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A System Dynamics Approach to
Transport Modelling
Simon Shepherd
Institute for Transport Studies
University of Leeds (UK)
Aims• Introduction Systems Dynamics• Some examples• Challenges
System Dynamics
• System dynamics is a computer-aided approach to policy analysis and design. It applies to dynamic problems arising in complex social, managerial, economic, or ecological systems -- literally any dynamic systems characterized by interdependence, mutual interaction, information feedback, and circular causality
Introduction :principles of Systems Dynamics
• Representation of systems
Qualitative
Quantitative
Verbal description
Cause-effect diagrams
Flow charts
Equations
Elements of CLD
Entities: are elements which affect other elements and get affected themselves. An entity represents an unspecified quantity. See Stocks later
Number of motorways
+
-
s
o
Links: Entities are related by causal links, shown by arrows. Each causal link is assigned a polarity, either positive (+, s) or negative (-, o) to indicate how the dependent entity changes when the independent entity changes.
CLD example
• Simple example
Eggs
Chicken +
+etc.
Time
Pop
ul a
ti on
Reinforcingfeedback loop
+
CLD example 2
• Simple example 2
Eggs
Chicken +
+
+
# Roadcrossing +
-
etc. Time
Pop
ul a
ti on
Balancingfeedback loop
-
CLD transport example
• “Congestion relief” by new road infrastructure
Need for new highways
Highways being built
Number of Highways
Number of traffic jams
Attractiveness of driving on highways
+
+
+
+
+- +
-
Source: Roberts, N.; et. al., Introduction to Computer simulation: The System Dynamics Approach. ed.; Addison-Wesley Publishing Company: London Amsterdam Don Mills Ontario Sydney, 1983
Stocks and flows
Stock
inflow outflow
t
ttStockdssoutflowsInflowtStock
0
)()()()( 0
Chickensbirthsdeaths
eggs+
+
road crossings
+
+-
Chickens
1,000
500
0
0 2 4 6 8 10Time (Month)
Chickens : with crossings
Chicken and eggs model
Note :
Populationbirths deaths
birth rate death rate
Population
800
400
0
0 20 40 60 80 100Time (Month)
Rab
bit
Population : Current
Simple population model
PopulationYoung
births aging young
average time in young
birth rate
PopulationMiddle
PopulationOld
aging middle aging old
average time in middle average time in old
initial popinfant
initial popmiddle
initial popold
FoxPopulation
fox food availability
fox foodrequirements
average fox life
fox consumptionof rabbits
fox birth rateinitial fox
population
fox mortalitylookup
fox births fox deaths
RabbitPopulation
rabbit births
rabbit crowding
carrying capacity
average rabbit liferabbit birth rate
initial rabbitpopulation
effect ofcrowding on
deaths lookup
fox rabbitconsumption
lookup
rabbit deaths
Rabbit Population
4,000
2,000
0
0 10 20 30 40 50Time (Year)
Rab
bit
Rabbit Population : Current
Fox Population
200
100
0
0 10 20 30 40 50Time (Year)
Fox
Fox Population : Current
SusceptiblePopulation
InfectedPopulation
infections
rate of potentialinfectious contacts
rate that peoplecontact other people
Fraction ofpopulation infected
total population
Contactsbetween infectedand unaffected
fraction infectedfrom contact
initial infectedinitial susceptible
Susceptible Population
1 M
750,000
500,000
250,000
0
0 10 20 30 40 50Time (day)
Per
son
Susceptible Population : Current
Infected Population
1 M
500,000
0
0 10 20 30 40 50Time (day)
Per
son
Infected Population
Simple epidemic model
Example – uptake of Electric Vehicles
Extended - Struben and Sterman (2008)
• Consideration of three types of car: conventional vehicle (CV), Plug-in Hybrid (PIHV), and Battery Electric (BEV),
