Patterns of cell loss in ATM multiplexers

Keywords: B-ISDN, congestion, ATM, statistical multiplexer, cell-loss. Cell loss is often assumed to occur at random. However, when an ATM cell is lost because of buffer overflow at a statistical multiplexer, there is an altered probability that the cells following it will be lost. In this report, conditional probabilities of cell-loss due to congestion are modelled mathematically, and then simulations used to verify the models are described. Conditional probabilities are modelled and simulated using M/M/1/K, MID/1/K, M/D/1/K with minimum interarrival times and SPP/D/1/K queues. Results from the models and simulations show that cell loss exhibits 'bursty' behaviour. If one cell is lost, the probability of following cells being lost is substantially higher than the overall cell loss probability. Consequently, cell loss has to be characterised by more than just an average rate. The average and variance of the number of cells lost are proposed as additional statistics to characterise cell loss caused by buffer overflow. In this paper these statistics are calculated and tabulated for M/M/1/K and M/D/1/K multiplexer models. Some of the repercussions of the bursty nature of cell loss for Broadband services are discussed.