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The corridor problem with discrete multiple bottlenecks

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  • Akamatsu, Takashi
  • Wada, Kentaro
  • Hayashi, Shunsuke

Abstract

This paper presents a transparent approach to the analysis of dynamic user equilibrium and clarifies the properties of a departure-time choice equilibrium of a corridor problem where discrete multiple bottlenecks exist along a freeway. The basis of our approach is the transformation of the formulation of equilibrium conditions in a conventional “Eulerian coordinate system” into one in a “Lagrangian-like coordinate system.” This enables us to evaluate dynamic travel times easily, and to achieve a deep understanding of the mathematical structure of the problem, in particular, about the properties of the demand and supply (queuing) sub-models, relations with dynamic system optimal assignment, and differences between the morning and evening rush problems. Building on these foundations, we establish rigorous results on the existence and uniqueness of equilibria.

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  • Akamatsu, Takashi & Wada, Kentaro & Hayashi, Shunsuke, 2015. "The corridor problem with discrete multiple bottlenecks," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 808-829.
    • Handle: RePEc:eee:transb:v:81:y:2015:i:p3:p:808-829
    DOI: 10.1016/j.trb.2015.07.015
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    Cited by:

    1. Akamatsu, Takashi & Wada, Kentaro & Iryo, Takamasa & Hayashi, Shunsuke, 2021. "A new look at departure time choice equilibrium models with heterogeneous users," Transportation Research Part B: Methodological, Elsevier, vol. 148(C), pages 152-182.
    2. Satsukawa, Koki & Wada, Kentaro & Iryo, Takamasa, 2020. "Reprint of “Stochastic stability of dynamic user equilibrium in unidirectional networks: Weakly acyclic game approach”," Transportation Research Part B: Methodological, Elsevier, vol. 132(C), pages 117-135.
    3. Takayama, Yuki & Kuwahara, Masao, 2017. "Bottleneck congestion and residential location of heterogeneous commuters," Journal of Urban Economics, Elsevier, vol. 100(C), pages 65-79.
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    5. 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).
    6. Bao, Yue & Verhoef, Erik T. & Koster, Paul, 2021. "Leaving the tub: The nature and dynamics of hypercongestion in a bathtub model with a restricted downstream exit," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).
    7. Fu, Haoran & Akamatsu, Takashi & Satsukawa, Koki & Wada, Kentaro, 2022. "Dynamic traffic assignment in a corridor network: Optimum versus equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 161(C), pages 218-246.
    8. Osawa, Minoru & Fu, Haoran & Akamatsu, Takashi, 2018. "First-best dynamic assignment of commuters with endogenous heterogeneities in a corridor network," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 811-831.
    9. Cortina, Mélanie & Chiabaut, Nicolas & Leclercq, Ludovic, 2023. "Fostering synergy between transit and Autonomous Mobility-on-Demand systems: A dynamic modeling approach for the morning commute problem," Transportation Research Part A: Policy and Practice, Elsevier, vol. 170(C).
    10. Tian, Qiong & Liu, Peng & Ong, Ghim Ping & Huang, Hai-Jun, 2021. "Morning commuting pattern and crowding pricing in a many-to-one public transit system with heterogeneous users," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 145(C).
    11. Wada, Kentaro & Satsukawa, Koki & Smith, Mike & Akamatsu, Takashi, 2019. "Network throughput under dynamic user equilibrium: Queue spillback, paradox and traffic control," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 391-413.
    12. Satsukawa, Koki & Wada, Kentaro & Iryo, Takamasa, 2019. "Stochastic stability of dynamic user equilibrium in unidirectional networks: Weakly acyclic game approach," Transportation Research Part B: Methodological, Elsevier, vol. 125(C), pages 229-247.
    13. 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.
    14. Akamatsu, Takashi & Wada, Kentaro & Iryo, Takamasa & Hayashi, Shunsuke, 2018. "Departure time choice equilibrium and optimal transport problems," MPRA Paper 90361, University Library of Munich, Germany.
    15. Wen-Long Jin, 2020. "Stable Day-to-Day Dynamics for Departure Time Choice," Transportation Science, INFORMS, vol. 54(1), pages 42-61, January.
    16. Li, Chuan-Yao & Huang, Hai-Jun, 2017. "Morning commute in a single-entry traffic corridor with early and late arrivals," Transportation Research Part B: Methodological, Elsevier, vol. 97(C), pages 23-49.
    17. Takayama, Yuki, 2018. "Time-varying congestion tolling and urban spatial structure," MPRA Paper 89896, University Library of Munich, Germany.

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