Maximum Queue Length of a Fluid Model with an Aggregated Fractional Brownian Input

Abstract

A fractional Brownian queueing model, that is, a fluid queue with an input of a fractional Brownian motion, has been applied in network model- ing since the self-similarity and long-range dependence were observed in Inter- net traffic. In this paper, a fluid queue with an aggregated fractional Brownian input, which is a generalization of a fractional Brownian queueing model, is considered and the maximum queue length over a time interval [0,t] is studied. The impact of an aggregated fractional Brownian input on the queue length process is analyzed and the main results on the maximum queue length are compared with some related known results in the literature.