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Dynamic and Static congestion models: A review

Author

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  • André de Palma

    (ENS Cachan - École normale supérieure - Cachan, X-DEP-ECO - Département d'Économie de l'École Polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris)

  • Mogens Fosgerau

    (DTU Transport - University of Denmark - Department of Transport)

Abstract

We begin by providing an overview of the conventional static equilibrium approach. In such model both the flow of trips and congestion delay are assumed to be constant. A drawback of the static model is that the time interval during which travel occurs is not specified so that the model cannot describe changes in the duration of congestion that result from changes in demand or capacity. This limitation is overcome in the Vickrey/Arnott, de Palma Lindsey bottleneck model, which combines congestion in the form of queuing behind a bottleneck with users' trip-timing preferences and departure time decisions. We derive the user equilibrium and social optimum for the basic bottleneck model, and explain how the optimum can be decentralized using a time-varying toll. They then review some extensions of the basic model that encompass elastic demand, user heterogeneity, stochastic demand and capacity and small networks. We conclude by identifying some unresolved modelling issues that apply not only to the bottleneck model but to trip-timing preferences and congestion dynamics in general

Suggested Citation

  • André de Palma & Mogens Fosgerau, 2010. "Dynamic and Static congestion models: A review," Working Papers hal-00539166, HAL.
  • Handle: RePEc:hal:wpaper:hal-00539166
    Note: View the original document on HAL open archive server: https://hal.science/hal-00539166
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    References listed on IDEAS

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    Cited by:

    1. Liang Chen & Eugene Choo & Alfred Galichon & Simon Weber, 2023. "Existence of a Competitive Equilibrium with Substitutes, with Applications to Matching and Discrete Choice Models," Papers 2309.11416, arXiv.org.
    2. Mogens Fosgerau & Kenneth Small, 2017. "Endogenous Scheduling Preferences And Congestion," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 58(2), pages 585-615, May.
    3. de Palma, André & Fosgerau, Mogens, 2013. "Random queues and risk averse users," European Journal of Operational Research, Elsevier, vol. 230(2), pages 313-320.
    4. Leonid Engelson & Ida Kristoffersson & Mohammad Saifuzzaman & André de Palma & Kiarash Motamedi, 2013. "Comparison of two dynamic transportation models: The case of Stockholm congestion charging," Working Papers hal-00779285, HAL.
    5. Lehe, Lewis J. & Pandey, Ayush, 2020. "Hyperdemand: A static traffic model with backward-bending demand curves," Economics of Transportation, Elsevier, vol. 24(C).
    6. Lehe, Lewis J. & Pandey, Ayush, 2024. "A bathtub model of transit congestion," Transportation Research Part B: Methodological, Elsevier, vol. 181(C).
    7. Pandey, Ayush & Lehe, Lewis J., 2024. "Congestive mode-switching and economies of scale on a bus route," Transportation Research Part B: Methodological, Elsevier, vol. 183(C).

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