Loss Correlation for Queues with Single and Multiple Input

The loss probability of a queueing system provides in many cases insuucient information for performance evaluation, for example, of le transfer retransmission protocols and real-time applications with signal reconstruction. This paper evaluates and characterizes the correlation between packet losses for three queu-eing systems in discrete time that are motivated by BISDN applications. In the rst, a single-stream batch-arrival queue operating in discrete time, we nd that the service discipline and buuer management policy for FIFO and LIFO do not innuence the loss correlation. The second, a two-class discrete-time queueing system, approximates the output queue of an ATM switch. The queue serves periodic foreground traac and random background traac. The background traac is modeled as i.i.d. batches of arbitrary distribution. It is shown that the conditional loss probability is independent of the buuer size if the buuer size is at least as large as the period of the foreground traac. Example calculations indicate that losses occur essentially randomly as long as the foreground traac uses less than 10% of the channel capacity. The nal analysis derives the conditional loss probability a selected stream in a slotted nite-buuer system with a superposition of interrupted Poisson sources, where the total number of arrivals may be correlated from slot to slot. Traac correlation is seen to have a strong innuence on loss correlation, while buuer size has virtually none.