Queue Behavior of Statistical Multiplexers

Abstract

In a statistical multiplexer, packets are assumed to be arriving at the multiplexer with the inter arrival times being Independent and Identically Distributed (IID). The service time is also IID. The inter arrival times are generated from the corresponding probability distribution. When a packet arrives to an empty or idle system, the packet is immediately served; otherwise, it is queued. In this paper, the queue behaviors in the multiplexer’s buffer were examined. The results show that the average number of packets in the multiplexer queue increases in an exponential form with increase in utilization; and at high utilization, there is a dramatic increase in the number of packets in the multiplexer queue which may lead to packet loss when there is no sufficient buffering. Comparison of the simulation and analytical results for the mean number of packets in an M/M/1 Multiplexer Queue reveals that results are within ±23% for offered load of up to 90%.