IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v139y2020icp1-37.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191261520303179
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.trb.2020.05.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Senlai Zhu & Hantao Yu & Congjun Fan, 2024. "Travel Plan Sharing and Regulation for Managing Traffic Bottleneck Based on Blockchain Technology," Sustainability, MDPI, vol. 16(4), pages 1-20, February.
    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Li, Zhi-Chun & Huang, Hai-Jun & Yang, Hai, 2020. "Fifty years of the bottleneck model: A bibliometric review and future research directions," Transportation Research Part B: Methodological, Elsevier, vol. 139(C), pages 311-342.
    2. Liu, Yang & Li, Yuanyuan & Hu, Lu, 2018. "Departure time and route choices in bottleneck equilibrium under risk and ambiguity," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 774-793.
    3. 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.
    4. Zhu, Tingting & Li, Yao & Long, Jiancheng, 2022. "Departure time choice equilibrium and tolling strategies for a bottleneck with continuous scheduling preference," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 159(C).
    5. 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.
    6. Xiao, Yu & Coulombel, Nicolas & Palma, André de, 2017. "The valuation of travel time reliability: does congestion matter?," Transportation Research Part B: Methodological, Elsevier, vol. 97(C), pages 113-141.
    7. Amirgholy, Mahyar & Gonzales, Eric J., 2017. "Efficient frontier of route choice for modeling the equilibrium under travel time variability with heterogeneous traveler preferences," Economics of Transportation, Elsevier, vol. 11, pages 1-14.
    8. Ren-Yong Guo & Hai Yang & Hai-Jun Huang, 2018. "Are We Really Solving the Dynamic Traffic Equilibrium Problem with a Departure Time Choice?," Transportation Science, INFORMS, vol. 52(3), pages 603-620, June.
    9. André de Palma & Mogens Fosgerau, 2011. "Dynamic Traffic Modeling," Chapters, in: André de Palma & Robin Lindsey & Emile Quinet & Roger Vickerman (ed.), A Handbook of Transport Economics, chapter 9, Edward Elgar Publishing.
    10. 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.
    11. Teppei Kato & Kenetsu Uchida & William H. K. Lam & Agachai Sumalee, 2021. "Estimation of the value of travel time and of travel time reliability for heterogeneous drivers in a road network," Transportation, Springer, vol. 48(4), pages 1639-1670, August.
    12. Wang, Hua & Meng, Qiang & Wang, Jing & Zhao, De, 2021. "An electric-vehicle corridor model in a dense city with applications to charging location and traffic management," Transportation Research Part B: Methodological, Elsevier, vol. 149(C), pages 79-99.
    13. Nicolas Coulombel & André de Palma, 2014. "The marginal social cost of travel time variability," Post-Print hal-01100105, HAL.
    14. André de Palma & Mogens Fosgerau, 2010. "Dynamic and Static congestion models: A review," Working Papers hal-00539166, HAL.
    15. 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.
    16. Kenneth Small, 2015. "The Bottleneck Model: An Assessment and Interpretation," Working Papers 141506, University of California-Irvine, Department of Economics.
    17. Zhu, Zheng & Li, Xinwei & Liu, Wei & Yang, Hai, 2019. "Day-to-day evolution of departure time choice in stochastic capacity bottleneck models with bounded rationality and various information perceptions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 131(C), pages 168-192.
    18. Nicolas Coulombel & André De Palma, 2014. "Variability of Travel Time, Congestion, and the Cost of Travel," Mathematical Population Studies, Taylor & Francis Journals, vol. 21(4), pages 220-242, December.
    19. Zhu, Zheng & Mardan, Atabak & Zhu, Shanjiang & Yang, Hai, 2021. "Capturing the interaction between travel time reliability and route choice behavior based on the generalized Bayesian traffic model," Transportation Research Part B: Methodological, Elsevier, vol. 143(C), pages 48-64.
    20. Takayama, Yuki, 2020. "Who gains and who loses from congestion pricing in a monocentric city with a bottleneck?," Economics of Transportation, Elsevier, vol. 24(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:transb:v:139:y:2020:i:c:p:1-37. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/548/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.