base lineBrockfeld et al concluded that the Taxi-FCD system is able todeliver valuable travel time information for mobility servicesand the average travel times can be detected and calculatedreliably [29] Table 1 shows some typical FCD records

22 Methodology

221 Map Matching Algorithm Because of the GPS error ordigital map measurement error the deviation phenomenonbetween FCD and map often exists The objective of thissection is to develop a map matching algorithm for FCD toassess the traffic condition The core of this map matchingalgorithm proceeds as follows (Figure 1) The original GPSpoints and roads are showed in Figure 1(a) Then location isdetermined for eachGPSpoint GPSpoints aremapmatchingto the corresponding position of the road in Figure 1(b)Furthermore the route of the adjacent points is determinedA route is given to describe the path of the points inFigure 1(c)




GPS pointsRoad

(a)



(c)



119891 (MM) = 119892 (Dis) + ℎ (Dir) + 119897 (Acc) (1)


Maxdis (2)


Maxdir (3)


Maxacc (4)










E1 E2

E5

E7E6

E3 E4

A1 A3

A8A5 A7

A2 A4

A6 A9

A10 A12

A11 A13


Graph

Node2

Node1

Nodelist

Node1

NodeID

Edge2

Edge1

EdgeList

Edge1

Length

EdgeID

bSingleWay

StartID

EndID

Time1 rate1

htTimeRate

Time rate

Time2 rate2

Weight





Edge

Edge

Node

Node
















800

Start point

End point

Road

N5

N6N7 N8

N4N3N2

N1






119877119890119898119886119894119899119894119899119892119879119894119898119890

= (119868119873119879 (119862119906119903119903119890119899119905119879119894119898119890 divide 119879119894119898119890119878119897119894119888119890) + 1)

times 119879119894119898119890119878119897119894119888119890 minus 119862119906119903119903119890119899119905119879119894119898119890

(5)

119890119882119890119894119892ℎ119905 = 119890119871119890119899119892119905ℎ divide 119862119906119903119877119886119905119890 (6)






5 1198736 1198737 1198733 1198734⟩ is short



2


3 Results




119879119894119898119890119878119897119894119888119890 = 119879119886119909119894119873119890119890119889 divide119879119886119909119894119873119906119898

119877119900119886119889119878119890119892119873119906119898

times119877119900119886119889119871119890119899119860V119892119878119901119890119890119889119860V119892

(7)





Table2Th

eprocessof

thes

hortesttraveltim

efor

Figure

4

Destin

ation

Thep

athandthea

rrivaltim

efrom

1198735to

othern

odes

1198731

infininfin

infin850

⟨1198735119873611987321198731⟩

850

⟨1198735119873611987321198731⟩

850

⟨1198735119873611987321198731⟩

1198732

infin830

⟨119873511987361198732⟩

830

⟨119873511987361198732⟩

mdashmdash

mdash1198733

infininfin

830

⟨1198735119873611987371198733⟩

830

⟨1198735119873611987371198733⟩

mdashmdash

1198734

infininfin

infininfin

840

⟨11987351198736119873711987331198734⟩

840

⟨11987351198736119873711987331198734⟩

1198736

810

⟨11987351198736⟩

mdashmdash

mdashmdash

mdash1198737

infin820

⟨119873511987361198737⟩

mdashmdash

mdashmdash

1198738

infininfin

835

⟨1198735119873611987371198738⟩

835

⟨1198735119873611987371198738⟩

835

⟨1198735119873611987371198738⟩

mdash119878

11987351198736

119873511987361198737

1198735119873611987371198732

11987351198736119873711987321198733

119873511987361198737119873211987331198738

1198735119873611987371198732119873311987381198734


(a) (b)


(a)

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14 16 18 20 22 24



Mea

n sp

eed

(ms

)

Time of day (hour)

(b)



Mea

n sp

eed

(ms

)

Time of day (hour)

02468

101214161820

0 2 4 6 8 10 12 14 16 18 20 22 24

(c)



Mea

n sp

eed

(ms

)

Time of day (hour)

0

2

4

6

8

10

12

14

16

18

0 2 4 6 8 10 12 14 16 18 20 22 24

(d)





0600plusmn

0ndash5

5ndash10

10ndash1

515

ndash20

20ndash2

5

(a)

0ndash5

5ndash10

10ndash1

515

ndash20

20ndash2

5

0800 plusmn

(b)


(a) (b)

(c)




4 Discussion




0005

01015

02025

03035

0 2 4 6 8 10 12 14 16 18 20 22 24Time of day (hour)

CV

(a)

