Volume 51, Number 4, October-December 2017
|Page(s)||1211 - 1250|
|Published online||24 November 2017|
Exact tail asymptotics for a two-stage queue: Complete solution via kernel method
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.
Received: 21 June 2016
Accepted: 25 April 2017
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.
Mathematics Subject Classification: 60K25 / 60F10
Key words: Random walk in the quarter plane / stationary distribution / Kernel method / exact tail asymptotics
© EDP Sciences, ROADEF, SMAI 2017
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