Exact Tail Asymptotics of a Queue with LRD Input Traffic

Abstract

In this work we compute the exact tail asymptotics of the stationary workload W, associated to a discretetime single server queue, with constant release rate, infinite buffer capacity, and with M/G/∞ input traffic exhibiting long-range dependence. We choose a regularly varying distribution with parameter α > 1 for the general distribution G. We show that the exact asymptotics of the workload is a specific regularly varying function under some assumptions on the parameters.