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Travel cost budget based user equilibrium in a bottleneck model with stochastic capacity

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  • Liu, Qiumin
  • Jiang, Rui
  • Liu, Ronghui
  • Zhao, Hui
  • Gao, Ziyou

Abstract

This paper studies a bottleneck model in which the capacity of the bottleneck is constant within a day but changes stochastically from day-to-day between a designed value (good condition) and a degraded one (bad condition). The study relates the travel cost variability due to stochastic capacity with commuters' departure time choice behaviors. We postulate that commuters acquire the variability of travel cost based on past experiences and factor such variability into their departure time choice consideration by minimizing their travel cost budget (TCB), defined as a weighted average of mean travel cost and standard deviation of travel cost. We show that the consideration of TCB yields seven possible equilibrium patterns. Closed form solutions to all possible equilibrium patterns and their corresponding parameter ranges are derived. The rationality of the patterns has been investigated. Dependence of travel cost and the duration of peak hours on the commuters' risk attitude has also been derived in each equilibrium pattern. Finally, numerical studies have been conducted to illustrate the properties.

Suggested Citation

  • Liu, Qiumin & Jiang, Rui & Liu, Ronghui & Zhao, Hui & Gao, Ziyou, 2020. "Travel cost budget based user equilibrium in a bottleneck model with stochastic capacity," Transportation Research Part B: Methodological, Elsevier, vol. 139(C), pages 1-37.
    • Handle: RePEc:eee:transb:v:139:y:2020:i:c:p:1-37
    DOI: 10.1016/j.trb.2020.05.002
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    1. Lindsey, Robin, 2009. "Cost recovery from congestion tolls with random capacity and demand," Journal of Urban Economics, Elsevier, vol. 66(1), pages 16-24, July.
    2. Brownstone, David & Ghosh, Arindam & Golob, Thomas F. & Kazimi, Camilla & Van Amelsfort, Dirk, 2003. "Drivers' willingness-to-pay to reduce travel time: evidence from the San Diego I-15 congestion pricing project," Transportation Research Part A: Policy and Practice, Elsevier, vol. 37(4), pages 373-387, May.
    3. Huang, Hai-Jun, 2000. "Fares and tolls in a competitive system with transit and highway: the case with two groups of commuters," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 36(4), pages 267-284, December.
    4. Nie, Yu (Marco) & Yin, Yafeng, 2013. "Managing rush hour travel choices with tradable credit scheme," Transportation Research Part B: Methodological, Elsevier, vol. 50(C), pages 1-19.
    5. Zhang, Xiang & Liu, Wei & Waller, S. Travis & Yin, Yafeng, 2019. "Modelling and managing the integrated morning-evening commuting and parking patterns under the fully autonomous vehicle environment," Transportation Research Part B: Methodological, Elsevier, vol. 128(C), pages 380-407.
    6. Robin Lindsey, C. & van den Berg, Vincent A.C. & Verhoef, Erik T., 2012. "Step tolling with bottleneck queuing congestion," Journal of Urban Economics, Elsevier, vol. 72(1), pages 46-59.
    7. Fosgerau, Mogens, 2008. "Congestion costs in bottleneck equilibrium with stochastic capacity and demand," MPRA Paper 10040, University Library of Munich, Germany.
    8. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1993. "A Structural Model of Peak-Period Congestion: A Traffic Bottleneck with Elastic Demand," American Economic Review, American Economic Association, vol. 83(1), pages 161-179, March.
    9. Hao Li & Michiel C.J. Bliemer & Piet H.L. Bovy, 2009. "Reliability-based Dynamic Discrete Network Design with Stochastic Networks," Springer Books, in: William H. K. Lam & S. C. Wong & Hong K. Lo (ed.), Transportation and Traffic Theory 2009: Golden Jubilee, chapter 0, pages 651-673, Springer.
    10. Nie, Yu (Marco), 2011. "Multi-class percentile user equilibrium with flow-dependent stochasticity," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1641-1659.
    11. Xiangdong Xu & Anthony Chen & Lin Cheng, 2013. "Assessing the effects of stochastic perception error under travel time variability," Transportation, Springer, vol. 40(3), pages 525-548, May.
    12. Watling, David, 2006. "User equilibrium traffic network assignment with stochastic travel times and late arrival penalty," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1539-1556, December.
