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Exact tail asymptotics for a discrete-time preemptive priority queue

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Abstract

In this paper, we consider a discrete-time preemptive priority queue with different service completion probabilities for two classes of customers, one with high-priority and the other with low-priority. This model corresponds to the classical preemptive priority queueing system with two classes of independent Poisson customers and a single exponential server. Due to the possibility of customers’ arriving and departing at the same time in a discrete-time queue, the model considered in this paper is more complicated than the continuous-time model. In this model, we focus on the characterization of the exact tail asymptotics for the joint stationary distribution of the queue length of the two types of customers, for the two boundary distributions and for the two marginal distributions, respectively. By using generating functions and the kernel method, we get the exact tail asymptotic properties along the direction of the low-priority queue, as well as along the direction of the high-priority queue.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central South University, Changsha, 410083, China

    Yang Song & Zai-ming Liu

  2. School of Statistics, Shandong University of Finance and Economics, Jinan, 250014, China

    Hong-shuai Dai

Authors
  1. Yang Song
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  2. Zai-ming Liu
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  3. Hong-shuai Dai
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Corresponding author

Correspondence to Hong-shuai Dai.

Additional information

Supported in part by the National Natural Science Foundation of China under Grant No. 11271373 and 11361007, and the Guangxi Natural Science Foundation under Grant No. 2014GXNSFCA118001 and 2012GXNSFBA053010.

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Song, Y., Liu, Zm. & Dai, Hs. Exact tail asymptotics for a discrete-time preemptive priority queue. Acta Math. Appl. Sin. Engl. Ser. 31, 43–58 (2015). https://doi.org/10.1007/s10255-015-0448-6

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  • DOI: https://doi.org/10.1007/s10255-015-0448-6

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