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On non-equilibria threshold strategies in ticket queues

Author

Listed:
  • Yoav Kerner

    (Ben-Gurion University)

  • Eliran Sherzer

    (Ben-Gurion University)

  • Mor Ann Yanco

    (Ben-Gurion University)

Abstract

In many real-life queueing systems, a customer may balk upon arrival at a queueing system, but other customers become aware of it only at the time the balking customer was to start service. Naturally, the balking is an outcome of the queue length, and the decision is based on a threshold. Yet the inspected queue length contains customers who balked. In this work, we consider a Markovian queue with infinite capacity and with customers that are homogeneous with respect to their cost reward functions. We show that that no threshold strategy can be a Nash equilibrium strategy. Furthermore, we show that for any threshold strategy adopted by all, the individual’s best response is a double threshold strategy. That is, join if and only if one of the following is true: (i) the inspected queue length is smaller than one threshold, or (ii) the inspected queue length is larger than a second threshold. Our model is under the assumption that the response time of the server when he finds out that a customer balked is negligible. We also discuss the validity of the result when the response time is not negligible.

Suggested Citation

  • Yoav Kerner & Eliran Sherzer & Mor Ann Yanco, 2017. "On non-equilibria threshold strategies in ticket queues," Queueing Systems: Theory and Applications, Springer, vol. 86(3), pages 419-431, August.
    • Handle: RePEc:spr:queues:v:86:y:2017:i:3:d:10.1007_s11134-017-9535-0
    DOI: 10.1007/s11134-017-9535-0
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    References listed on IDEAS

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    1. Antonis Economou & Athanasia Manou, 2013. "Equilibrium balking strategies for a clearing queueing system in alternating environment," Annals of Operations Research, Springer, vol. 208(1), pages 489-514, September.
    2. Susan H. Xu & Long Gao & Jihong Ou, 2007. "Service Performance Analysis and Improvement for a Ticket Queue with Balking Customers," Management Science, INFORMS, vol. 53(6), pages 971-990, June.
    3. Naor, P, 1969. "The Regulation of Queue Size by Levying Tolls," Econometrica, Econometric Society, vol. 37(1), pages 15-24, January.
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    Cited by:

    1. Tesnim Naceur & Yezekael Hayel, 2020. "Deterministic state-based information disclosure policies and social welfare maximization in strategic queueing systems," Queueing Systems: Theory and Applications, Springer, vol. 96(3), pages 303-328, December.
    2. Zhongbin Wang & Luyi Yang & Shiliang Cui & Jinting Wang, 2021. "In-queue priority purchase: a dynamic game approach," Queueing Systems: Theory and Applications, Springer, vol. 97(3), pages 343-381, April.
    3. Gabi Hanukov & Shoshana Anily & Uri Yechiali, 2020. "Ticket queues with regular and strategic customers," Queueing Systems: Theory and Applications, Springer, vol. 95(1), pages 145-171, June.
    4. Brill, P.H. & Huang, M.L. & Hlynka, M., 2020. "On the service time in a workload-barrier M/G/1 queue with accepted and blocked customers," European Journal of Operational Research, Elsevier, vol. 283(1), pages 235-243.

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