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On the Equilibrium in a Queuing System with Retrials and Strategic Arrivals

Author

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  • Alexandra Borodina

    (Institute of Applied Mathematical Research, Karelian Research Centre, Russian Academy of Sciences, 185910 Petrozavodsk, Russia
    Institute of Mathematics and Information Technologies, Petrozavodsk State University, 185035 Petrozavodsk, Russia
    These authors contributed equally to this work.)

  • Vladimir Mazalov

    (Institute of Applied Mathematical Research, Karelian Research Centre, Russian Academy of Sciences, 185910 Petrozavodsk, Russia
    Institute of Mathematics and Information Technologies, Petrozavodsk State University, 185035 Petrozavodsk, Russia
    These authors contributed equally to this work.)

Abstract

This paper considers a callback single-server system with an orbit and a First-Come First-Served (FCFS) service discipline. Customers (users, clients) that encounter a busy server are sent into orbit and then have the option to retry service after an exponential period of time. In addition, each customer entering the system uses a strategy and must independently decide when to arrive in the system within a fixed admission period of time so that the expected sojourn time is minimal. We interpret the arrival process as a Nash equilibrium solution of a noncooperative game when the arrival intensity is completely described by an unknown distribution function, and then we propose a way to find an equilibrium for the case when the client’s waiting time for service is obviously limited. The analytical solution for the equilibrium is illustrated numerically for two-person and three-person games.

Suggested Citation

  • Alexandra Borodina & Vladimir Mazalov, 2023. "On the Equilibrium in a Queuing System with Retrials and Strategic Arrivals," Mathematics, MDPI, vol. 11(16), pages 1-15, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3535-:d:1218143
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    References listed on IDEAS

    as
    1. Julia Chirkova & Vladimir Mazalov & Evsey Morozov, 2022. "Equilibrium in a Queueing System with Retrials," Mathematics, MDPI, vol. 10(3), pages 1-15, January.
    2. Moshe Haviv, 2022. "Optimal timing of arrival to a queue," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 433-435, April.
    3. Jeongsim Kim & Bara Kim, 2016. "A survey of retrial queueing systems," Annals of Operations Research, Springer, vol. 247(1), pages 3-36, December.
    4. 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.
    5. Moshe Haviv & Liron Ravner, 2021. "A survey of queueing systems with strategic timing of arrivals," Queueing Systems: Theory and Applications, Springer, vol. 99(1), pages 163-198, October.
    Full references (including those not matched with items on IDEAS)

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