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Stochastic transit equilibrium

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  • Cortés, Cristián E.
  • Jara-Moroni, Pedro
  • Moreno, Eduardo
  • Pineda, Cristobal

Abstract

We present a transit equilibrium model in which boarding decisions are stochastic. The model incorporates congestion, reflected in higher waiting times at bus stops and increasing in-vehicle travel time. The stochastic behavior of passengers is introduced through a probability for passengers to choose boarding a specific bus of a certain service. The modeling approach generates a stochastic common-lines problem, in which every line has a chance to be chosen by each passenger. The formulation is a generalization of deterministic transit assignment models where passengers are assumed to travel according to shortest hyperpaths. We prove existence of equilibrium in the simplified case of parallel lines (stochastic common-lines problem) and provide a formulation for a more general network problem (stochastic transit equilibrium). The resulting waiting time and network load expressions are validated through simulation. An algorithm to solve the general stochastic transit equilibrium is proposed and applied to a sample network; the algorithm works well and generates consistent results when considering the stochastic nature of the decisions, which motivates the implementation of the methodology on a real-size network case as the next step of this research.

Suggested Citation

  • Cortés, Cristián E. & Jara-Moroni, Pedro & Moreno, Eduardo & Pineda, Cristobal, 2013. "Stochastic transit equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 51(C), pages 29-44.
    • Handle: RePEc:eee:transb:v:51:y:2013:i:c:p:29-44
    DOI: 10.1016/j.trb.2013.02.001
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    References listed on IDEAS

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    Cited by:

    1. Du, Muqing & Chen, Anthony, 2022. "Sensitivity analysis for transit equilibrium assignment and applications to uncertainty analysis," Transportation Research Part B: Methodological, Elsevier, vol. 157(C), pages 175-202.
    2. 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.
    3. Dea van Lierop & Madhav G. Badami & Ahmed M. El-Geneidy, 2018. "What influences satisfaction and loyalty in public transport? A review of the literature," Transport Reviews, Taylor & Francis Journals, vol. 38(1), pages 52-72, January.
    4. 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).
    5. 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.
    6. Suman, Hemant & Larrain, Homero & Muñoz, Juan Carlos, 2021. "The impact of using a naïve approach in the limited-stop bus service design problem," Transportation Research Part A: Policy and Practice, Elsevier, vol. 149(C), pages 45-61.
    7. Soto, Guillermo & Larrain, Homero & Muñoz, Juan Carlos, 2017. "A new solution framework for the limited-stop bus service design problem," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 67-85.
    8. Szeto, W.Y. & Jiang, Y., 2014. "Transit route and frequency design: Bi-level modeling and hybrid artificial bee colony algorithm approach," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 235-263.
    9. Jiang, Y. & Szeto, W.Y., 2016. "Reliability-based stochastic transit assignment: Formulations and capacity paradox," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 181-206.
    10. Hamdouch, Younes & Szeto, W.Y. & Jiang, Y., 2014. "A new schedule-based transit assignment model with travel strategies and supply uncertainties," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 35-67.

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