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Dynamic and Static congestion models: A review

  • André De Palma

    (ENS Cachan - Ecole Normale Supérieure de Cachan - École normale supérieure de Cachan - ENS Cachan, Department of Economics, Ecole Polytechnique - CNRS : UMR7176 - Polytechnique - X)

  • Mogens Fosgerau

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

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

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Paper provided by HAL in its series Working Papers with number hal-00539166.

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Date of creation: 24 Nov 2010
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Handle: RePEc:hal:wpaper:hal-00539166
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  1. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1999. "Information and time-of-usage decisions in the bottleneck model with stochastic capacity and demand," European Economic Review, Elsevier, vol. 43(3), pages 525-548, March.
  2. Chen-Hsiu Laih, 2004. "Effects of the optimal step toll scheme on equilibrium commuter behaviour," Applied Economics, Taylor & Francis Journals, vol. 36(1), pages 59-81.
  3. Victor Aguirregabiria & Pedro mira, 2007. "Dynamic Discrete Choice Structural Models: A Survey," Working Papers tecipa-297, University of Toronto, Department of Economics.
  4. Fosgerau, Mogens & Karlström, Anders, 2007. "The value of reliability," MPRA Paper 5733, University Library of Munich, Germany.
  5. Fosgerau, Mogens, 2010. "On the relation between the mean and variance of delay in dynamic queues with random capacity and demand," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 598-603, April.
  6. David M Kreps & Evan L Porteus, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Levine's Working Paper Archive 625018000000000009, David K. Levine.
  7. Shen, Wei & Zhang, H.M., 2010. "Pareto-improving ramp metering strategies for reducing congestion in the morning commute," Transportation Research Part A: Policy and Practice, Elsevier, vol. 44(9), pages 676-696, November.
  8. Wilson, Paul W., 1988. "Wage variation resulting from staggered work hours," Journal of Urban Economics, Elsevier, vol. 24(1), pages 9-26, July.
  9. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1993. "A Structural Model of Peak-Period Congestion: A Traffic Bottleneck with Elastic Demand," American Economic Review, American Economic Association, vol. 83(1), pages 161-79, March.
  10. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1991. "A temporal and spatial equilibrium analysis of commuter parking," Journal of Public Economics, Elsevier, vol. 45(3), pages 301-335, August.
  11. Tseng, Yin-Yen & Verhoef, Erik T., 2008. "Value of time by time of day: A stated-preference study," Transportation Research Part B: Methodological, Elsevier, vol. 42(7-8), pages 607-618, August.
  12. Fosgerau, Mogens & Engelson, Leonid, 2010. "The value of travel time variance," MPRA Paper 42272, University Library of Munich, Germany.
  13. Small, Kenneth A, 1982. "The Scheduling of Consumer Activities: Work Trips," American Economic Review, American Economic Association, vol. 72(3), pages 467-79, June.
  14. Henderson, J. Vernon, 1981. "The economics of staggered work hours," Journal of Urban Economics, Elsevier, vol. 9(3), pages 349-364, May.
  15. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-60, May.
  16. Richard Arnott & John Rowse, 2007. "Downtown Parking in Auto City," Boston College Working Papers in Economics 665, Boston College Department of Economics.
  17. Fosgerau, Mogens, 2009. "The marginal social cost of headway for a scheduled service," Transportation Research Part B: Methodological, Elsevier, vol. 43(8-9), pages 813-820, September.
  18. Laih, Chen-Hsiu, 1994. "Queueing at a bottleneck with single- and multi-step tolls," Transportation Research Part A: Policy and Practice, Elsevier, vol. 28(3), pages 197-208, May.
  19. Mogens Fosgerau, 2004. "Investigating the distribution of the value of travel time savings," Urban/Regional 0410005, EconWPA, revised 25 Nov 2004.
  20. de Palma, André & Lindsey, Robin & Proost, Stef, 2007. "Chapter 1 Investment and the use of tax and toll revenues in the transport sector: The research agenda," Research in Transportation Economics, Elsevier, vol. 19(1), pages 1-26, January.
  21. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1990. "Economics of a bottleneck," Journal of Urban Economics, Elsevier, vol. 27(1), pages 111-130, January.
  22. Lindsey, Robin, 2009. "Cost recovery from congestion tolls with random capacity and demand," Journal of Urban Economics, Elsevier, vol. 66(1), pages 16-24, July.
  23. Xiaoning Zhang & H. Zhang, 2010. "Simultaneous Departure Time/Route Choices in Queuing Networks and a Novel Paradox," Networks and Spatial Economics, Springer, vol. 10(1), pages 93-112, March.
  24. Arnott, R. & De Palma, A. & Lindsey, R., 1992. "Properties of Dynamic Traffic Equilibrium Involving Bottlenecks, Including A Paradox and Metering," Papers 9201, Universite Libre de Bruxelles - C.E.M.E..
  25. Henderson, J. V., 1974. "Road congestion : A reconsideration of pricing theory," Journal of Urban Economics, Elsevier, vol. 1(3), pages 346-365, July.
  26. Robert E. Hall, 1989. "Temporal Agglomeration," NBER Working Papers 3143, National Bureau of Economic Research, Inc.
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