0005

01015

02025

03035

04

0 2 4 6 8 10 12 14 16 18 20 22 24Time of day (hour)

CV

(b)

0005

01015

02025

03035

04

0 2 4 6 8 10 12 14 16 18 20 22 24

CV

Time of day (hour)

(c)






CV =

10038161003816100381610038161003816V minus 119881

10038161003816100381610038161003816

119881

(8)







Planningpath in

Figure 8(a)

Planningpath in

Figure 8(b)

Planningpath in





5 Conclusions




Competing Interests


Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












GPS pointsRoad

(a)



(c)



119891 (MM) = 119892 (Dis) + ℎ (Dir) + 119897 (Acc) (1)


Maxdis (2)


Maxdir (3)


Maxacc (4)










E1 E2

E5

E7E6

E3 E4

A1 A3

A8A5 A7

A2 A4

A6 A9

A10 A12

A11 A13


Graph

Node2

Node1

Nodelist

Node1

NodeID

Edge2

Edge1

EdgeList

Edge1

Length

EdgeID

bSingleWay

StartID

EndID

Time1 rate1

htTimeRate

Time rate

Time2 rate2

Weight





Edge

Edge

Node

Node
















800

Start point

End point

Road

N5

N6N7 N8

N4N3N2

N1






119877119890119898119886119894119899119894119899119892119879119894119898119890

= (119868119873119879 (119862119906119903119903119890119899119905119879119894119898119890 divide 119879119894119898119890119878119897119894119888119890) + 1)

times 119879119894119898119890119878119897119894119888119890 minus 119862119906119903119903119890119899119905119879119894119898119890

(5)

119890119882119890119894119892ℎ119905 = 119890119871119890119899119892119905ℎ divide 119862119906119903119877119886119905119890 (6)






5 1198736 1198737 1198733 1198734⟩ is short



2


3 Results




119879119894119898119890119878119897119894119888119890 = 119879119886119909119894119873119890119890119889 divide119879119886119909119894119873119906119898

119877119900119886119889119878119890119892119873119906119898

times119877119900119886119889119871119890119899119860V119892119878119901119890119890119889119860V119892

(7)





Table2Th

eprocessof

thes

hortesttraveltim

efor

Figure

4

Destin

ation

Thep

athandthea

rrivaltim

efrom

1198735to

othern

odes

1198731

infininfin

infin850

⟨1198735119873611987321198731⟩

850

⟨1198735119873611987321198731⟩

850

⟨1198735119873611987321198731⟩

1198732

infin830

⟨119873511987361198732⟩

830

⟨119873511987361198732⟩

mdashmdash

mdash1198733

infininfin

830

⟨1198735119873611987371198733⟩

830

⟨1198735119873611987371198733⟩

mdashmdash

1198734

infininfin

infininfin

840

⟨11987351198736119873711987331198734⟩

840

⟨11987351198736119873711987331198734⟩

1198736

810

⟨11987351198736⟩

mdashmdash

mdashmdash

mdash1198737

infin820

⟨119873511987361198737⟩

mdashmdash

mdashmdash

1198738

infininfin

835

⟨1198735119873611987371198738⟩

835

⟨1198735119873611987371198738⟩

835

⟨1198735119873611987371198738⟩

mdash119878

11987351198736

119873511987361198737

1198735119873611987371198732

11987351198736119873711987321198733

119873511987361198737119873211987331198738

1198735119873611987371198732119873311987381198734


(a) (b)


(a)

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14 16 18 20 22 24



Mea

n sp

eed

(ms

)

Time of day (hour)

(b)



Mea

n sp

eed

(ms

)

Time of day (hour)

02468

101214161820

0 2 4 6 8 10 12 14 16 18 20 22 24

(c)



Mea

n sp

eed

(ms

)

Time of day (hour)

0

2

4

6

8

10

12

14

16

18

0 2 4 6 8 10 12 14 16 18 20 22 24

(d)





0600plusmn

0ndash5

5ndash10

10ndash1

515

ndash20

20ndash2

5

(a)

0ndash5

5ndash10

10ndash1

515

ndash20

20ndash2

5

0800 plusmn

(b)


(a) (b)

(c)




4 Discussion




0005

01015

02025

03035

0 2 4 6 8 10 12 14 16 18 20 22 24Time of day (hour)

CV

(a)

0005

01015

02025

03035

04

0 2 4 6 8 10 12 14 16 18 20 22 24Time of day (hour)

CV

(b)

0005

01015

02025

03035

04

0 2 4 6 8 10 12 14 16 18 20 22 24

CV

Time of day (hour)

(c)






CV =

10038161003816100381610038161003816V minus 119881

10038161003816100381610038161003816

119881

(8)







