Exact tail asymptotics for a two-stage queue: Complete solution via kernel method
Dai, Hongshuai1 ; Kong, Lingtao1 ; Song, Yang2
1 School of Statistics, Shandong University of Finance and Economics, Jinan, 250014, China.
2 Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China.
RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 4, pp. 1211-1250.

In this paper, we are interested in tail asymptotics of stationary distributions for a two-stage tandem queue with coupled processors, Poisson arrivals, and exponential service times. The model was motivated by data transfer in cable networks regulated by a reservation procedure, and has been studied in the literature by several researchers. In the present paper, by using the kernel method, we obtain exact tail asymptotics for the stationary distributions. What is the more important is that we give a complete solution of this topic, which means that, given the parameters of the model, exact tail asymptotics for the stationary distributions of this two-stage queue can be obtained based on our results.

Reçu le :
Accepté le :
DOI : 10.1051/ro/2017034
Classification : 60K25, 60F10
Mots-clés : Random walk in the quarter plane, stationary distribution, Kernel method, exact tail asymptotics
Dai, Hongshuai 1 ; Kong, Lingtao 1 ; Song, Yang 2

1 School of Statistics, Shandong University of Finance and Economics, Jinan, 250014, China.
2 Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China. 
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     title = {Exact tail asymptotics for a two-stage queue: {Complete} solution via kernel method},
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Dai, Hongshuai; Kong, Lingtao; Song, Yang. Exact tail asymptotics for a two-stage queue: Complete solution via kernel method. RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 4, pp. 1211-1250. doi : 10.1051/ro/2017034. http://www.numdam.org/articles/10.1051/ro/2017034/

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