Generalized sub-Gaussian fractional Brownian motion queueing model

Abstract

It is well known that often the one-dimensional distribution of a queue content is not Gaussian but its tails behave like a Gaussian. We propose to consider a general class of processes, namely the class of \(\varphi \)-sub-Gaussian random processes, which is more general than the Gaussian one and includes non-Gaussian processes. The class of sub-Gaussian random processes contains Gaussian processes also and therefore is of special interest. In this paper we provide an estimate for the queue content distribution of a fluid queue fed by \(N\) independent strictly \(\varphi \)-sub-Gaussian generalized fractional Brownian motion input processes. We obtain an upper estimate of buffer overflow probability in a finite buffer system defined on any finite time interval \([a,b]\) or infinite interval \([0,\infty )\). The derived estimate captures more accurately the performance of the queueing system for a wider-range of input processes.