IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/90361.html
   My bibliography  Save this paper

Departure time choice equilibrium and optimal transport problems

Author

Listed:
  • Akamatsu, Takashi
  • Wada, Kentaro
  • Iryo, Takamasa
  • Hayashi, Shunsuke

Abstract

This paper presents a systematic approach for analyzing the departure-time choice equilibrium (DTCE) problem of a single bottleneck with heterogeneous commuters. The approach is based on the fact that the DTCE is equivalently represented as a linear programming problem with a special structure, which can be analytically solved by exploiting the theory of optimal transport combined with a decomposition technique. By applying the proposed approach to several types of models with heterogeneous commuters, it is shown that the dynamic equilibrium distribution of departure times exhibits striking regularities under mild assumptions regarding schedule delay functions, in which commuters sort themselves according to their attributes, such as desired arrival times, schedule delay functions (value of times), and travel distances to a destination.

Suggested Citation

  • 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.
  • Handle: RePEc:pra:mprapa:90361
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/90361/1/MPRA_paper_90361.pdf
    File Function: original version
    Download Restriction: no

    File URL: https://mpra.ub.uni-muenchen.de/103069/1/MPRA_paper_103069.pdf
    File Function: revised version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Han, Ke & Friesz, Terry L. & Yao, Tao, 2013. "A partial differential equation formulation of Vickrey’s bottleneck model, part I: Methodology and theoretical analysis," Transportation Research Part B: Methodological, Elsevier, vol. 49(C), pages 55-74.
    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. Marcus Berliant & Takatoshi Tabuchi, 2018. "Equilibrium commuting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(3), pages 609-627, May.
    4. Gubins, Sergejs & Verhoef, Erik T., 2014. "Dynamic bottleneck congestion and residential land use in the monocentric city," Journal of Urban Economics, Elsevier, vol. 80(C), pages 51-61.
    5. 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.
    6. 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.
    7. Burkard, Rainer E., 2007. "Monge properties, discrete convexity and applications," European Journal of Operational Research, Elsevier, vol. 176(1), pages 1-14, January.
    8. Jin, Wen-Long, 2015. "Point queue models: A unified approach," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 1-16.
    9. Fosgerau, Mogens & de Palma, André, 2012. "Congestion in a city with a central bottleneck," Journal of Urban Economics, Elsevier, vol. 71(3), pages 269-277.
    10. Han, Ke & Friesz, Terry L. & Yao, Tao, 2013. "A partial differential equation formulation of Vickrey’s bottleneck model, part II: Numerical analysis and computation," Transportation Research Part B: Methodological, Elsevier, vol. 49(C), pages 75-93.
    11. Liu, Yang & Nie, Yu (Marco) & Hall, Jonathan, 2015. "A semi-analytical approach for solving the bottleneck model with general user heterogeneity," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 56-70.
    12. Wheaton, William C., 1974. "Linear programming and locational equilibrium : The Herbert-Stevens model revisited," Journal of Urban Economics, Elsevier, vol. 1(3), pages 278-287, July.
    13. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1992. "Route choice with heterogeneous drivers and group-specific congestion costs," Regional Science and Urban Economics, Elsevier, vol. 22(1), pages 71-102, March.
    14. Gordon F. Newell, 1987. "The Morning Commute for Nonidentical Travelers," Transportation Science, INFORMS, vol. 21(2), pages 74-88, May.
    15. Robin Lindsey, 2004. "Existence, Uniqueness, and Trip Cost Function Properties of User Equilibrium in the Bottleneck Model with Multiple User Classes," Transportation Science, INFORMS, vol. 38(3), pages 293-314, August.
    16. Fosgerau, Mogens, 2015. "Congestion in the bathtub," Economics of Transportation, Elsevier, vol. 4(4), pages 241-255.
    17. Ramadurai, Gitakrishnan & Ukkusuri, Satish V. & Zhao, Jinye & Pang, Jong-Shi, 2010. "Linear complementarity formulation for single bottleneck model with heterogeneous commuters," Transportation Research Part B: Methodological, Elsevier, vol. 44(2), pages 193-214, February.
    18. 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.
    19. 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.
    20. van den Berg, Vincent & Verhoef, Erik T., 2011. "Winning or losing from dynamic bottleneck congestion pricing?," Journal of Public Economics, Elsevier, vol. 95(7), pages 983-992.
    21. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-260, May.
    22. Doan, Kien & Ukkusuri, Satish & Han, Lanshan, 2011. "On the existence of pricing strategies in the discrete time heterogeneous single bottleneck model," Transportation Research Part B: Methodological, Elsevier, vol. 45(9), pages 1483-1500.
    23. Kuwahara, Masao & Akamatsu, Takashi, 1997. "Decomposition of the reactive dynamic assignments with queues for a many-to-many origin-destination pattern," Transportation Research Part B: Methodological, Elsevier, vol. 31(1), pages 1-10, February.
    24. 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.
    Full references (including those not matched with items on IDEAS)

