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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
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    1. 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.
    2. 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.
    3. Fosgerau, Mogens, 2015. "Congestion in the bathtub," Economics of Transportation, Elsevier, vol. 4(4), pages 241-255.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. A. Higgins & E. Kozan, 1998. "Modeling Train Delays in Urban Networks," Transportation Science, INFORMS, vol. 32(4), pages 346-357, November.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
    16. 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.
    17. Tabuchi Takatoshi, 1993. "Bottleneck Congestion and Modal Split," Journal of Urban Economics, Elsevier, vol. 34(3), pages 414-431, November.
    18. 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.
    19. 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.
    20. 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.
    21. Daganzo, Carlos F., 2007. "Urban gridlock: Macroscopic modeling and mitigation approaches," Transportation Research Part B: Methodological, Elsevier, vol. 41(1), pages 49-62, January.
    22. 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.
    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.
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