Power-law vs exponential queueing in a network traffic model

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|G|∞M|G|∞ 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.