language: en

Loss Correlation for Queues with Bursty Input Streams

Henning Schulzrinne James F. Kurose and Donald F. Towsley
Dept. of ECE Dept. of Computer Science University of Massachusetts
Amherst, MA 01003
hgschulz,kurose,towsley@cs.umass.edu

Abstract The loss probability of a queueing system provides, in many cases, insufficient 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 first, a two-class discrete-time queueing system, approximates the output queue of an ATM switch. The queue serves periodic foreground traffic and random background traffic. The background traffic is modeled as i.i.d. batches of arbitrary distribution. It is shown that the conditional loss probability (CLP) is independent of the buffer size if the buffer size is at least as large as the period of the foreground traffic. Example calculations indicate that losses occur essentially randomly as long as the foreground traffic uses less than 10% of the channel capacity. The second analysis derives the CLP seen by a selected stream in a slotted finite-buffer system with a superposition of interrupted Poisson sources. Here, the total number of arrivals may be correlated from slot to slot. Traffic correlation is seen to have a strong influence on loss correlation, while buffer size is seen to have virtually none.

1 Introduction