    13. Wuping Xin & David Levinson, 2015. "Stochastic Congestion and Pricing Model with Endogenous Departure Time Selection and Heterogeneous Travelers," Mathematical Population Studies, Taylor & Francis Journals, vol. 22(1), pages 37-52, March.
    14. 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.
    15. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-260, May.
    16. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1990. "Economics of a bottleneck," Journal of Urban Economics, Elsevier, vol. 27(1), pages 111-130, January.
    17. Wang, Judith Y.T. & Ehrgott, Matthias & Chen, Anthony, 2014. "A bi-objective user equilibrium model of travel time reliability in a road network," Transportation Research Part B: Methodological, Elsevier, vol. 66(C), pages 4-15.
    18. Ma, Rui & Zhang, H.M., 2017. "The morning commute problem with ridesharing and dynamic parking charges," Transportation Research Part B: Methodological, Elsevier, vol. 106(C), pages 345-374.
    19. Barbara W.Y. Siu & Hong K. Lo, 2009. "Equilibrium Trip Scheduling in Congested Traffic under Uncertainty," Springer Books, in: William H. K. Lam & S. C. Wong & Hong K. Lo (ed.), Transportation and Traffic Theory 2009: Golden Jubilee, chapter 0, pages 147-167, Springer.
    20. Fosgerau, Mogens, 2010. "On the relation between the mean and variance of delay in dynamic queues with random capacity and demand," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 598-603, April.
    21. 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.
    22. Arnott, R. & de Palma, A. & Lindsey, R., 1990. "Departure time and route choice for the morning commute," Transportation Research Part B: Methodological, Elsevier, vol. 24(3), pages 209-228, June.
    23. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1999. "Information and time-of-usage decisions in the bottleneck model with stochastic capacity and demand," European Economic Review, Elsevier, vol. 43(3), pages 525-548, March.
    24. de Palma, André & Picard, Nathalie, 2005. "Route choice decision under travel time uncertainty," Transportation Research Part A: Policy and Practice, Elsevier, vol. 39(4), pages 295-324, May.
    25. Kou, Weibin & Chen, Xumei & Yu, Lei & Qi, Yi & Wang, Ying, 2017. "Urban commuters’ valuation of travel time reliability based on stated preference survey: A case study of Beijing," Transportation Research Part A: Policy and Practice, Elsevier, vol. 95(C), pages 372-380.
    26. Lo, Hong K. & Luo, X.W. & Siu, Barbara W.Y., 2006. "Degradable transport network: Travel time budget of travelers with heterogeneous risk aversion," Transportation Research Part B: Methodological, Elsevier, vol. 40(9), pages 792-806, November.
    27. Fosgerau, Mogens & Karlström, Anders, 2010. "The value of reliability," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 38-49, January.
    28. Ling-Ling Xiao & Hai-Jun Huang & Ronghui Liu, 2015. "Congestion Behavior and Tolls in a Bottleneck Model with Stochastic Capacity," Transportation Science, INFORMS, vol. 49(1), pages 46-65, February.
    29. Small, Kenneth A, 1982. "The Scheduling of Consumer Activities: Work Trips," American Economic Review, American Economic Association, vol. 72(3), pages 467-479, June.
    30. Lo, Hong K. & Tung, Yeou-Koung, 2003. "Network with degradable links: capacity analysis and design," Transportation Research Part B: Methodological, Elsevier, vol. 37(4), pages 345-363, May.
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    2. Yu, Xiaojuan & van den Berg, Vincent A.C. & Li, Zhi-Chun, 2023. "Congestion pricing and information provision under uncertainty: Responsive versus habitual pricing," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 175(C).
    3. Fan, Wenbo & Xiao, Feng & Nie, Yu (Macro), 2022. "Managing bottleneck congestion with tradable credits under asymmetric transaction cost," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 158(C).
    4. Zhang, Yuan & Zhao, Hui & Jiang, Rui, 2024. "Manage morning commute for household travels with parking space constraints," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 185(C).
    5. Qiumin Liu & Vincent A.C. van den Berg & Erik T. Verhoef & Rui Jiang, 2024. "Pricing in the Stochastic Bottleneck Model with Price-Sensitive Demand," Tinbergen Institute Discussion Papers 24-011/VIII, Tinbergen Institute, revised 22 Oct 2024.

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