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Equilibrium strategic behavior of customers in the M/M/1 queue with partial failures and repairs

Author

Listed:
  • Biao Xu

    (Yanshan University
    Beihang University)

  • Xiuli Xu

    (Yanshan University)

Abstract

This paper analyzes the customers’ equilibrium strategic behavior in the M/M/1 queue subject to Poisson generated partial failures and repairs. In such a queueing system, whenever a partial failure occurs, the system does not admit any customer and continues the service at a lower rate instead of stopping working completely. This goes on till the system becomes empty and, at that point, an exponential repair time is sent on. The arriving customer’s dilemma is whether to enter or balk based on a linear reward-cost structure. We discuss the fully observable and fully unobservable queues respectively. For each type of queue, the corresponding equilibrium balking strategies of customers and the expected social benefits per time unit are derived. Finally, we illustrate the theoretical results by presenting some numerical examples.

Suggested Citation

  • Biao Xu & Xiuli Xu, 2018. "Equilibrium strategic behavior of customers in the M/M/1 queue with partial failures and repairs," Operational Research, Springer, vol. 18(2), pages 273-292, July.
    • Handle: RePEc:spr:operea:v:18:y:2018:i:2:d:10.1007_s12351-016-0264-7
    DOI: 10.1007/s12351-016-0264-7
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    References listed on IDEAS

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    1. Edelson, Noel M & Hildebrand, David K, 1975. "Congestion Tolls for Poisson Queuing Processes," Econometrica, Econometric Society, vol. 43(1), pages 81-92, January.
    2. 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. Xinlei Liu & Xiuli Xu & Mingxin Liu, 2024. "Strategy Analysis of Retrial Queue with Parallel Customer and Standby Server," Methodology and Computing in Applied Probability, Springer, vol. 26(3), pages 1-22, September.
    2. Yingying Pan & Jingchuan Zhang & Zaiming Liu, 2024. "Equilibrium Strategies in an M n /M/1 Queue with Server Breakdowns and Delayed Repairs," Mathematics, MDPI, vol. 12(23), pages 1-14, November.

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