Cell Loss Probabilities in a Statistical Multiplexer in an ATM Network

Abstract

In this paper we evaluate the loss probability of cells generated by a burst/silence source which is mixed with a superposition of M independent identical burst/silence traffic streams in a statistical multiplexer with a finite buffer capacity. The model incorporates the main stochastic characteristics of the system, namely the periodicity of an active source and the modulation effect produced by the alternation between active and silent periods of each source. The resulting queueing system is a discrete-time Markov chain and the queue length distribution seen by an arriving cell of the tagged source is evaluated. The loss probability of a string of consecutive cells of this source is computed, together with the conditional loss probability of such a string, given that the first cell was lost. Numerical results show that, although the tagged source has a small single cell loss probability, it may experience a high conditional loss of a string of consecutive cells, and hence may suffer from a quality of service degradation. The impact of the buffer size of the multiplexer, the burst length of sources and the load of the system on this conditional loss probability is studied.

This work was supported in part by the Commission of the European Communities, under project RACE R1022 (Research and Development on Advanced Communications in Europe) on ATD Techniques.