Performance of a single server queue with self similar input

Abstract

To evaluate analytically the performance of a discrete time single server queue where the input process has a general marginal distribution, its index of dispersion for counts (IDC) may be infinite, and where the tail of the unfinished work distribution is not necessarily dominant, we use the following two principles. Firstly, we use the observation that only a finite duration of time is required for consideration of the effect of correlation on queueing performance. Secondly, by a certain transformation, queueing performance results for a queue with correlated input having arbitrary marginal distribution can be evaluated using that of its noncorrelated counterpart. We confirm the results by simulation using real traffic measurements from a high speed data network.