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Strategic behavior and optimization in a hybrid M/M/1 queue with retrials

Author

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  • Yoav Kerner

    (Ben Gurion University of the Negev)

  • Ophir Shmuel-Bittner

    (Ben Gurion University of the Negev)

Abstract

In standard queues, when there are waiting customers, service completions are followed by service commencements. In retrial queues, this is not the case. In such systems, customers try to receive service at a time of their choosing, or the server seeks the next customer for a non-negligible time. In this note, we consider a hybrid model with both a finite standard queue and an orbit. While in the orbit, customers try to join the standard queue in their own time. We assume that the retrial rate is a decision variable, and study both the Nash equilibrium and the socially optimal retrial rates, under a cost model that considers both waiting costs and retrial costs.

Suggested Citation

  • Yoav Kerner & Ophir Shmuel-Bittner, 2020. "Strategic behavior and optimization in a hybrid M/M/1 queue with retrials," Queueing Systems: Theory and Applications, Springer, vol. 96(3), pages 285-302, December.
    • Handle: RePEc:spr:queues:v:96:y:2020:i:3:d:10.1007_s11134-020-09672-w
    DOI: 10.1007/s11134-020-09672-w
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    References listed on IDEAS

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    1. Antonis Economou & Spyridoula Kanta, 2011. "Equilibrium customer strategies and social–profit maximization in the single‐server constant retrial queue," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(2), pages 107-122, March.
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    4. Kerner, Yoav, 2011. "Equilibrium joining probabilities for an M/G/1 queue," Games and Economic Behavior, Elsevier, vol. 71(2), pages 521-526, March.
    5. J. Artalejo, 1999. "A classified bibliography of research on retrial queues: Progress in 1990–1999," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 187-211, December.
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