Use of the supremum distribution of Gaussian Processes in queueing analysis with long-range Dependence and self-similarity

Abstract

In this paper we study the supremum distribution of a general class of Gaussian processes with stationary increments. This distribution is directly related to the steady state queue length distribution of a queueing system. Hence, its study is also important for different queueing applications such as delay analysis in communication networks. Our study is based on Extreme Value Theory and we show that asymptotically grows at most (on the order of) log x, where mx is the reciprocal of the maximum (normalized) variance of Xt This result is considerably stronger than the existing results in the literature based on Large Deviation Theory. We further show that this improvement can be critical in characterizing the asymptotic behavior of . Our results cover a large class of self-similar, short range dependent, and long-range dependent Gaussian processes