Accurate bounds for the asymptotic constant in a statistical multiplexer with homogeneous generalized binary Markov sources

Abstract

This paper considers the asymptotic tail distribution of the number of cells queued in a statistical multiplexer fed with homogeneous generalized binary Markov sources. As the asymptotic decay rate is easy to obtain, we focus our effort on bounding the asymptotic constant, which is dependent on the initial phase combination of the sources and is hard to compute even for a moderate number of sources. We derive upper and lower bounds for the asymptotic constant, taking the initial phase combination into account. Numerical experiments show the accuracy of these bounds. They also show that, while the asymptotic decay rates are the same, the variation of initial phase combination of the sources may significantly affect the asymptotic constants.