Loss Correlation for Queues with Bursty Input Streams

The loss probability of a queueing system provides, in many cases , insuucient information for performance evaluation, for example , of data link layer protocols and applications with forward error correction. This paper evaluates and characterizes the correlation between packet losses for two queueing systems in discrete time that are motivated by BISDN applications. The rst, 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 (CLP) 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 second analysis derives the CLP seen by a selected stream in a slotted nite-buuer system with a superposition of interrupted Poisson sources. Here, 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 is seen to have virtually none.