• inclusion of choice model coefficients from a UK-based SP study (Batley et al, 2004),
• inclusion of a price-volume effect • calibration to match the “business as usual” projection by BERR (2008)• testing a failing market case where we remove high profile marketing,• inclusion of a “revenue preserving” tax designed to replace any loss in
revenues from fuel duty, • estimation of CO2 emissions
Source: Shepherd, S.P., Bonsall, P.W., and Harrison G. (2012) Factors affecting future demand for electric vehicles : a model based study. Transport Policy, (20) March 2012, pp 62-74. DOI :10.1016/j.tranpol.2011.12.006
Struben and Sterman (2008) Take up of AFV
Calibrated to BERR 2030
Sensitivity to word of mouth
Word of mouth between CV drivers is crucial for success – as was marketing
Example CM/failing regime vs BAU
market share EV
0.4
0.3
0.2
0.1
04 4 4 4 4 4 4 4 4 4 43 3 3 3 3 3 3 3 3 3 3
2 2 2 2 2 2 2 2 2 2 21 1 1 11
11
11
11
1
0 4 8 12 16 20 24 28 32 36 40Time (Year)
market share EV[PIHV] : BAU base 1 1 1 1 1 1 1
market share EV[PIHV] : BAU failing 2 2 2 2 2 2
market share EV[BEV] : BAU base 3 3 3 3 3 3
market share EV[BEV] : BAU failing 4 4 4 4 4 4
Willingness to consider EV
1
0.75
0.5
0.25
0 22
22
22 2 2 2 2 2 2 2 2 21
11
1
1
1
1
1
1
11
1 1 1 1
0 4 8 12 16 20 24 28 32 36 40Time (Year)
Willingness to consider EV : BAU base 1 1 1 1 1 1 1 1
Willingness to consider EV : BAU failing 2 2 2 2 2 2 2
Willingness to consider collapses when high profile marketing is removedin year 10
Tipping point analysisChange required by year 10 to maintain marketing threshold and hence a successful marketing regime: • a 6.8% increase in CV operating costs• a 10.6% decrease in PIHV operating costs• a 66% decrease in BEV operating costs• 160 mile range for BEV• 130mph max speed for BEV; or• fuel availability increasing from 40% to 55% for BEV
• Subsidies were seen to be crucial in the failing/CM case – but at a cost!
Control panel to vary scenarios
Installed base EV
10 M
5 M
04 4 4 4
3 33
3
22
2
2
2
11
1
1
1
0 6 12 18 24 30 36Time (Year)
Installed base EV[PIHV] : BEV-range-300-20 1 1Installed base EV[PIHV] : Low case 2 2Installed base EV[BEV] : BEV-range-300-20 3Installed base EV[BEV] : Low case 4 4
sales EV
1 M
500,000
04 4
4 43
3
33
2
2
2
2
11
1
1 1
0 8 16 24 32 40Time (Year)
sales EV[PIHV] : BEV-range-300-20 1 1 1sales EV[PIHV] : Low case 2 2 2 2sales EV[BEV] : BEV-range-300-20 3 3sales EV[BEV] : Low case 4 4 4
subsidy duration1 3010
subsidy BEV0 10,0000
Initial fuel availability BEV0 105
Initial operating cost BEV1 2012
Initial range BEV0 50.8
Initial emission rating BEV0 105
BEV Attributes
pence/mile
miles/100
0-10 with 10poor
0-10 with10=100%
Initial max speed BEV1 209mph/10
Short Term Sales
600,000
300,000
0 4 44
4
33
3
3
2 2 2 21
11
1
1
0 4 8 12 16 20Year
sales EV[PIHV] : Low case 1 1 1sales EV[BEV] : Low case 2 2 2 2sales EV[PIHV] : BEV-range-300-20 3 3sales EV[BEV] : BEV-range-300-20 4 4
SW Price Volume ON0 11
Market Shares 2010-2050
0.4
0.2
04 4 4 4
3 3
3
3
3
2 2 22
2
1 11
1
1
0 8 16 24 32 40Year
market share EV[PIHV] : BEV-range-300-20 1 1market share EV[BEV] : BEV-range-300-20 2"Ricardo Low % PIHV" : BEV-range-300-20 3"Ricardo Low % BEV" : BEV-range-300-20 4 4
final range BEV0 43
Time final range BEV1 4020
range BEV
4
0 2 2 21
11 1
0 12 24 36Time (Year)
range BEV : BEV-range-300-20 1range BEV : Low case 2
Price BEV
20
10
2 2 21
1 1
0 14 28Time (Year)
Price BEV : BEV-range-300-20Price BEV : Low case 2
final fuel availability BEV1 105
Time final fuel availability BEV1 4040
