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Random queues and risk averse users

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  • De Palma, André
  • Fosgerau, Mogens

Abstract

We analyse Nash equilibrium in time of use of a congested facility. Users are risk averse with general concave utility. Queues are subject to varying degrees of random sorting, ranging from strict queue priority to a completely random queue. We define the key "no residual queue" property, which holds when there is no queue at the time the last user arrives at the queue, and prove that this property holds in equilibrium under all queueing regimes considered. The no residual queue property leads to simple results concerning the equilibrium utility of users and the timing of the queue.

Suggested Citation

  • De Palma, André & Fosgerau, Mogens, 2010. "Random queues and risk averse users," MPRA Paper 24215, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:24215
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    References listed on IDEAS

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    1. 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.
    2. Becker, Gary S, 1991. "A Note on Restaurant Pricing and Other Examples of Social Influences on Price," Journal of Political Economy, University of Chicago Press, vol. 99(5), pages 1109-1116, October.
    3. De Palma, Andre & Arnott, Richard, 1989. "The temporal use of a telephone line," Information Economics and Policy, Elsevier, vol. 4(2), pages 155-174.
    4. 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.
    5. Blanc, J.P.C., 2009. "Bad luck when joining the shortest queue," European Journal of Operational Research, Elsevier, vol. 195(1), pages 167-173, May.
    6. Arnott, Richard J., 1979. "Unpriced transport congestion," Journal of Economic Theory, Elsevier, vol. 21(2), pages 294-316, October.
    7. Michael Sattinger, 2002. "A Queuing Model of the Market for Access to Trading Partners," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(2), pages 533-548, May.
    8. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1996. "Information and Usage of Free-Access Congestible Facilities with Stochastic Capacity and Demand," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(1), pages 181-203, February.
    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 161-179, March.
    10. Osorio, Carolina & Bierlaire, Michel, 2009. "An analytic finite capacity queueing network model capturing the propagation of congestion and blocking," European Journal of Operational Research, Elsevier, vol. 196(3), pages 996-1007, August.
    11. Yoshida, Yuichiro, 2008. "Commuter arrivals and optimal service in mass transit: Does queuing behavior at transit stops matter?," Regional Science and Urban Economics, Elsevier, vol. 38(3), pages 228-251, May.
    12. Naor, P, 1969. "The Regulation of Queue Size by Levying Tolls," Econometrica, Econometric Society, vol. 37(1), pages 15-24, January.
    13. Glazer, Amihai & Hassin, Refael, 1983. "?/M/1: On the equilibrium distribution of customer arrivals," European Journal of Operational Research, Elsevier, vol. 13(2), pages 146-150, June.
    14. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-260, May.
    15. André De Palma & Mogens Fosgerau, 2010. "Dynamic and Static congestion models: A review," Working Papers hal-00539166, HAL.
    16. Knudsen, Niels Chr, 1972. "Individual and Social Optimization in a Multiserver Queue with a General Cost-Benefit Structure," Econometrica, Econometric Society, vol. 40(3), pages 515-528, May.
    17. Hassin, Refael, 1985. "On the Optimality of First Come Last Served Queues," Econometrica, Econometric Society, vol. 53(1), pages 201-202, January.
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    Citations

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    Cited by:

    1. Tian, Li-Jun & Huang, Hai-Jun, 2015. "Modeling the modal split and trip scheduling with commuters’ uncertainty expectation," European Journal of Operational Research, Elsevier, vol. 244(3), pages 815-822.
    2. Fosgerau, Mogens & de Palma, André, 2012. "Congestion in a city with a central bottleneck," Journal of Urban Economics, Elsevier, vol. 71(3), pages 269-277.
    3. Fosgerau, Mogens & Lindsey, Robin, 2013. "Trip-timing decisions with traffic incidents," Regional Science and Urban Economics, Elsevier, vol. 43(5), pages 764-782.
    4. Knockaert, Jasper & Verhoef, Erik T. & Rouwendal, Jan, 2016. "Bottleneck congestion: Differentiating the coarse charge," Transportation Research Part B: Methodological, Elsevier, vol. 83(C), pages 59-73.
    5. 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.
    6. Jesper Breinbjerg & Alexander Sebald & Lars Peter Østerdal, 2016. "Strategic behavior and social outcomes in a bottleneck queue: experimental evidence," Review of Economic Design, Springer;Society for Economic Design, vol. 20(3), pages 207-236, September.
    7. Fosgerau, Mogens, 2011. "How a fast lane may replace a congestion toll," Transportation Research Part B: Methodological, Elsevier, vol. 45(6), pages 845-851, July.
    8. Arnott, Richard, 2013. "A bathtub model of downtown traffic congestion," Journal of Urban Economics, Elsevier, vol. 76(C), pages 110-121.
    9. Fosgerau, Mogens & de Palma, André, 2013. "The dynamics of urban traffic congestion and the price of parking," Journal of Public Economics, Elsevier, vol. 105(C), pages 106-115.
    10. Mogens Fosgerau & André De Palma & Anders Karlstrom & Kenneth A. Small, 2012. "Trip timing and scheduling preferences," Working Papers hal-00742267, HAL.
    11. repec:eee:transb:v:108:y:2018:i:c:p:21-38 is not listed on IDEAS
    12. Fosgerau, Mogens & de Palma, André, 2013. "The dynamics of urban traffic congestion and the price of parking�," MPRA Paper 48433, University Library of Munich, Germany.
    13. Li, Chuan-Yao & Huang, Hai-Jun, 2017. "Morning commute in a single-entry traffic corridor with early and late arrivals," Transportation Research Part B: Methodological, Elsevier, vol. 97(C), pages 23-49.

    More about this item

    Keywords

    Congestion; Queuing; Risk aversion; Endogenous arrivals;

    JEL classification:

    • D00 - Microeconomics - - General - - - General
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General

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