IDEAS home Printed from https://ideas.repec.org/a/kap/transp/v50y2023i4d10.1007_s11116-022-10281-0.html
   My bibliography  Save this article

Fundamental diagram of urban rail transit considering train–passenger interaction

Author

Listed:
  • Toru Seo

    (Tokyo Institute of Technology)

  • Kentaro Wada

    (University of Tsukuba)

  • Daisuke Fukuda

    (The University of Tokyo)

Abstract

Urban rail transit often operates with high service frequencies to serve heavy passenger demand during rush hours. Such operations can be delayed by two types of congestion: train congestion and passenger congestion, both of which interact with each other. This delay is problematic for many transit systems, since it can be amplified due to the interaction. However, there are no tractable models describing them; and it makes difficult to analyze management strategies of congested transit systems in general and tractable ways. To fill this gap, this article proposes simple yet physical and dynamic model of urban rail transit. First, a fundamental diagram of transit system (i.e., theoretical relation among train-flow, train-density, and passenger-flow) is analytically derived considering the aforementioned physical interaction. Then, a macroscopic model of transit system for dynamic transit assignment is developed based on the fundamental diagram. Finally, accuracy of the macroscopic model is investigated by comparing to microscopic simulation. The proposed models would be useful for mathematical analysis on management strategies of urban rail transit systems, such as optimal dynamic pricing for travel demand management.