Planningpath in

Figure 8(a)

Planningpath in

Figure 8(b)

Planningpath in





5 Conclusions




Competing Interests


Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










E1 E2

E5

E7E6

E3 E4

A1 A3

A8A5 A7

A2 A4

A6 A9

A10 A12

A11 A13


Graph

Node2

Node1

Nodelist

Node1

NodeID

Edge2

Edge1

EdgeList

Edge1

Length

EdgeID

bSingleWay

StartID

EndID

Time1 rate1

htTimeRate

Time rate

Time2 rate2

Weight





Edge

Edge

Node

Node
















800

Start point

End point

Road

N5

N6N7 N8

N4N3N2

N1






119877119890119898119886119894119899119894119899119892119879119894119898119890

= (119868119873119879 (119862119906119903119903119890119899119905119879119894119898119890 divide 119879119894119898119890119878119897119894119888119890) + 1)

times 119879119894119898119890119878119897119894119888119890 minus 119862119906119903119903119890119899119905119879119894119898119890

(5)

119890119882119890119894119892ℎ119905 = 119890119871119890119899119892119905ℎ divide 119862119906119903119877119886119905119890 (6)






5 1198736 1198737 1198733 1198734⟩ is short



2


3 Results




119879119894119898119890119878119897119894119888119890 = 119879119886119909119894119873119890119890119889 divide119879119886119909119894119873119906119898

119877119900119886119889119878119890119892119873119906119898

times119877119900119886119889119871119890119899119860V119892119878119901119890119890119889119860V119892

(7)





Table2Th

eprocessof

thes

hortesttraveltim

efor

Figure

4

Destin

ation

Thep

athandthea

rrivaltim

efrom

1198735to

othern

odes

1198731

infininfin

infin850

⟨1198735119873611987321198731⟩

850

⟨1198735119873611987321198731⟩

850

⟨1198735119873611987321198731⟩

1198732

infin830

⟨119873511987361198732⟩

830

⟨119873511987361198732⟩

mdashmdash

mdash1198733

infininfin

830

⟨1198735119873611987371198733⟩

830

⟨1198735119873611987371198733⟩

mdashmdash

1198734

infininfin

infininfin

840

⟨11987351198736119873711987331198734⟩

840

⟨11987351198736119873711987331198734⟩

1198736

810

⟨11987351198736⟩

mdashmdash

mdashmdash

mdash1198737

infin820

⟨119873511987361198737⟩

mdashmdash

mdashmdash

1198738

infininfin

835

⟨1198735119873611987371198738⟩

835

⟨1198735119873611987371198738⟩

835

⟨1198735119873611987371198738⟩

mdash119878

11987351198736

119873511987361198737

1198735119873611987371198732

11987351198736119873711987321198733

119873511987361198737119873211987331198738

1198735119873611987371198732119873311987381198734


(a) (b)


(a)

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14 16 18 20 22 24



Mea

n sp

eed

(ms

)

Time of day (hour)

(b)



Mea

n sp

eed

(ms

)

Time of day (hour)

02468

101214161820

0 2 4 6 8 10 12 14 16 18 20 22 24

(c)



Mea

n sp

eed

(ms

)

Time of day (hour)

0

2

4

6

8

10

12

14

16

18

0 2 4 6 8 10 12 14 16 18 20 22 24

(d)





0600plusmn

0ndash5

5ndash10

10ndash1

515

ndash20

20ndash2

5

(a)

0ndash5

5ndash10

10ndash1

515

ndash20

20ndash2

5

0800 plusmn

(b)


(a) (b)

(c)




4 Discussion




0005

01015

02025

03035

0 2 4 6 8 10 12 14 16 18 20 22 24Time of day (hour)

CV

(a)

0005

01015

02025

03035

04

0 2 4 6 8 10 12 14 16 18 20 22 24Time of day (hour)

CV

(b)

0005

01015

02025

03035

04

0 2 4 6 8 10 12 14 16 18 20 22 24

CV

Time of day (hour)

(c)






CV =

10038161003816100381610038161003816V minus 119881

10038161003816100381610038161003816

119881

(8)







Planningpath in

Figure 8(a)

Planningpath in

Figure 8(b)

Planningpath in





5 Conclusions




Competing Interests


Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










800

Start point

End point

Road

N5

N6N7 N8

N4N3N2

N1






119877119890119898119886119894119899119894119899119892119879119894119898119890

= (119868119873119879 (119862119906119903119903119890119899119905119879119894119898119890 divide 119879119894119898119890119878119897119894119888119890) + 1)

times 119879119894119898119890119878119897119894119888119890 minus 119862119906119903119903119890119899119905119879119894119898119890

