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Strategic joining rules in a single server Markovian queue with Bernoulli vacation

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  • Jie Liu

    (Beijing Jiaotong University)

  • Jinting Wang

    (Beijing Jiaotong University)

Abstract

The strategic joining behavior of customers in a single-server Markovian queueing system with Bernoulli vacation is studied. It is assumed that the server begins a vacation period if the queue is empty upon completion of a service, and if the queue is not empty, the server will take a Bernoulli type vacation. Assuming that arriving customers can observe various levels of the system information, we study strategic customers’ decision on whether to join or balk the queue based on a linear reward-cost structure. The Nash equilibrium strategies in the fully observable case and the unobservable cases are investigated. The effect of the information level as well as several parameters on the equilibrium behavior is illustrated via numerical examples.

Suggested Citation

  • Jie Liu & Jinting Wang, 2017. "Strategic joining rules in a single server Markovian queue with Bernoulli vacation," Operational Research, Springer, vol. 17(2), pages 413-434, July.
    • Handle: RePEc:spr:operea:v:17:y:2017:i:2:d:10.1007_s12351-016-0231-3
    DOI: 10.1007/s12351-016-0231-3
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    References listed on IDEAS

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    1. B. Krishna Kumar & S. Pavai Madheswari, 2009. "Analysis of an M/M/N queue with Bernoulli service schedule," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 5(1), pages 48-72.
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    3. Naishuo Tian & Zhe George Zhang, 2006. "Vacation Queueing Models Theory and Applications," International Series in Operations Research and Management Science, Springer, number 978-0-387-33723-4, December.
    4. Guo, Pengfei & Hassin, Refael, 2012. "Strategic behavior and social optimization in Markovian vacation queues: The case of heterogeneous customers," European Journal of Operational Research, Elsevier, vol. 222(2), pages 278-286.
    5. Pengfei Guo & Refael Hassin, 2011. "Strategic Behavior and Social Optimization in Markovian Vacation Queues," Operations Research, INFORMS, vol. 59(4), pages 986-997, August.
    6. Naishuo Tian & Zhe George Zhang, 2006. "Applications of Vacation Models," International Series in Operations Research & Management Science, in: Vacation Queueing Models Theory and Applications, chapter 0, pages 343-358, Springer.
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    Cited by:

    1. 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.
    2. Shan Gao & Hua Dong & Xianchao Wang, 2021. "Equilibrium and pricing analysis for an unreliable retrial queue with limited idle period and single vacation," Operational Research, Springer, vol. 21(1), pages 621-643, March.
    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.

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