Suggested Citation

  • Toru Seo & Kentaro Wada & Daisuke Fukuda, 2023. "Fundamental diagram of urban rail transit considering train–passenger interaction," Transportation, Springer, vol. 50(4), pages 1399-1424, August.
    • Handle: RePEc:kap:transp:v:50:y:2023:i:4:d:10.1007_s11116-022-10281-0
    DOI: 10.1007/s11116-022-10281-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11116-022-10281-0
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11116-022-10281-0?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. Chiabaut, Nicolas, 2015. "Evaluation of a multimodal urban arterial: The passenger macroscopic fundamental diagram," Transportation Research Part B: Methodological, Elsevier, vol. 81(P2), pages 410-420.
    2. Li, Shukai & Dessouky, Maged M. & Yang, Lixing & Gao, Ziyou, 2017. "Joint optimal train regulation and passenger flow control strategy for high-frequency metro lines," Transportation Research Part B: Methodological, Elsevier, vol. 99(C), pages 113-137.
    3. A. Higgins & E. Kozan, 1998. "Modeling Train Delays in Urban Networks," Transportation Science, INFORMS, vol. 32(4), pages 346-357, November.
    4. Dennis Huisman & Leo G. Kroon & Ramon M. Lentink & Michiel J. C. M. Vromans, 2005. "Operations Research in passenger railway transportation," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(4), pages 467-497, November.
    5. Cats, Oded & West, Jens & Eliasson, Jonas, 2016. "A dynamic stochastic model for evaluating congestion and crowding effects in transit systems," Transportation Research Part B: Methodological, Elsevier, vol. 89(C), pages 43-57.
    6. Joaquín de Cea & Enrique Fernández, 1993. "Transit Assignment for Congested Public Transport Systems: An Equilibrium Model," Transportation Science, INFORMS, vol. 27(2), pages 133-147, May.
    7. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
    8. de Palma, André & Kilani, Moez & Proost, Stef, 2015. "Discomfort in mass transit and its implication for scheduling and pricing," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 1-18.
    9. Gonzales, Eric J. & Daganzo, Carlos F., 2012. "Morning commute with competing modes and distributed demand: User equilibrium, system optimum, and pricing," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1519-1534.
    10. Takahiko Kusakabe & Takamasa Iryo & Yasuo Asakura, 2010. "Estimation method for railway passengers’ train choice behavior with smart card transaction data," Transportation, Springer, vol. 37(5), pages 731-749, September.
    11. Daganzo, Carlos F., 2007. "Urban gridlock: Macroscopic modeling and mitigation approaches," Transportation Research Part B: Methodological, Elsevier, vol. 41(1), pages 49-62, January.
    12. Tian, Qiong & Huang, Hai-Jun & Yang, Hai, 2007. "Equilibrium properties of the morning peak-period commuting in a many-to-one mass transit system," Transportation Research Part B: Methodological, Elsevier, vol. 41(6), pages 616-631, July.
    13. Newell, G. F., 1993. "A simplified theory of kinematic waves in highway traffic, part III: Multi-destination flows," Transportation Research Part B: Methodological, Elsevier, vol. 27(4), pages 305-313, August.
    14. Fosgerau, Mogens, 2015. "Congestion in the bathtub," Economics of Transportation, Elsevier, vol. 4(4), pages 241-255.
    15. Ke-Ping Li & Zi-You Gao & Bin Ning, 2005. "Modeling The Railway Traffic Using Cellular Automata Model," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 16(06), pages 921-932.
    16. Trozzi, Valentina & Gentile, Guido & Bell, Michael G.H. & Kaparias, Ioannis, 2013. "Dynamic user equilibrium in public transport networks with passenger congestion and hyperpaths," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 266-285.
    17. Daganzo, Carlos F., 2009. "A headway-based approach to eliminate bus bunching: Systematic analysis and comparisons," Transportation Research Part B: Methodological, Elsevier, vol. 43(10), pages 913-921, December.
    18. Carey, Malachy & Kwiecinski, Andrzej, 1994. "Stochastic approximation to the effects of headways on knock-on delays of trains," Transportation Research Part B: Methodological, Elsevier, vol. 28(4), pages 251-267, August.
    19. Jens Parbo & Otto Anker Nielsen & Carlo Giacomo Prato, 2016. "Passenger Perspectives in Railway Timetabling: A Literature Review," Transport Reviews, Taylor & Francis Journals, vol. 36(4), pages 500-526, July.
    20. Tabuchi Takatoshi, 1993. "Bottleneck Congestion and Modal Split," Journal of Urban Economics, Elsevier, vol. 34(3), pages 414-431, November.
    21. Newell, G. F., 1993. "A simplified theory of kinematic waves in highway traffic, part I: General theory," Transportation Research Part B: Methodological, Elsevier, vol. 27(4), pages 281-287, August.
    22. Newell, G. F., 2002. "A simplified car-following theory: a lower order model," Transportation Research Part B: Methodological, Elsevier, vol. 36(3), pages 195-205, March.
    23. Serge P. Hoogendoorn & W. Daamen, 2005. "Pedestrian Behavior at Bottlenecks," Transportation Science, INFORMS, vol. 39(2), pages 147-159, May.
    24. Kraus, Marvin & Yoshida, Yuichiro, 2002. "The Commuter's Time-of-Use Decision and Optimal Pricing and Service in Urban Mass Transit," Journal of Urban Economics, Elsevier, vol. 51(1), pages 170-195, January.
    25. Deepak K. Merchant & George L. Nemhauser, 1978. "A Model and an Algorithm for the Dynamic Traffic Assignment Problems," Transportation Science, INFORMS, vol. 12(3), pages 183-199, August.
    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. Liang, Zhiyuan & Tang, Yili & Yu, Jianing & Wang, Yacan, 2024. "A collective incentive strategy to manage ridership rebound and consumer surplus in mass transit systems," Transportation Research Part A: Policy and Practice, Elsevier, vol. 182(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. Jin, Wen-Long, 2020. "Generalized bathtub model of network trip flows," Transportation Research Part B: Methodological, Elsevier, vol. 136(C), pages 138-157.
    2. Jiang, Chenming & Bhat, Chandra R. & Lam, William H.K., 2020. "A bibliometric overview of Transportation Research Part B: Methodological in the past forty years (1979–2019)," Transportation Research Part B: Methodological, Elsevier, vol. 138(C), pages 268-291.
    3. Lu, Chung-Cheng & Liu, Jiangtao & Qu, Yunchao & Peeta, Srinivas & Rouphail, Nagui M. & Zhou, Xuesong, 2016. "Eco-system optimal time-dependent flow assignment in a congested network," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 217-239.
    4. Wang, Yi & Szeto, W.Y. & Han, Ke & Friesz, Terry L., 2018. "Dynamic traffic assignment: A review of the methodological advances for environmentally sustainable road transportation applications," Transportation Research Part B: Methodological, Elsevier, vol. 111(C), pages 370-394.
    5. 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.
    6. Ludovic Leclercq & Mahendra Paipuri, 2019. "Macroscopic Traffic Dynamics Under Fast-Varying Demand," Transportation Science, INFORMS, vol. 53(6), pages 1526-1545, November.
    7. Wen-Long Jin, 2021. "A Link Queue Model of Network Traffic Flow," Transportation Science, INFORMS, vol. 55(2), pages 436-455, March.
    8. Huanping Li & Jian Wang & Guopeng Bai & Xiaowei Hu, 2021. "Exploring the Distribution of Traffic Flow for Shared Human and Autonomous Vehicle Roads," Energies, MDPI, vol. 14(12), pages 1-21, June.
    9. Dantsuji, Takao & Takayama, Yuki & Fukuda, Daisuke, 2023. "Perimeter control in a mixed bimodal bathtub model," Transportation Research Part B: Methodological, Elsevier, vol. 173(C), pages 267-291.
    10. Hao, Peng & Ban, Xuegang, 2015. "Long queue estimation for signalized intersections using mobile data," Transportation Research Part B: Methodological, Elsevier, vol. 82(C), pages 54-73.
    11. Jin, Wen-Long & Gan, Qi-Jian & Gayah, Vikash V., 2013. "A kinematic wave approach to traffic statics and dynamics in a double-ring network," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 114-131.
    12. Jin, Wen-Long, 2017. "On the stability of stationary states in general road networks," Transportation Research Part B: Methodological, Elsevier, vol. 98(C), pages 42-61.
    13. de Palma, André & Lindsey, Robin & Monchambert, Guillaume, 2017. "The economics of crowding in rail transit," Journal of Urban Economics, Elsevier, vol. 101(C), pages 106-122.
    14. Daganzo, Carlos F., 2011. "On the macroscopic stability of freeway traffic," Transportation Research Part B: Methodological, Elsevier, vol. 45(5), pages 782-788, June.
    15. Jin, Wen-Long, 2013. "A multi-commodity Lighthill–Whitham–Richards model of lane-changing traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 361-377.
    16. 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).
    17. Smits, Erik-Sander & Bliemer, Michiel C.J. & Pel, Adam J. & van Arem, Bart, 2015. "A family of macroscopic node models," Transportation Research Part B: Methodological, Elsevier, vol. 74(C), pages 20-39.
    18. Lehe, Lewis J. & Pandey, Ayush, 2024. "A bathtub model of transit congestion," Transportation Research Part B: Methodological, Elsevier, vol. 181(C).
    19. Aghamohammadi, Rafegh & Laval, Jorge A., 2020. "Dynamic traffic assignment using the macroscopic fundamental diagram: A Review of vehicular and pedestrian flow models," Transportation Research Part B: Methodological, Elsevier, vol. 137(C), pages 99-118.
    20. Seo, Toru & Kawasaki, Yutaka & Kusakabe, Takahiko & Asakura, Yasuo, 2019. "Fundamental diagram estimation by using trajectories of probe vehicles," Transportation Research Part B: Methodological, Elsevier, vol. 122(C), pages 40-56.

    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:kap:transp:v:50:y:2023:i:4:d:10.1007_s11116-022-10281-0. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.