(5)

119890119882119890119894119892ℎ119905 = 119890119871119890119899119892119905ℎ divide 119862119906119903119877119886119905119890 (6)






5 1198736 1198737 1198733 1198734⟩ is short



2


3 Results




119879119894119898119890119878119897119894119888119890 = 119879119886119909119894119873119890119890119889 divide119879119886119909119894119873119906119898

119877119900119886119889119878119890119892119873119906119898

times119877119900119886119889119871119890119899119860V119892119878119901119890119890119889119860V119892

(7)





Table2Th

eprocessof

thes

hortesttraveltim

efor

Figure

4

Destin

ation

Thep

athandthea

rrivaltim

efrom

1198735to

othern

odes

1198731

infininfin

infin850

⟨1198735119873611987321198731⟩

850

⟨1198735119873611987321198731⟩

850

⟨1198735119873611987321198731⟩

1198732

infin830

⟨119873511987361198732⟩

830

⟨119873511987361198732⟩

mdashmdash

mdash1198733

infininfin

830

⟨1198735119873611987371198733⟩

830

⟨1198735119873611987371198733⟩

mdashmdash

1198734

infininfin

infininfin

840

⟨11987351198736119873711987331198734⟩

840

⟨11987351198736119873711987331198734⟩

1198736

810

⟨11987351198736⟩

mdashmdash

mdashmdash

mdash1198737

infin820

⟨119873511987361198737⟩

mdashmdash

mdashmdash

1198738

infininfin

835

⟨1198735119873611987371198738⟩

835

⟨1198735119873611987371198738⟩

835

⟨1198735119873611987371198738⟩

mdash119878

11987351198736

119873511987361198737

1198735119873611987371198732

11987351198736119873711987321198733

119873511987361198737119873211987331198738

1198735119873611987371198732119873311987381198734


(a) (b)


(a)

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14 16 18 20 22 24



Mea

n sp

eed

(ms

)

Time of day (hour)

(b)



Mea

n sp

eed

(ms

)

Time of day (hour)

02468

101214161820

0 2 4 6 8 10 12 14 16 18 20 22 24

(c)



Mea

n sp

eed

(ms

)

Time of day (hour)

0

2

4

6

8

10

12

14

16

18

0 2 4 6 8 10 12 14 16 18 20 22 24

(d)





0600plusmn

0ndash5

5ndash10

10ndash1

515

ndash20

20ndash2

5

(a)

0ndash5

5ndash10

10ndash1

515

ndash20

20ndash2

5

0800 plusmn

(b)


(a) (b)

(c)




4 Discussion




0005

01015

02025

03035

0 2 4 6 8 10 12 14 16 18 20 22 24Time of day (hour)

CV

(a)

0005

01015

02025

03035

04

0 2 4 6 8 10 12 14 16 18 20 22 24Time of day (hour)

CV

(b)

0005

01015

02025

03035

04

0 2 4 6 8 10 12 14 16 18 20 22 24

CV

Time of day (hour)

(c)






CV =

10038161003816100381610038161003816V minus 119881

10038161003816100381610038161003816

119881

(8)







Planningpath in

Figure 8(a)

Planningpath in

Figure 8(b)

Planningpath in





5 Conclusions




Competing Interests


Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Table2Th

eprocessof

thes

hortesttraveltim

efor

Figure

4

Destin

ation

Thep

athandthea

rrivaltim

efrom

1198735to

othern

odes

1198731

infininfin

infin850

⟨1198735119873611987321198731⟩

850

⟨1198735119873611987321198731⟩

850

⟨1198735119873611987321198731⟩

1198732

infin830

⟨119873511987361198732⟩

830

⟨119873511987361198732⟩

mdashmdash

mdash1198733

infininfin

830

⟨1198735119873611987371198733⟩

830

⟨1198735119873611987371198733⟩

mdashmdash

1198734

infininfin

infininfin

840

⟨11987351198736119873711987331198734⟩

840

⟨11987351198736119873711987331198734⟩

1198736

810

⟨11987351198736⟩

mdashmdash

mdashmdash

mdash1198737

infin820

⟨119873511987361198737⟩

mdashmdash

mdashmdash

1198738

infininfin

835

⟨1198735119873611987371198738⟩

835

⟨1198735119873611987371198738⟩

835

⟨1198735119873611987371198738⟩

mdash119878

11987351198736

119873511987361198737

1198735119873611987371198732

11987351198736119873711987321198733

119873511987361198737119873211987331198738

1198735119873611987371198732119873311987381198734


(a) (b)


