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Equilibrium Arrival Times to Queues: The Case of Last-Come First-Serve Preemptive-Resume

Author

Listed:
  • Breinbjerg, Jesper

    () (Department of Business and Economics)

  • Østerdal, Lars Peter

    () (Department of Economics)

Abstract

We consider a non-cooperative queueing environment where a finite number of customers independently choose when to arrive at a queueing system that opens at a given point in time and serves customers on a last-come first-serve preemptive-resume (LCFS-PR) basis. Each customer has a service time requirement which is identically and independently distributed according to some general probability distribution, and they want to complete service as early as possible while minimizing the time spent in the queue. In this setting, we establish the existence of an arrival time strategy that constitutes a symmetric (mixed) Nash equilibrium, and show that there is at most one symmetric equilibrium. We provide a numerical method to compute this equilibrium and demonstrate by a numerical example that the social efficiency can be lower than the efficiency induced by a similar queueing system that serves customers on a first-come first-serve (FCFS) basis.

Suggested Citation

  • Breinbjerg, Jesper & Østerdal, Lars Peter, 2017. "Equilibrium Arrival Times to Queues: The Case of Last-Come First-Serve Preemptive-Resume," Discussion Papers of Business and Economics 3/2017, University of Southern Denmark, Department of Business and Economics.
  • Handle: RePEc:hhs:sdueko:2017_003
    as

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    File URL: http://www.sdu.dk/-/media/files/om_sdu/institutter/ivoe/disc_papers/disc_2017/dpbe3_2017.pdf?la=en
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    References listed on IDEAS

    as
    1. Guo, Pengfei & Hassin, Refael, 2012. "Strategic behavior and social optimization in Markovian vacation queues: The case of heterogeneous customers," European Journal of Operational Research, Elsevier, vol. 222(2), pages 278-286.
    2. Stein, William E. & Rapoport, Amnon & Seale, Darryl A. & Zhang, Hongtao & Zwick, Rami, 2007. "Batch queues with choice of arrivals: Equilibrium analysis and experimental study," Games and Economic Behavior, Elsevier, vol. 59(2), pages 345-363, May.
    3. 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.
    4. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-260, May.
    5. 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.
    6. Verhoef, Erik T., 2003. "Inside the queue:: hypercongestion and road pricing in a continuous time-continuous place model of traffic congestion," Journal of Urban Economics, Elsevier, vol. 54(3), pages 531-565, November.
    7. A. Glazer & R. Hassin, 1987. "Equilibrium Arrivals in Queues with Bulk Service at Scheduled Times," Transportation Science, INFORMS, vol. 21(4), pages 273-278, November.
    8. Rapoport, Amnon & Stein, William E. & Parco, James E. & Seale, Darryl A., 2004. "Equilibrium play in single-server queues with endogenously determined arrival times," Journal of Economic Behavior & Organization, Elsevier, vol. 55(1), pages 67-91, September.
    9. repec:eee:ejores:v:261:y:2017:i:2:p:595-605 is not listed on IDEAS
    10. 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.
    11. 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.
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    More about this item

    Keywords

    Queueing; strategic arrival times to a queue; non-cooperative games;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D62 - Microeconomics - - Welfare Economics - - - Externalities
    • R41 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics - - - Transportation: Demand, Supply, and Congestion; Travel Time; Safety and Accidents; Transportation Noise

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