This document discusses using system dynamics modeling to approach transport modeling. It begins with introducing system dynamics and its use of feedback loops, stocks and flows to model complex systems. Examples are given of causal loop diagrams modeling chicken-egg feedback and balancing loops. Further examples model population dynamics, epidemics, electric vehicle uptake, and other transport problems. The approach allows scenario analysis and accounting for lagged effects, resource limits, and other dynamics. System dynamics provides a holistic approach compared to traditional network models and can provide new insights into transport systems and inform policy decisions.

1. A System Dynamics Approach to
Transport Modelling
Simon Shepherd
Institute for Transport Studies
University of Leeds (UK)
S.P.Shepherd@its.leeds.ac.uk

2. Aims
• Introduction Systems Dynamics
• Some examples
• Challenges

3. 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

4. Introduction :principles of
Systems Dynamics
• Representation of systems
Qualitative
Quantitative
Verbal description
Cause-effect diagrams
Flow charts
Equations

5. 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.

6. CLD example
• Simple example
Eggs
Chicken
+
+
etc.
Time
Population
Reinforcing
feedback loop
+

7. CLD example 2
• Simple example 2
Eggs
Chicken
+
+
+
# Road
crossing +
-
etc. Time
Population
Balancing
feedback loop
-

8. 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

9. Stocks and flows
Stock
inflow outflow
  
t
t
tStockdssoutflowsInflowtStock
0
)()()()( 0

10. Chickens
birthsdeaths
eggs
+
+
road crossings
+
+
-
Chickens
1,000
500
0
0 2 4 6 8 10
Time (Month)
Chickens : with crossings
Chicken and eggs model
Note : 𝑑𝑒𝑎𝑡ℎ𝑠(𝑡) =
𝑟𝑜𝑎𝑑 𝑐𝑟𝑜𝑠𝑠𝑖𝑛𝑔𝑠(𝑡)2
1000

11. Population
births deaths
birth rate death rate
Population
800
400
0
0 20 40 60 80 100
Time (Month)
Rabbit
Population : Current
Simple population model
𝒑𝒐𝒑𝒖𝒍𝒂𝒕𝒊𝒐𝒏 = 𝒃𝒊𝒓𝒕𝒉𝒔 − 𝒅𝒆𝒂𝒕𝒉𝒔
𝒅𝒆𝒂𝒕𝒉𝒔 = 𝒑𝒐𝒑𝒖𝒍𝒂𝒕𝒊𝒐𝒏 ∗ 𝒅𝒆𝒂𝒕𝒉 𝒓𝒂𝒕𝒆
𝒃𝒊𝒓𝒕𝒉𝒔 = 𝒑𝒐𝒑𝒖𝒍𝒂𝒕𝒊𝒐𝒏 ∗ 𝒃𝒊𝒓𝒕𝒉 𝒓𝒂𝒕𝒆
Population
Young
births aging young
average time in young
birth rate
Population
Middle
Population
Old
aging middle aging old
average time in middle average time in old
initial pop
infant
initial pop
middle
initial pop
old

12. Fox
Population
fox food availability
fox food
requirements
average fox life
fox consumption
of rabbits
fox birth rate
initial fox
population
fox mortality
lookup
fox births fox deaths
Rabbit
Population
rabbit births
rabbit crowding
carrying capacity
average rabbit liferabbit birth rate
initial rabbit
population
effect of
crowding on
deaths lookup
fox rabbit
consumption
lookup
rabbit deaths
Rabbit Population
4,000
2,000
0
0 10 20 30 40 50
Time (Year)
Rabbit
Rabbit Population : Current
Fox Population
200
100
0
0 10 20 30 40 50
Time (Year)
Fox
Fox Population : Current

13. Susceptible
Population
Infected
Population
infections
rate of potential
infectious contacts
rate that people
contact other people
Fraction of
population infected
total population
Contacts
between infected
and unaffected
fraction infected
from contact
initial infectedinitial susceptible
Susceptible Population
1 M
750,000
500,000
250,000
0
0 10 20 30 40 50
Time (day)
Person
Susceptible Population : Current
Infected Population
1 M
500,000
0
0 10 20 30 40 50
Time (day)
Person
Infected Population
Simple epidemic model

