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A Strategic Markovian Traffic Equilibrium Model for Capacitated Networks

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  • Maëlle Zimmermann

    (Department of Computer Science and Operations Research, Université de Montréal, Montréal, Quebec H3T 1N8, Canada; Interuniversity Research Centre on Enterprise Networks, Logistics, and Transportation, Montréal, Quebec H3T 1N8, Canada)

  • Emma Frejinger

    (Department of Computer Science and Operations Research, Université de Montréal, Montréal, Quebec H3T 1N8, Canada; Interuniversity Research Centre on Enterprise Networks, Logistics, and Transportation, Montréal, Quebec H3T 1N8, Canada)

  • Patrice Marcotte

    (Department of Computer Science and Operations Research, Université de Montréal, Montréal, Quebec H3T 1N8, Canada; Interuniversity Research Centre on Enterprise Networks, Logistics, and Transportation, Montréal, Quebec H3T 1N8, Canada)

Abstract

In the realm of traffic assignment over a network involving rigid arc capacities, the aim of the present work is to generalize the model of Marcotte, Nguyen, and Schoeb [Marcotte P, Nguyen S, Schoeb A (2004) A strategic flow model of traffic assignment in static capacitated networks. Oper. Res. 52(2):191–212.] by casting it within a stochastic user equilibrium framework. The strength of the proposed model is to incorporate two sources of stochasticity stemming, respectively, from the users’ imperfect knowledge regarding arc costs (represented by a discrete choice model) and the probability of not accessing saturated arcs. Moreover, the arc-based formulation extends the Markovian traffic equilibrium model of Baillon and Cominetti [Baillon JB, Cominetti R ( 2008 ) Markovian traffic equilibrium. Math. Programming 111(1-2):33–56.] through the explicit consideration of capacities. This paper is restricted to the case of acyclic networks, for which we present solution algorithms and numerical experiments.

Suggested Citation

  • Maëlle Zimmermann & Emma Frejinger & Patrice Marcotte, 2021. "A Strategic Markovian Traffic Equilibrium Model for Capacitated Networks," Transportation Science, INFORMS, vol. 55(3), pages 574-591, May.
    • Handle: RePEc:inm:ortrsc:v:55:y:2021:i:3:p:574-591
    DOI: 10.1287/trsc.2020.1033
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    References listed on IDEAS

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    1. Fosgerau, Mogens & Frejinger, Emma & Karlstrom, Anders, 2013. "A link based network route choice model with unrestricted choice set," Transportation Research Part B: Methodological, Elsevier, vol. 56(C), pages 70-80.
    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. Larsson, Torbjörn & Patriksson, Michael, 1999. "Side constrained traffic equilibrium models-- analysis, computation and applications," Transportation Research Part B: Methodological, Elsevier, vol. 33(4), pages 233-264, May.
    4. Wie, Byung-Wook & Tobin, Roger L. & Carey, Malachy, 2002. "The existence, uniqueness and computation of an arc-based dynamic network user equilibrium formulation," Transportation Research Part B: Methodological, Elsevier, vol. 36(10), pages 897-918, December.
    5. Nie, Yu & Zhang, H. M. & Lee, Der-Horng, 2004. "Models and algorithms for the traffic assignment problem with link capacity constraints," Transportation Research Part B: Methodological, Elsevier, vol. 38(4), pages 285-312, May.
    6. Patrice Marcotte & Sang Nguyen & Alexandre Schoeb, 2004. "A Strategic Flow Model of Traffic Assignment in Static Capacitated Networks," Operations Research, INFORMS, vol. 52(2), pages 191-212, April.
    7. Boyles, Stephen D. & Tang, Shoupeng & Unnikrishnan, Avinash, 2015. "Parking search equilibrium on a network," Transportation Research Part B: Methodological, Elsevier, vol. 81(P2), pages 390-409.
    8. Rambha, Tarun & Boyles, Stephen D. & Unnikrishnan, Avinash & Stone, Peter, 2018. "Marginal cost pricing for system optimal traffic assignment with recourse under supply-side uncertainty," Transportation Research Part B: Methodological, Elsevier, vol. 110(C), pages 104-121.
    9. Stella Dafermos, 1980. "Traffic Equilibrium and Variational Inequalities," Transportation Science, INFORMS, vol. 14(1), pages 42-54, February.
    10. Akamatsu, Takashi, 1996. "Cyclic flows, Markov process and stochastic traffic assignment," Transportation Research Part B: Methodological, Elsevier, vol. 30(5), pages 369-386, October.
    11. Dial, Robert B., 2006. "A path-based user-equilibrium traffic assignment algorithm that obviates path storage and enumeration," Transportation Research Part B: Methodological, Elsevier, vol. 40(10), pages 917-936, December.
    12. Avinash Unnikrishnan & Steven Waller, 2009. "User Equilibrium with Recourse," Networks and Spatial Economics, Springer, vol. 9(4), pages 575-593, December.
    13. Carlos F. Daganzo & Yosef Sheffi, 1977. "On Stochastic Models of Traffic Assignment," Transportation Science, INFORMS, vol. 11(3), pages 253-274, August.
    14. Jacques Guélat & Michael Florian & Teodor Gabriel Crainic, 1990. "A Multimode Multiproduct Network Assignment Model for Strategic Planning of Freight Flows," Transportation Science, INFORMS, vol. 24(1), pages 25-39, February.
    15. Larsson, Torbjörn & Patriksson, Michael, 1995. "An augmented lagrangean dual algorithm for link capacity side constrained traffic assignment problems," Transportation Research Part B: Methodological, Elsevier, vol. 29(6), pages 433-455, December.
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    3. Ye, Jiao & Cao, Ruide & He, Biao & Kuai, Xi & Guo, Renzhong, 2024. "Disaggregated spatiotemporal traffic assignment for road reservation service and supply-demand statistical analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 645(C).

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