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Equilibrium and optimal behavior of customers in Markovian queues with multiple working vacations

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  • Wei Sun
  • Shiyong Li

Abstract

This paper studies the customers’ equilibrium and socially optimal joining–balking behavior in single-server Markovian queues with multiple working vacations. Different from the classical vacation policies, the server does not completely stop service but maintains a low service rate in vacation state in case there are customer arrivals. Based on different precision levels of the system information, we discuss the observable queues, the partially observable queues, and the unobservable queues, respectively. For each type of queues, we get both the customers’ equilibrium and socially optimal joining–balking strategies and make numerical comparisons between them. We numerically observe that their equilibrium strategy is unique, and especially, the customers’ equilibrium joining probability in vacation state is not necessarily smaller than that in busy state in the partially observable queues. Moreover, we also find that the customers’ individual behavior always deviates from the social expectation and makes the system more congested. Copyright Sociedad de Estadística e Investigación Operativa 2014

Suggested Citation

  • Wei Sun & Shiyong Li, 2014. "Equilibrium and optimal behavior of customers in Markovian queues with multiple working vacations," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 694-715, July.
    • Handle: RePEc:spr:topjnl:v:22:y:2014:i:2:p:694-715
    DOI: 10.1007/s11750-013-0288-6
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    Cited by:

    1. Abdoun Sylia & Taleb Samira, 2024. "Strategic Joining in an Unobservable Markovian Queue with Differentiated Vacations," SN Operations Research Forum, Springer, vol. 5(3), pages 1-27, September.
    2. Economou, Antonis & Logothetis, Dimitrios & Manou, Athanasia, 2022. "The value of reneging for strategic customers in queueing systems with server vacations/failures," European Journal of Operational Research, Elsevier, vol. 299(3), pages 960-976.
    3. Gopinath Panda & Veena Goswami, 2022. "Equilibrium Joining Strategies of Positive Customers in a Markovian Queue with Negative Arrivals and Working Vacations," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1439-1466, September.
    4. Qingqing Ma & Yiqiang Q. Zhao & Weiqi Liu & Jihong Li, 2019. "Customer Strategic Joining Behavior in Markovian Queues with Working Vacations and Vacation Interruptions Under Bernoulli Schedule," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(01), pages 1-26, February.
    5. Gopinath Panda & Veena Goswami & Abhijit Datta Banik, 2016. "Equilibrium and Socially Optimal Balking Strategies in Markovian Queues with Vacations and Sequential Abandonment," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(05), pages 1-34, October.

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