Exact tail asymptotics for a two-stage queue: Complete solution via kernel method

Abstract

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.