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Stochastic user equilibrium in the presence of state dependence

Author

Listed:
  • Claudia Castaldi

    (University of Rome “La Sapienza”)

  • Paolo Delle Site

    (University Niccolò Cusano)

  • Francesco Filippi

    (University of Rome “La Sapienza”)

Abstract

We consider the following two state-dependent effects at the level of route choice: inertia to change and, as a consequence of experience, lower perception variance for the currently used route. A heteroscedastic extreme value model embodying heterogeneity across alternatives in the mean of the random terms is used. Estimations based on stated preference data confirm the presence of both state-dependent effects. We introduce a new class of stochastic user equilibrium (SUE) models that take state-dependent effects into account. The class includes conventional SUE as special case. The equilibrium conditions are formulated as fixed-point states of deterministic day-to-day assignment processes. At the equilibrium (1) no user can improve her/his utility by unilaterally changing route, and (2) if each user shifts from her/his current route to her/his newly chosen route the observed route flows do not change. The existence of the equilibrium is guaranteed under usually satisfied conditions. A modified method of successive averages is proposed for solution. Examples related to a two arc network and to the Nguyen-Dupuis network illustrate the model.

Suggested Citation

  • Claudia Castaldi & Paolo Delle Site & Francesco Filippi, 2019. "Stochastic user equilibrium in the presence of state dependence," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 8(5), pages 535-559, December.
    • Handle: RePEc:spr:eurjtl:v:8:y:2019:i:5:d:10.1007_s13676-018-0135-x
    DOI: 10.1007/s13676-018-0135-x
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    as
    1. Fisk, Caroline, 1980. "Some developments in equilibrium traffic assignment," Transportation Research Part B: Methodological, Elsevier, vol. 14(3), pages 243-255, September.
    2. Warren B. Powell & Yosef Sheffi, 1982. "The Convergence of Equilibrium Algorithms with Predetermined Step Sizes," Transportation Science, INFORMS, vol. 16(1), pages 45-55, February.
    3. Ennio Cascetta, 2009. "Transportation Systems Analysis," Springer Optimization and Its Applications, Springer, number 978-0-387-75857-2, September.
    4. Amos Tversky & Daniel Kahneman, 1991. "Loss Aversion in Riskless Choice: A Reference-Dependent Model," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(4), pages 1039-1061.
    5. Paolo Delle Site, 2017. "On the Equivalence Between SUE and Fixed-Point States of Day-to-Day Assignment Processes with Serially-Correlated Route Choice," Networks and Spatial Economics, Springer, vol. 17(3), pages 935-962, September.
    6. G. E. Cantarella & D. P. Watling, 2016. "Modelling road traffic assignment as a day-to-day dynamic, deterministic process: a unified approach to discrete- and continuous-time models," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 5(1), pages 69-98, March.
    7. De Borger, Bruno & Fosgerau, Mogens, 2008. "The trade-off between money and travel time: A test of the theory of reference-dependent preferences," Journal of Urban Economics, Elsevier, vol. 64(1), pages 101-115, July.
    8. Karthik Natarajan & Miao Song & Chung-Piaw Teo, 2009. "Persistency Model and Its Applications in Choice Modeling," Management Science, INFORMS, vol. 55(3), pages 453-469, March.
    9. Damla Ahipaşaoğlu, Selin & Arıkan, Uğur & Natarajan, Karthik, 2016. "On the flexibility of using marginal distribution choice models in traffic equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 91(C), pages 130-158.
    10. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555, January.
    11. Qing Li & Feixiong Liao & Harry J. P. Timmermans & Jing Zhou, 2016. "A reference-dependent user equilibrium model for activity-travel scheduling," Transportation, Springer, vol. 43(6), pages 1061-1077, November.
    12. Hess, Stephane & Rose, John M. & Hensher, David A., 2008. "Asymmetric preference formation in willingness to pay estimates in discrete choice models," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 44(5), pages 847-863, September.
    13. Wen, Chieh-Hua & Koppelman, Frank S., 2001. "The generalized nested logit model," Transportation Research Part B: Methodological, Elsevier, vol. 35(7), pages 627-641, August.
    14. Xie, Chi & Liu, Zugang, 2014. "On the stochastic network equilibrium with heterogeneous choice inertia," Transportation Research Part B: Methodological, Elsevier, vol. 66(C), pages 90-109.
    15. Horowitz, Joel L., 1984. "The stability of stochastic equilibrium in a two-link transportation network," Transportation Research Part B: Methodological, Elsevier, vol. 18(1), pages 13-28, February.
    16. 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.
    17. Chen, Anthony & Pravinvongvuth, Surachet & Xu, Xiangdong & Ryu, Seungkyu & Chootinan, Piya, 2012. "Examining the scaling effect and overlapping problem in logit-based stochastic user equilibrium models," Transportation Research Part A: Policy and Practice, Elsevier, vol. 46(8), pages 1343-1358.
    18. Víctor Cantillo & Juan de Dios Ortúzar & Huw C. W. L. Williams, 2007. "Modeling Discrete Choices in the Presence of Inertia and Serial Correlation," Transportation Science, INFORMS, vol. 41(2), pages 195-205, May.
    19. Xu, Xiangdong & Chen, Anthony & Kitthamkesorn, Songyot & Yang, Hai & Lo, Hong K., 2015. "Modeling absolute and relative cost differences in stochastic user equilibrium problem," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 686-703.
    20. Ahipaşaoğlu, Selin Damla & Meskarian, Rudabeh & Magnanti, Thomas L. & Natarajan, Karthik, 2015. "Beyond normality: A cross moment-stochastic user equilibrium model," Transportation Research Part B: Methodological, Elsevier, vol. 81(P2), pages 333-354.
    21. Sang Nguyen & Clermont Dupuis, 1984. "An Efficient Method for Computing Traffic Equilibria in Networks with Asymmetric Transportation Costs," Transportation Science, INFORMS, vol. 18(2), pages 185-202, May.
    22. Carlos F. Daganzo & Yosef Sheffi, 1977. "On Stochastic Models of Traffic Assignment," Transportation Science, INFORMS, vol. 11(3), pages 253-274, August.
    23. Bekhor, Shlomo & Toledo, Tomer, 2005. "Investigating path-based solution algorithms to the stochastic user equilibrium problem," Transportation Research Part B: Methodological, Elsevier, vol. 39(3), pages 279-295, March.
    24. Castillo, Enrique & Menéndez, José María & Jiménez, Pilar & Rivas, Ana, 2008. "Closed form expressions for choice probabilities in the Weibull case," Transportation Research Part B: Methodological, Elsevier, vol. 42(4), pages 373-380, May.
    25. Bhat, Chandra R., 1995. "A heteroscedastic extreme value model of intercity travel mode choice," Transportation Research Part B: Methodological, Elsevier, vol. 29(6), pages 471-483, December.
    26. G. E. Cantarella & E. Cascetta, 1995. "Dynamic Processes and Equilibrium in Transportation Networks: Towards a Unifying Theory," Transportation Science, INFORMS, vol. 29(4), pages 305-329, November.
    27. Vinit Kumar Mishra & Karthik Natarajan & Dhanesh Padmanabhan & Chung-Piaw Teo & Xiaobo Li, 2014. "On Theoretical and Empirical Aspects of Marginal Distribution Choice Models," Management Science, INFORMS, vol. 60(6), pages 1511-1531, June.
    28. Maher, M. J. & Hughes, P. C., 1997. "A probit-based stochastic user equilibrium assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 31(4), pages 341-355, August.
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