a system dynamics approach to transport modelling

A System Dynamics Approach to

Transport Modelling

Simon Shepherd

Institute for Transport Studies

University of Leeds (UK)

S.P.Shepherd@its.leeds.ac.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;

Future challenges

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).

Thank you for listening

S.P.Shepherd@its.leeds.ac.uk