14. Example – uptake of Electric Vehicles

15. 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

16. Struben and Sterman (2008) Take up of AFV

17. Calibrated to BERR 2030

18. Sensitivity to word of mouth
Word of mouth between CV drivers is
crucial for success – as was marketing

19. Example CM/failing regime vs BAU
market shareEV
0.4
0.3
0.2
0.1
0
0 4 8 12 16 20 24 28 32 36 40
Time (Year)
marketshare EV[PIHV]:BAUbase
marketshare EV[PIHV]:BAUfailing
marketshare EV[BEV]:BAUbase
marketshare EV[BEV]:BAUfailing
Willingnessto considerEV
1
0.75
0.5
0.25
0
0 4 8 12 16 20 24 28 32 36 40
Time(Year)
WillingnesstoconsiderEV:BAUbase
WillingnesstoconsiderEV:BAUfailing
Willingness to consider collapses when high profile marketing is removed
in year 10

20. Tipping point analysis
Change 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!

21. Control panel to vary scenarios
Installed base EV
10 M
5 M
0
4 4
4 4
3 3
3
3
2
2
2
2
2
1
1
1
1
1
0 6 12 18 24 30 36
Time (Year)
Installed base EV[PIHV] : BEV-range-300-20 1 1
Installed base EV[PIHV] : Low case 2 2
Installed base EV[BEV] : BEV-range-300-20 3
Installed base EV[BEV] : Low case 4 4
sales EV
1 M
500,000
0 4 4
4 4
3
3
3
3
2
2
2
2
1
1
1
1 1
0 8 16 24 32 40
Time (Year)
sales EV[PIHV] : BEV-range-300-20 1 1 1
sales EV[PIHV] : Low case 2 2 2 2
sales EV[BEV] : BEV-range-300-20 3 3
sales EV[BEV] : Low case 4 4 4
subsidy duration
1 3010
subsidy BEV
0 10,0000
Initial fuel availability BEV
0 105
Initial operating cost BEV
1 2012
Initial range BEV
0 50.8
Initial emission rating BEV
0 105
BEV Attributes
pence/mile
miles/100
0-10 with 10
poor
0-10 with
10=100%
Initial max speed BEV
1 209mph/10
Short Term Sales
600,000
300,000
0 4 4
4
4
3
3
3
3
2 2 2 2
1
1
1
1
1
0 4 8 12 16 20
Year
sales EV[PIHV] : Low case 1 1 1
sales EV[BEV] : Low case 2 2 2 2
sales EV[PIHV] : BEV-range-300-20 3 3
sales EV[BEV] : BEV-range-300-20 4 4
SW Price Volume ON
0 11
Market Shares 2010-2050
0.4
0.2
0
4 4 4 4
3 3
3
3
3
2 2 2
2
2
1 1
1
1
1
0 8 16 24 32 40
Year
market share EV[PIHV] : BEV-range-300-20 1 1
market 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 BEV
0 43
Time final range BEV
1 4020
range BEV
4
0 2 2 21
1
1 1
0 12 24 36
Time (Year)
range BEV : BEV-range-300-20 1
range BEV : Low case 2
Price BEV
20
10
2
2 2
1
1 1
0 14 28
Time (Year)
Price BEV : BEV-range-300-20
Price BEV : Low case 2
final fuel availability BEV
1 105
Time final fuel availability BEV
1 4040
fuel availability BEV
6
4
2 2 21 1 1 1
0 12 24 36
Time (Year)
fuel availability BEV : BEV-range-300-20
fuel availability BEV : Low case
final operating cost BEV
0 2012
Time final operating cost BEV
1 4040
final max speed BEV
6 129
Time final max speed BEV
1 4040
final emission rating BEV
0 105
Time final emission rating BEV
1 4040
Initial operating cost PIHV
10 2017pence/mile
final operating cost PIHV
5 2017
Time final operating cost PIHV
1 4040
Initial operating cost CV
10 2522
final operating cost CV
5 3022
Time final operating cost CV
1 4040
subsidy PIHV
0 10,0000
initial budget
100 M 1 B500 M
budget limited
0 10
PIHV and CV Operating costs

22. 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.

23. 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.

24. EU White paper challenge
• Halve the use of ‘conventionally fuelled’
cars in urban transport by 2030; phase
them out in cities by 2050;

25. Future challenges

26. Behaviour change

27. Growth and business cycles

28. Uncertainty
Source adapted from Zurek, M. and T. Henrichs (2007): Linking scenarios across geographical
scales in international environmental assessments. Technological Forecasting and Social Change.

29. Technology or behaviour
change?

30. 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

31. 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

32. 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

33. 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).

34. Thank you for listening
S.P.Shepherd@its.leeds.ac.uk