Exact tail asymptotics for fluid models driven by an M/M/c queue

Abstract

In this paper, we investigate exact tail asymptotics for the stationary distribution of a fluid model driven by the M/M/c queue, which is a two-dimensional queueing system with a discrete phase and a continuous level. We extend the kernel method to study tail asymptotics of its stationary distribution, and a total of three types of exact tail asymptotics is identified from our study and reported in the paper. Keywords fluid queue driven by an M/M/c queue; kernel method; exact tail asymptotics; stationary distribution; asymptotic analysis MSC 2010 Subject Classification 60K25, 60J27, 30E15, 05A15.