Characterization of the departure process of M/G/1 queue with heavy-tailed service time distribution

Recent studies have demonstrated that local-area and wide-area network traffic exhibit long-range dependence, a property that has significant implications on the design and dimensioning of telecommunication networks. Most of the previous work characterizes the long-range dependence of the departure process of a queue driven by long-range dependent input in a binary fashion; does it exist or not. We present a characterization of the departure process that enables us to determine the intensity of the long-range dependence of the departure process. We show analytically that the departure process of the queue is long-race dependent and that its intensity does not strengthen nor weaken relative to the arrival process, but rather has the same Hurst parameter.