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Network Equilibrium under Cumulative Prospect Theory and Endogenous Stochastic Demand and Supply

In: Transportation and Traffic Theory 2009: Golden Jubilee

Author

Listed:
  • Agachai Sumalee

    (The Hong Kong Polytechnic University)

  • Richard D. Connors

    (University of Leeds)

  • Paramet Luathep

    (The Hong Kong Polytechnic University)

Abstract

In this paper we consider a network whose travel demands and road capacities are endogenously considered to be random variables. With stochastic demand and supply the route travel times are also random variables. In this scenario travelers choose their routes under travel time uncertainties. Several evidences suggest that the decision making process under uncertainty is significantly different from that without uncertainty. Therefore, the paper applies the decision framework of cumulative prospect theory (CPT) to capture this difference. We first formulate a stochastic network model whose travel demands and link capacities follow lognormal distributions. The stochastic travel times can then be derived under a given route choice modeling framework. For the route choice, we consider a modeling framework where the perceived value and perceived probabilities of travel time outcomes are obtained via transformations following CPT. We then formulate an equilibrium condition similar to that of User Equilibrium in which travelers choose the routes that maximizes their perceived utility values in the face of transformed stochastic travel times. Conditions are established guaranteeing existence (but not uniqueness) of this equilibrium. The paper then proposes a solution algorithm for the proposed model which is then tested with a test network.

Suggested Citation

  • Agachai Sumalee & Richard D. Connors & Paramet Luathep, 2009. "Network Equilibrium under Cumulative Prospect Theory and Endogenous Stochastic Demand and Supply," Springer Books, in: William H. K. Lam & S. C. Wong & Hong K. Lo (ed.), Transportation and Traffic Theory 2009: Golden Jubilee, chapter 0, pages 19-38, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4419-0820-9_2
    DOI: 10.1007/978-1-4419-0820-9_2
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    Citations

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    Cited by:

    1. Gao, Kun & Sun, Lijun & Yang, Ying & Meng, Fanyu & Qu, Xiaobo, 2021. "Cumulative prospect theory coupled with multi-attribute decision making for modeling travel behavior," Transportation Research Part A: Policy and Practice, Elsevier, vol. 148(C), pages 1-21.
    2. Chen, Anthony & Zhou, Zhong & Lam, William H.K., 2011. "Modeling stochastic perception error in the mean-excess traffic equilibrium model," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1619-1640.
    3. Zhang, Chao & Chen, Xiaojun & Sumalee, Agachai, 2011. "Robust Wardrop's user equilibrium assignment under stochastic demand and supply: Expected residual minimization approach," Transportation Research Part B: Methodological, Elsevier, vol. 45(3), pages 534-552, March.
    4. Amit Kothiyal & Vitalie Spinu & Peter Wakker, 2011. "Prospect theory for continuous distributions: A preference foundation," Journal of Risk and Uncertainty, Springer, vol. 42(3), pages 195-210, June.
    5. Li-Jun Tian & Hai-Jun Huang & Zi-You Gao, 2012. "A Cumulative Perceived Value-Based Dynamic User Equilibrium Model Considering the Travelers’ Risk Evaluation on Arrival Time," Networks and Spatial Economics, Springer, vol. 12(4), pages 589-608, December.
    6. Hongli Xu & Hai Yang & Jing Zhou & Yafeng Yin, 2017. "A Route Choice Model with Context-Dependent Value of Time," Transportation Science, INFORMS, vol. 51(2), pages 536-548, May.
    7. Zhaoqi Zang & Xiangdong Xu & Kai Qu & Ruiya Chen & Anthony Chen, 2022. "Travel time reliability in transportation networks: A review of methodological developments," Papers 2206.12696, arXiv.org, revised Jul 2022.
    8. Li, Hao & Tu, Huizhao & Hensher, David A., 2016. "Integrating the mean–variance and scheduling approaches to allow for schedule delay and trip time variability under uncertainty," Transportation Research Part A: Policy and Practice, Elsevier, vol. 89(C), pages 151-163.
    9. de Moraes Ramos, Giselle & Daamen, Winnie & Hoogendoorn, Serge, 2013. "Modelling travellers' heterogeneous route choice behaviour as prospect maximizers," Journal of choice modelling, Elsevier, vol. 6(C), pages 17-33.
    10. Xu, Hongli & Lou, Yingyan & Yin, Yafeng & Zhou, Jing, 2011. "A prospect-based user equilibrium model with endogenous reference points and its application in congestion pricing," Transportation Research Part B: Methodological, Elsevier, vol. 45(2), pages 311-328, February.
    11. Xiangfeng Ji & Xuegang (Jeff) Ban & Mengtian Li & Jian Zhang & Bin Ran, 2017. "Non-expected Route Choice Model under Risk on Stochastic Traffic Networks," Networks and Spatial Economics, Springer, vol. 17(3), pages 777-807, September.
    12. Giselle Moraes Ramos & Winnie Daamen & Serge Hoogendoorn, 2014. "A State-of-the-Art Review: Developments in Utility Theory, Prospect Theory and Regret Theory to Investigate Travellers' Behaviour in Situations Involving Travel Time Uncertainty," Transport Reviews, Taylor & Francis Journals, vol. 34(1), pages 46-67, January.

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