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Vickrey's model of traffic congestion discretized

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  • Otsubo, Hironori
  • Rapoport, Amnon

Abstract

Vickrey's seminal analysis of urban traffic congestion assumes a continuum of commuters acting selfishly and a continuous strategy space. We propose a discrete version of his model that assumes a finite number of commuters and a discrete strategy space. We then present an algorithm for numerically computing a symmetric mixed-strategy equilibrium solution for the discrete model and compare it with the deterministic equilibrium solution for the continuous model due to Arnott et al. [Arnott, R., de Palma, A., Lindsey, R., 1990. Economics of a bottleneck. Journal of Urban Economics 27(1), 111-130]. We report significant discrepancies in travel costs and distributions of departure time between the two solutions that slowly decrease as the number of commuters increases. We then propose and exemplify two extensions of the discrete model that allow for an uncertain number of commuters and an alternative mode of transportation not subject to congestion.

Suggested Citation

  • Otsubo, Hironori & Rapoport, Amnon, 2008. "Vickrey's model of traffic congestion discretized," Transportation Research Part B: Methodological, Elsevier, vol. 42(10), pages 873-889, December.
    • Handle: RePEc:eee:transb:v:42:y:2008:i:10:p:873-889
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    Cited by:

    1. Terry E. Daniel & Eyran J. Gisches & Amnon Rapoport, 2009. "Departure Times in Y-Shaped Traffic Networks with Multiple Bottlenecks," American Economic Review, American Economic Association, vol. 99(5), pages 2149-2176, December.
    2. Ravner, Liron & Haviv, Moshe & Vu, Hai L., 2016. "A strategic timing of arrivals to a linear slowdown processor sharing system," European Journal of Operational Research, Elsevier, vol. 255(2), pages 496-504.
    3. Platz, Trine Tornøe & Østerdal, Lars Peter, 2017. "The curse of the first-in–first-out queue discipline," Games and Economic Behavior, Elsevier, vol. 104(C), pages 165-176.
    4. Xiao, Feng & Shen, Wei & Michael Zhang, H., 2012. "The morning commute under flat toll and tactical waiting," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1346-1359.
    5. Garrouste, Christelle & Loi, Massimo, 2009. "Applications De La Theorie Des Jeux A L'Education: Pour Quels Types Et Niveaux D'Education, Quels Modeles, Quels Resultats? [Applications of Game Theory in Education - What Types and At What Levels," MPRA Paper 31825, University Library of Munich, Germany.
    6. Sakuma, Yutaka & Masuyama, Hiroyuki & Fukuda, Emiko, 2020. "A discrete-time single-server Poisson queueing game: Equilibria simulated by an agent-based model," European Journal of Operational Research, Elsevier, vol. 283(1), pages 253-264.
    7. Hugo E. Silva & Robin Lindsey & André de Palma & Vincent A. C. van den Berg, 2017. "On the Existence and Uniqueness of Equilibrium in the Bottleneck Model with Atomic Users," Transportation Science, INFORMS, vol. 51(3), pages 863-881, August.
    8. 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.
    9. Ravner, Liron, 2014. "Equilibrium arrival times to a queue with order penalties," European Journal of Operational Research, Elsevier, vol. 239(2), pages 456-468.
    10. Moshe Haviv & Liron Ravner, 2014. "Strategic timing of arrivals to a finite queue multi-server loss system," Discussion Paper Series dp675, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.

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