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Tail Asymptotics for a Retrial Queue with Bernoulli Schedule

Author

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  • Bin Liu

    (School of Mathematics & Physics, Anhui Jianzhu University, Hefei 230601, China)

  • Yiqiang Q. Zhao

    (School of Mathematics and Statistics, Carleton University, Ottawa, ON K1S 5B6, Canada)

Abstract

In this paper, we study the asymptotic behaviour of the tail probability of the number of customers in the steady-state M / G / 1 retrial queue with Bernoulli schedule, under the assumption that the service time distribution has a regularly varying tail. Detailed tail asymptotic properties are obtained for the conditional probability of the number of customers in the (priority) queue and orbit, respectively, in terms of the recently proposed exhaustive stochastic decomposition approach. Numerical examples are presented to show the impacts of system parameters on the tail asymptotic probabilities.

Suggested Citation

  • Bin Liu & Yiqiang Q. Zhao, 2022. "Tail Asymptotics for a Retrial Queue with Bernoulli Schedule," Mathematics, MDPI, vol. 10(15), pages 1-13, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2799-:d:882267
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    References listed on IDEAS

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    1. Asmussen, Søren & Klüppelberg, Claudia & Sigman, Karl, 1999. "Sampling at subexponential times, with queueing applications," Stochastic Processes and their Applications, Elsevier, vol. 79(2), pages 265-286, February.
    2. Jeongsim Kim & Bara Kim, 2016. "A survey of retrial queueing systems," Annals of Operations Research, Springer, vol. 247(1), pages 3-36, December.
    3. Li, Hui & Yang, Tao, 1998. "Geo/G/1 discrete time retrial queue with Bernoulli schedule," European Journal of Operational Research, Elsevier, vol. 111(3), pages 629-649, December.
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    Cited by:

    1. Alexey V. Yakovlev & Vladimir V. Alekseev & Maria V. Volchikhina & Sergey V. Petrenko, 2022. "A Combinatorial Model for Determining Information Loss in Organizational and Technical Systems," Mathematics, MDPI, vol. 10(19), pages 1-12, September.

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