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Tail asymptotics for the $$M_1,M_2/G_1,G_2/1$$ M 1 , M 2 / G 1 , G 2 / 1 retrial queue with non-preemptive priority

Author

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  • Bin Liu

    (Anhui Jianzhu University)

  • Yiqiang Q. Zhao

    (Carleton University)

Abstract

Stochastic networks with complex structures are key modelling tools for many important applications. In this paper, we consider a specific type of network: retrial queueing systems with priority. This type of queueing system is important in various applications, including telecommunication and computer management networks with big data. The system considered here receives two types of customers, of which Type-1 customers (in a queue) have non-pre-emptive priority to receive service over Type-2 customers (in an orbit). For this type of system, we propose an exhaustive version of the stochastic decomposition approach, which is one of the main contributions made in this paper, for the purpose of studying asymptotic behaviour of the tail probability of the number of customers in the steady state for this retrial queue with two types of customers. Under the assumption that the service times of Type-1 customers have a regularly varying tail and the service times of Type-2 customers have a tail lighter than Type-1 customers, we obtain tail asymptotic properties for the numbers of customers in the queue and in the orbit, respectively, conditioning on the server’s status, in terms of the exhaustive stochastic decomposition results. These tail asymptotic results are new, which is another main contribution made in this paper. Tail asymptotic properties are very important, not only on their own merits but also often as key tools for approximating performance metrics and constructing numerical algorithms.

Suggested Citation

  • Bin Liu & Yiqiang Q. Zhao, 2020. "Tail asymptotics for the $$M_1,M_2/G_1,G_2/1$$ M 1 , M 2 / G 1 , G 2 / 1 retrial queue with non-preemptive priority," Queueing Systems: Theory and Applications, Springer, vol. 96(1), pages 169-199, October.
    • Handle: RePEc:spr:queues:v:96:y:2020:i:1:d:10.1007_s11134-020-09666-8
    DOI: 10.1007/s11134-020-09666-8
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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.
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    Cited by:

    1. Dieter Fiems, 2023. "Retrial queues with constant retrial times," Queueing Systems: Theory and Applications, Springer, vol. 103(3), pages 347-365, April.
    2. Bin Liu & Jie Min & Yiqiang Q. Zhao, 2023. "Refined tail asymptotic properties for the $$M^X/G/1$$ M X / G / 1 retrial queue," Queueing Systems: Theory and Applications, Springer, vol. 104(1), pages 65-105, June.

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