New constant service time Polya/D/n traffic model with peaked input stream

Abstract

In this paper, we study the buffer queueing behaviour in high-speed networks. Some limited analytical derivations of queue models have been proposed in literature but their solutions are often a great mathematical challenge. We propose to use the Polya distribution to overcome such limitations. The specific behaviour of an IP interface with bursty traffic and long-range dependence is investigated by a version of the “classical” M/D/n queueing model called Polya/D/n. This is queueing system with a Polya input stream (a negative binomial distributed number of arrivals in a fixed time interval), a constant service time, multiple servers, and infinite waiting rooms. The model is considered a renewal process because of its quasi-random input stream and constant service time. We develop balance equations for the state of the system and obtain results for the packet loss and delay. The finding that the Polya distribution is adequate to model bursty input streams in IP network interfaces has motivated the proposal to evaluate the Polya/D/n system. It is shown that the variance in the input stream significantly changes the characteristics of the waiting system. The suggested model is new and allows defining different bursty traffic and evaluating losses and delays relatively easily.