A. Chakirov (2014) Heterogeneous values of time in a multimodal context: An
activity and agent-based simulation approach, MATSim User Meeting 2015,
Singapore, March 2015.
Heterogeneous values of time in a multimodal context:
An activity- and agent-based simulation approach
Artem Chakirov
Heterogeneity in VOT
α: Value of Time β: Schedule delay early γ – Schedule delay late
Proportional Heterogeneity: α, β, γ vary proportionally => µ, η, λ = const.
- usually strongly income dependent
α- Heterogeneity: α varies, β, γ = const. (µ, λ ≠ const., η = const.)
e.g. type of job, family situation
γ- Heterogeneity: α,β = const., γ = varies (η, µ, λ ≠ const., µ = const.)
e.g. shift workers vs. flexible hours
Small, K. A. and E. T. Verhoef (2007) The Economics of Urban Transportation, Routledge, Abingdon.
3
Introducing Heterogeneous Values of Time in MATSim
Using continuous interaction from Axhausen et al. (2008):
Nagel, K., B. Kickhöfer and J. W. Joubert (2014) Heterogeneous tolls and values of time in multi-agent transport simulation, Procedia Computer Science, 32 (0) 762 – 768.
Kickhöfer, B., D. Grether and K. Nagel (2011) Income-contingent user preferences in policy evaluation: application and discussion based on multi-agent transport
simulations, Transportation, 38 (6) 849–870.
Axhausen, K. W., S. Hess, A. König, G. Abay, J. J. Bates and M. Bierlaire (2008) Income and distance elasticities of values of travel time savings: New Swiss results, Transport
Policy, 15 (3) 173–185.
4
Value of Time and Schedule Delay in MATSim
è
Proportional heterogeneity
α- heterogeneity
γ- heterogeneity
Nagel, K. and G. Flötteröd (2009) Agent-based trac assignment: Going from trips to behavioral travelers, paper presented at the 12th International
Conference on Travel Behaviour Research (IATBR), Jaipur, December 2009.
5
Corridor scenario
Home location
density
Work locations
density
2 km
- 
- 
- 
- 
- 
- 
- 
12000 agents
Home – Work – Home activity chains
Distance between bus stops: 600m
Bus headway: 5 min
Bus capacity: 90 (MAN NL323F)
Bus length: 7.5m
Dwell time per passenger: 1 sec
20km corridor with bus network
(Bus stop every 600m)
6
Behavioural and monetary parameters and activity constrains
Tirachini, A. D.A. Hensher and J.M. Rose (2012) Multimodal Pricing and Optimal Design of Public Transport Services: The Interplay between Traffic Congestion and Bus
Crowding, in Proceedings of the Kuhmo Nectar Conference on Transportation Economics, Berlin.
Chakirov, A. and P. Fourie (2014) Enriched Sioux Falls Scenario with Dynamic and Disaggregate Demand, Working paper, FCL, SEC, Singapore.
7
Income distribution from Sioux Falls synthetic population
Income distribution
Chakirov, A. and P. Fourie (2014) Enriched Sioux Falls Scenario with Dynamic and Disaggregate Demand, Working paper, FCL, SEC, Singapore.
8
Income-based heterogeneity in VOT
Axhausen et al. (2008) estimate λ = 0.1697 for
Different degree of heterogeneity are tested for η *
with n = 0,1,2,3,5,10.
Lorenz curves
Axhausen, K. W., S. Hess, A. König, G. Abay, J. J. Bates and M. Bierlaire (2008) Income and distance elasticities of values of travel time savings: New Swiss results, Transport
Policy, 15 (3) 173–185.
9
First – best pricing approximation
10
First Results
11
Change in realized consumer welfare in % (all toll is returned)
Proportional heterogeneity
α- heterogeneity
γ- heterogeneity
12
Schedule delay cost
α- heterogeneity
γ- heterogeneity
First-best toll
No Toll
Proportional heterogeneity
13
First-Best Toll Benefits with Proportional Heterogeneity (relative)
Changes in Consumer Surplus in %
Changes in Consumer Welfare in %
14
Car Mode shares – Proportional Heterogeneity
No Toll
First-best toll
15
Morning Departure Times vs. Income
Prop hetero n=1
Prop hetero n=3
Alpha hetero n=1
Alpha hetero n=3
First-best toll
No Toll
Homogeneous VOT
16
Evening Departure Times vs. Income
Prop hetero n=1
Prop hetero n=3
Alpha hetero n=1
Alpha hetero n=3
First-best toll
No Toll
Homogeneous
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Outlook
•  Systematic comparison to transportation economics literature
(e.g. Verhoef, van den Berg)
•  Transfer to a realistic medium to large scale scenario (e.g. Sioux Falls, Singapore)
•  Questions of spatial inequality
•  Combination of different heterogeneity characteristics (Value of Time, Schedule Delay,
Trip Distances, Activity Types)
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Toll revenue variations during the last 50 iterations
19
First-Best Toll Benefits with Proportional Heterogeneity (absolute)
Changes in Consumer Surplus
Changes in Consumer Welfare
20