Stochastic Models for ATM Switching Networks

It is widely recognized that the input streams to cell switching networks cannot, in general, be adequately modeled as Poisson point processes. The fact that the traffic passing through such systems often displays marked burstiness must be taken into account, and many contributions are concerned with the practical and analytical consequences of the resulting dependencies between the cell interarrival times. The models considered in this paper include yet another feature that is usually ignored, namely that the switching speed may be appreciably greater than the speed at which some sources generate their respective cells. It is therefore important, as we do here, to investigate the situation where the cells making up individual bursts are spaced according to some prescribed probability distribution. The purpose of this paper is to show that the switch performance is strongly dependent on the input parameters and, at the same time, to demonstrate that analytical approaches provide useful alternatives to the lengthy simulation runs needed to evaluate probabilities of rare events such as cell losses.