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Equilibrium arrival times to queues with general service times and non-linear utility functions

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  • Breinbjerg, Jesper

Abstract

We examine a non-cooperative queueing game where a finite number of customers seek service at a bottleneck facility which opens at a given point in time. The facility serves one customer at a time on a first-come, first-serve basis and the amount of time required to service each customer is identically and independently distributed according to some general probability distribution. The customers must individually choose when to arrive at the facility, and they prefer to complete service as early as possible, while minimizing the time spent waiting in the queue. These preferences are captured by a general utility function which is decreasing in the waiting time and service completion time of each customer. Applications of such queueing games range from people choosing when to arrive at a grand opening sale to travellers choosing when to line up at the gate when boarding an airplane. We develop a constructive procedure that characterizes an arrival strategy which constitutes a symmetric Nash equilibrium, and we show that there exists at most one symmetric equilibrium. We accompany the equilibrium characterization with numerically computed examples of several symmetric equilibria induced by a non-linear utility function.

Suggested Citation

  • Breinbjerg, Jesper, 2017. "Equilibrium arrival times to queues with general service times and non-linear utility functions," European Journal of Operational Research, Elsevier, vol. 261(2), pages 595-605.
  • Handle: RePEc:eee:ejores:v:261:y:2017:i:2:p:595-605
    DOI: 10.1016/j.ejor.2017.03.010
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    References listed on IDEAS

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    6. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-260, May.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    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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    Cited by:

    1. 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.
    2. Sakuma, Yutaka & Masuyama, Hiroyuki & Fukuda, Emiko, 2020. "A discrete-time single-server Poisson queueing game: Equilibria simulated by an agent-based model," European Journal of Operational Research, Elsevier, vol. 283(1), pages 253-264.

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