Power-law vs exponential queueing in a network traffic model

Abstract

We examine the impact of network traffic dependencies on queueing performance in the context of a popular stochastic model, namely the infinite capacity discrete-time queue with deterministic service rate and M vertical bar G vertical bar infinity arrival process. We propose approximations to the stationary queue size distribution which are generated by interpolating between heavy and light traffic extremes. This is done under both long- and short-range dependent network traffic. Under long-range dependence, the heavy traffic results can be expressed in terms of Mittag-Leffler special functions which generalize the exponential distribution and yet display power-law decay. Numerical results from exact expressions (when available), approximations and simulations support the following conclusions: Network traffic dependencies need to be carefully accounted for, but whether this is accomplished through a short-or long-range dependent stochastic model bears little impact on queueing performance. The differences between exponential and power-law queueing are negligible at the "head" of the distribution, and manifest themselves only for large buffers. (C) 2007 Published by Elsevier B.V.