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Congestion costs in bottleneck equilibrium with stochastic capacity and demand

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  • Fosgerau, Mogens

Abstract

I analyse congestion costs in the Vickrey bottleneck model of a congestible facility with a peak load in demand. The shape of the peak is endogenous, being the sum of individual scheduling decisions. Capacity and demand are random, which introduces uncertainty into the individual scheduling choices. These are essential features of actual peak loads. Based on work by Arnott, de Palma and Lindsey, I derive the expected marginal and total congestion costs and compare to the case with fixed capacity and demand. Using stylised values for scheduling costs relative to the value of time, I find that randomness of capacity and demand increases congestions cost by up to 50 percent relative to the deterministic case. The bound is general for any distribution of random capacity and demand.

Suggested Citation

  • Fosgerau, Mogens, 2008. "Congestion costs in bottleneck equilibrium with stochastic capacity and demand," MPRA Paper 10040, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:10040
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    File URL: https://mpra.ub.uni-muenchen.de/10040/1/MPRA_paper_10040.pdf
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    References listed on IDEAS

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    1. Anas, Alex & Rhee, Hyok-Joo, 2007. "When are urban growth boundaries not second-best policies to congestion tolls?," Journal of Urban Economics, Elsevier, vol. 61(2), pages 263-286, March.
    2. 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 161-179, March.
    3. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-260, May.
    4. DeSerpa, A C, 1971. "A Theory of the Economics of Time," Economic Journal, Royal Economic Society, vol. 81(324), pages 828-846, December.
    5. Daniel, Joseph I, 1995. "Congestion Pricing and Capacity of Large Hub Airports: A Bottleneck Model with Stochastic Queues," Econometrica, Econometric Society, vol. 63(2), pages 327-370, March.
    6. 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.
    7. Fosgerau, Mogens & Karlström, Anders, 2010. "The value of reliability," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 38-49, January.
    8. Small, Kenneth A, 1982. "The Scheduling of Consumer Activities: Work Trips," American Economic Review, American Economic Association, vol. 72(3), pages 467-479, June.
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    Cited by:

    1. Zhu, Tingting & Li, Yao & Long, Jiancheng, 2022. "Departure time choice equilibrium and tolling strategies for a bottleneck with continuous scheduling preference," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 159(C).
    2. Han, Xiao & Yu, Yun & Gao, Zi-You & Zhang, H. Michael, 2021. "The value of pre-trip information on departure time and route choice in the morning commute under stochastic traffic conditions," Transportation Research Part B: Methodological, Elsevier, vol. 152(C), pages 205-226.
    3. Eva Gutiérrez-i-Puigarnau & Jos N. Van Ommeren, 2012. "Start Time and Worker Compensation Implications for Staggered-Hours Programmes," Journal of Transport Economics and Policy, University of Bath, vol. 46(2), pages 205-220, May.
    4. Xiao, Yu & Coulombel, Nicolas & Palma, André de, 2017. "The valuation of travel time reliability: does congestion matter?," Transportation Research Part B: Methodological, Elsevier, vol. 97(C), pages 113-141.
    5. Liu, Yang & Li, Yuanyuan & Hu, Lu, 2018. "Departure time and route choices in bottleneck equilibrium under risk and ambiguity," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 774-793.
    6. 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.
    7. Liu, Qiumin & Jiang, Rui & Liu, Ronghui & Zhao, Hui & Gao, Ziyou, 2020. "Travel cost budget based user equilibrium in a bottleneck model with stochastic capacity," Transportation Research Part B: Methodological, Elsevier, vol. 139(C), pages 1-37.
    8. Ling-Ling Xiao & Hai-Jun Huang & Ronghui Liu, 2015. "Congestion Behavior and Tolls in a Bottleneck Model with Stochastic Capacity," Transportation Science, INFORMS, vol. 49(1), pages 46-65, February.

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    More about this item

    Keywords

    Bottleneck model; Scheduling; Reliability; Congestion;
    All these keywords.

    JEL classification:

    • R40 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics - - - General

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