    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. 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. 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.
    3. 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.
    4. Takayama, Yuki, 2018. "Time-varying congestion tolling and urban spatial structure," MPRA Paper 89896, University Library of Munich, Germany.
    5. Takayama, Yuki & Kuwahara, Masao, 2017. "Bottleneck congestion and residential location of heterogeneous commuters," Journal of Urban Economics, Elsevier, vol. 100(C), pages 65-79.
    6. Amirgholy, Mahyar & Gao, H. Oliver, 2017. "Modeling the dynamics of congestion in large urban networks using the macroscopic fundamental diagram: User equilibrium, system optimum, and pricing strategies," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 215-237.
    7. 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).
    8. Amirgholy, Mahyar & Shahabi, Mehrdad & Gao, H. Oliver, 2017. "Optimal design of sustainable transit systems in congested urban networks: A macroscopic approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 103(C), pages 261-285.
    9. Liu, Yang & Nie, Yu (Marco) & Hall, Jonathan, 2015. "A semi-analytical approach for solving the bottleneck model with general user heterogeneity," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 56-70.
    10. 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.
    11. 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).
    12. Guo, Ren-Yong & Yang, Hai & Huang, Hai-Jun & Li, Xinwei, 2018. "Day-to-day departure time choice under bounded rationality in the bottleneck model," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 832-849.
    13. Liu, Wei & Zhang, Fangni & Yang, Hai, 2017. "Modeling and managing morning commute with both household and individual travels," Transportation Research Part B: Methodological, Elsevier, vol. 103(C), pages 227-247.
    14. Lu, Gongyuan & Nie, Yu(Marco) & Liu, Xiaobo & Li, Denghui, 2019. "Trajectory-based traffic management inside an autonomous vehicle zone," Transportation Research Part B: Methodological, Elsevier, vol. 120(C), pages 76-98.
    15. Konagane, Joji & Kono, Tatsuhito, 2021. "Heterogeneous Households’ Choices of Departure Time and Residential Location in a Multiple-origin Single-destination Rail System: Market Equilibrium and the First-best Solution," MPRA Paper 108507, University Library of Munich, Germany.
    16. Xiaojuan Yu & Vincent van den Berg & Erik Verhoef, 2019. "Autonomous cars and dynamic bottleneck congestion revisited: how in-vehicle activities determine aggregate travel patterns," Tinbergen Institute Discussion Papers 19-067/VIII, Tinbergen Institute.
    17. Robin Lindsey, 2004. "Existence, Uniqueness, and Trip Cost Function Properties of User Equilibrium in the Bottleneck Model with Multiple User Classes," Transportation Science, INFORMS, vol. 38(3), pages 293-314, August.
    18. Chen, Hongyu & Nie, Yu (Marco) & Yin, Yafeng, 2015. "Optimal multi-step toll design under general user heterogeneity," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 775-793.
    19. Fu, Xinying & van den Berg, Vincent A.C. & Verhoef, Erik T., 2018. "Private road supply in networks with heterogeneous users," Transportation Research Part A: Policy and Practice, Elsevier, vol. 118(C), pages 430-443.
    20. 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.

    More about this item

    Keywords

    departure time choice equilibrium; linear programming; optimal transport; sorting;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • R41 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics - - - Transportation: Demand, Supply, and Congestion; Travel Time; Safety and Accidents; Transportation Noise

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:pra:mprapa:90361. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.