(a)

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14 16 18 20 22 24



Mea

n sp

eed

(ms

)

Time of day (hour)

(b)



Mea

n sp

eed

(ms

)

Time of day (hour)

02468

101214161820

0 2 4 6 8 10 12 14 16 18 20 22 24

(c)



Mea

n sp

eed

(ms

)

Time of day (hour)

0

2

4

6

8

10

12

14

16

18

0 2 4 6 8 10 12 14 16 18 20 22 24

(d)





0600plusmn

0ndash5

5ndash10

10ndash1

515

ndash20

20ndash2

5

(a)

0ndash5

5ndash10

10ndash1

515

ndash20

20ndash2

5

0800 plusmn

(b)


(a) (b)

(c)




4 Discussion




0005

01015

02025

03035

0 2 4 6 8 10 12 14 16 18 20 22 24Time of day (hour)

CV

(a)

0005

01015

02025

03035

04

0 2 4 6 8 10 12 14 16 18 20 22 24Time of day (hour)

CV

(b)

0005

01015

02025

03035

04

0 2 4 6 8 10 12 14 16 18 20 22 24

CV

Time of day (hour)

(c)






CV =

10038161003816100381610038161003816V minus 119881

10038161003816100381610038161003816

119881

(8)







Planningpath in

Figure 8(a)

Planningpath in

Figure 8(b)

Planningpath in





5 Conclusions




Competing Interests


Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b)


(a)

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14 16 18 20 22 24



Mea

n sp

eed

(ms

)

Time of day (hour)

(b)



Mea

n sp

eed

(ms

)

Time of day (hour)

02468

101214161820

0 2 4 6 8 10 12 14 16 18 20 22 24

(c)



Mea

n sp

eed

(ms

)

Time of day (hour)

0

2

4

6

8

10

12

14

16

18

0 2 4 6 8 10 12 14 16 18 20 22 24

(d)





0600plusmn

0ndash5

5ndash10

10ndash1

515

ndash20

20ndash2

5

(a)

0ndash5

5ndash10

10ndash1

515

ndash20

20ndash2

5

0800 plusmn

(b)


(a) (b)

(c)




4 Discussion




0005

01015

02025

03035

0 2 4 6 8 10 12 14 16 18 20 22 24Time of day (hour)

CV

(a)

0005

01015

02025

03035

04

0 2 4 6 8 10 12 14 16 18 20 22 24Time of day (hour)

CV

(b)

0005

01015

02025

03035

04

0 2 4 6 8 10 12 14 16 18 20 22 24

CV

Time of day (hour)

(c)






CV =

10038161003816100381610038161003816V minus 119881

10038161003816100381610038161003816

119881

(8)







Planningpath in

Figure 8(a)

Planningpath in

Figure 8(b)

Planningpath in





5 Conclusions




Competing Interests


Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0600plusmn

0ndash5

5ndash10

10ndash1

515

ndash20

20ndash2

5

(a)

0ndash5

5ndash10

10ndash1

515

ndash20

20ndash2

5

0800 plusmn

(b)


(a) (b)

(c)




4 Discussion




0005

01015

02025

03035

0 2 4 6 8 10 12 14 16 18 20 22 24Time of day (hour)

CV

(a)

0005

01015

02025

03035

04

0 2 4 6 8 10 12 14 16 18 20 22 24Time of day (hour)

CV

(b)

0005

01015

02025

03035

04

0 2 4 6 8 10 12 14 16 18 20 22 24

CV

Time of day (hour)

(c)






CV =

10038161003816100381610038161003816V minus 119881

10038161003816100381610038161003816

119881

(8)







Planningpath in

Figure 8(a)

Planningpath in

Figure 8(b)

Planningpath in





5 Conclusions




Competing Interests


Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0005

01015

02025

03035

0 2 4 6 8 10 12 14 16 18 20 22 24Time of day (hour)

CV

(a)

0005

01015

02025

03035

04

0 2 4 6 8 10 12 14 16 18 20 22 24Time of day (hour)

CV

(b)

0005

01015

02025

03035

04

0 2 4 6 8 10 12 14 16 18 20 22 24

CV

Time of day (hour)

(c)






CV =

10038161003816100381610038161003816V minus 119881

10038161003816100381610038161003816

119881

(8)







Planningpath in

Figure 8(a)

Planningpath in

Figure 8(b)

Planningpath in





5 Conclusions




Competing Interests


Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Planningpath in

Figure 8(a)

Planningpath in

Figure 8(b)

Planningpath in





5 Conclusions




Competing Interests


Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Documents

Research Article Route Choice of the Shortest Travel Time