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A Variational Inequality Reformulation of a Congested Transit Assignment Model by Cominetti, Correa, Cepeda, and Florian

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  • Esteve Codina

    (Statistics and Operations Research Department, Universitat Politècnica de Catalunya, Campus Nord, Barcelona 08034, Spain)

Abstract

In the paper by Cominetti and Correa (2001) [Common-lines and passenger assignment in congested transit networks. Transportation Sci. 35(3):250--267], an extension to the common-lines problem for general multidestination networks under congestion is analyzed. Their transit equilibrium assignment model allows for a full representation of congestion effects caused by the variation of effective frequencies experienced by passengers at transit stops. This model is the first to address these characteristics consistently with the concept of strategies. In a subsequent paper by Cepeda, Cominetti, and Florian (2006) [A frequency-based assignment model for congested transit networks with strict capacity constraints: Characterization and computation of equilibria. Transportation Res. 40B(6):437--459], the computation of equilibrium is performed heuristically by the minimization of a gap function, using the method of successive averages. In this paper, a reformulation of this congested transit equilibrium assignment model is performed, demonstrating that the problem can be expressed as an equivalent variational inequality. The case of strictly capacitated transit networks is explored under the scope of this new reformulation, and new, broader conditions for the existence of solutions to this congested transit assignment model are determined.

Suggested Citation

  • Esteve Codina, 2013. "A Variational Inequality Reformulation of a Congested Transit Assignment Model by Cominetti, Correa, Cepeda, and Florian," Transportation Science, INFORMS, vol. 47(2), pages 231-246, May.
    • Handle: RePEc:inm:ortrsc:v:47:y:2013:i:2:p:231-246
    DOI: 10.1287/trsc.1120.0427
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    References listed on IDEAS

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    1. Nguyen, S. & Pallottino, S., 1988. "Equilibrium traffic assignment for large scale transit networks," European Journal of Operational Research, Elsevier, vol. 37(2), pages 176-186, November.
    2. Spiess, Heinz & Florian, Michael, 1989. "Optimal strategies: A new assignment model for transit networks," Transportation Research Part B: Methodological, Elsevier, vol. 23(2), pages 83-102, April.
    3. Cepeda, M. & Cominetti, R. & Florian, M., 2006. "A frequency-based assignment model for congested transit networks with strict capacity constraints: characterization and computation of equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 40(6), pages 437-459, July.
    4. 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.
    5. Smith, M. J., 1979. "The existence, uniqueness and stability of traffic equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 13(4), pages 295-304, December.
    6. Claude Chriqui & Pierre Robillard, 1975. "Common Bus Lines," Transportation Science, INFORMS, vol. 9(2), pages 115-121, May.
    7. Roberto Cominetti & José Correa, 2001. "Common-Lines and Passenger Assignment in Congested Transit Networks," Transportation Science, INFORMS, vol. 35(3), pages 250-267, August.
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    Cited by:

    1. Ren, Hualing & Song, Yingjie & Long, Jiancheng & Si, Bingfeng, 2021. "A new transit assignment model based on line and node strategies," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 121-142.
    2. Xu, Zhandong & Xie, Jun & Liu, Xiaobo & Nie, Yu (Marco), 2020. "Hyperpath-based algorithms for the transit equilibrium assignment problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 143(C).
    3. Cortés, Cristián E. & Donoso, Pedro & Gutiérrez, Leonel & Herl, Daniel & Muñoz, Diego, 2023. "A recursive stochastic transit equilibrium model estimated using passive data from Santiago, Chile," Transportation Research Part B: Methodological, Elsevier, vol. 174(C).
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    5. Codina, Esteve & Rosell, Francisca, 2017. "A heuristic method for a congested capacitated transit assignment model with strategies," Transportation Research Part B: Methodological, Elsevier, vol. 106(C), pages 293-320.

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