fuel availability BEV
6
42 2 21 1 1 1
0 12 24 36Time (Year)
fuel availability BEV : BEV-range-300-20fuel availability BEV : Low case
final operating cost BEV0 2012
Time final operating cost BEV1 4040
final max speed BEV6 129
Time final max speed BEV1 4040
final emission rating BEV0 105
Time final emission rating BEV1 4040
Initial operating cost PIHV10 2017pence/mile
final operating cost PIHV5 2017
Time final operating cost PIHV1 4040
Initial operating cost CV10 2522
final operating cost CV5 3022
Time final operating cost CV1 4040
subsidy PIHV0 10,0000
initial budget100 M 1 B500 M
budget limited0 10
PIHV and CV Operating costs
Some of the conclusions
• BAU assumptions are crucial!• Word of mouth assumptions can have a larger impact• Subsidies have no real impact in BAU but are crucial in a
failing market – but expensive! (required for 6 years minimum – could cost in excess of £500m depending on other factors)
• If EVs take off then we see significant loss of fuel duty = £10bn p.a. 2050 in most optimistic case.
• Revenue preserver per vehicle could range between £300-£650 p.a. by 2050.
• A further 9% reduction in emissions from CV gives similar results in terms of CO2 at much lower cost to government.
Some other examples
• Over 50 journal papers since 1994• Shepherd, S.P. (2014) A review of system dynamics models applied in
transportation. Transportmetrica B: Transport Dynamics, 2014. http://dx.doi.org/10.1080/21680566.2014.916236
• Examples cover 6 main areas – airports and airlines, strategic polic/regional models, supply chain management with transport, highway construction/maintenance, uptake of AFVs and miscellaneous.
EU White paper challenge
• Halve the use of ‘conventionally fuelled’ cars in urban transport by 2030; phase them out in cities by 2050;
Behaviour change
Growth and business cycles
Uncertainty
Source adapted from Zurek, M. and T. Henrichs (2007): Linking scenarios across geographical scales in international environmental assessments. Technological Forecasting and Social Change.
Technology or behaviour change?
C-ROADS at COP-15
• Scoreboard went viral• Real-time analysis
picked up by media, negotiators
• US State Dept used as common platform, picked up by other delegations “This capability, had it been
available to me when we negotiated Kyoto, would have yielded a different outcome.”
Tim Wirth, President, UN Foundation, former Senator
Summary• SD has been applied widely in transport problems• It has the advantage of being transparent (with client
involvement in building CLDs)• Small models can show underlying structure and
dynamics of the problem – providing new insights• Can deal with cycles, resource limits, lagged
responses, softer variables• Easy to introduce scenario and sensitivity analysis• Can deal naturally with cohorts (population or fleet)• Can bring in more systems and learn from structures in
other fields
Summary 2
• Provides a holistic approach to modelling• Not suited to traditional network assignment problems• Future applications - competition dynamics, freight and
the development of ports, sensitivity of systems and transport demand to changing external factors related to demographics and the economy;
• modelling behavioural change whether this is at the user level of some higher level stakeholder
• modelling the decision making process and game playing to inform
And finally
• “System dynamics helps us expand the boundaries of our mental models so that we become aware of and take responsibility for the feedbacks created by our decisions”, Sterman (2002).
