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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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    1. Carlos F. Daganzo, 1983. "Stochastic Network Equilibrium with Multiple Vehicle Types and Asymmetric, Indefinite Link Cost Jacobians," Transportation Science, INFORMS, vol. 17(3), pages 282-300, August.
    2. Charles D. Kolstad & Lars Mathiesen, 1987. "Necessary and Sufficient Conditions for Uniqueness of a Cournot Equilibrium," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(4), pages 681-690.
    3. Michael J. Smith, 1984. "The Existence of a Time-Dependent Equilibrium Distribution of Arrivals at a Single Bottleneck," Transportation Science, INFORMS, vol. 18(4), pages 385-394, November.
    4. Carlos F. Daganzo & Reinaldo C. Garcia, 2000. "A Pareto Improving Strategy for the Time-Dependent Morning Commute Problem," Transportation Science, INFORMS, vol. 34(3), pages 303-311, August.
    5. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    6. Richard Arnott & André de Palma & Robin Lindsey, 1993. "Properties of Dynamic Traffic Equilibrium Involving Bottlenecks, Including a Paradox and Metering," Transportation Science, INFORMS, vol. 27(2), pages 148-160, May.
    7. 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.
    8. Arnott, Richard & DePalma, Elijah, 2011. "The corridor problem: Preliminary results on the no-toll equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 45(5), pages 743-768, June.
    9. Han, Ke & Friesz, Terry L. & Yao, Tao, 2013. "Existence of simultaneous route and departure choice dynamic user equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 53(C), pages 17-30.
    10. Ban, Xuegang (Jeff) & Pang, Jong-Shi & Liu, Henry X. & Ma, Rui, 2012. "Continuous-time point-queue models in dynamic network loading," Transportation Research Part B: Methodological, Elsevier, vol. 46(3), pages 360-380.
    11. Chris Hendrickson & George Kocur, 1981. "Schedule Delay and Departure Time Decisions in a Deterministic Model," Transportation Science, INFORMS, vol. 15(1), pages 62-77, February.
    12. Masao Kuwahara, 1990. "Equilibrium Queueing Patterns at a Two-Tandem Bottleneck during the Morning Peak," Transportation Science, INFORMS, vol. 24(3), pages 217-229, August.
    13. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-260, May.
    14. Carlos F. Daganzo, 1985. "The Uniqueness of a Time-dependent Equilibrium Distribution of Arrivals at a Single Bottleneck," Transportation Science, INFORMS, vol. 19(1), pages 29-37, February.
    15. Takashi Akamatsu, 2001. "An Efficient Algorithm for Dynamic Traffic Equilibrium Assignment with Queues," Transportation Science, INFORMS, vol. 35(4), pages 389-404, November.
    16. Lago, Alejandro & Daganzo, Carlos F., 2007. "Spillovers, merging traffic and the morning commute," Transportation Research Part B: Methodological, Elsevier, vol. 41(6), pages 670-683, July.
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    2. Takayama, Yuki & Kuwahara, Masao, 2017. "Bottleneck congestion and residential location of heterogeneous commuters," Journal of Urban Economics, Elsevier, vol. 100(C), pages 65-79.
    3. 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.
    4. 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.
    5. 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.
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    8. 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.
    9. 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.
    10. 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.
    11. Sakai, Takara & Akamatsu, Takashi & Satsukawa, Koki, 2024. "Queue replacement principle for corridor problems with heterogeneous commuters," Transportation Research Part B: Methodological, Elsevier, vol. 187(C).
    12. Satsukawa, Koki & Wada, Kentaro & Watling, David, 2022. "Dynamic system optimal traffic assignment with atomic users: Convergence and stability," Transportation Research Part B: Methodological, Elsevier, vol. 155(C), pages 188-209.
    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. 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).
    16. Wen-Long Jin, 2020. "Stable Day-to-Day Dynamics for Departure Time Choice," Transportation Science, INFORMS, vol. 54(1), pages 42-61, January.
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    18. Takayama, Yuki, 2018. "Time-varying congestion tolling and urban spatial structure," MPRA Paper 89896, University Library of Munich, Germany.

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