DELAY ANALYSIS OF A PACKET VOICE MULTIPLEXER BY THE SIGMA-DI/D/1 QUEUE

We study the performance of a statistical multiplexer whose inputs consists of a superposition of voice packets from c trunks. Voice calls are established according to a Poisson process and call holding times have a general distribution. Each voice call, while in progress, generates packets at a fixed intervals of DELTA. Thus, when n calls are in progress, the packet generation process is a superposition of n renewal processes, each one with an interarrival time of exactly-DELTA. These packets are fed to a transmitter whose service time for all packets is exactly-beta. We assume that c-beta < DELTA, i.e., the transmitter queue is stable even when all trunks are busy. We analyze the delay for such a system by solving the SIGMA-D(i)/D/1 queue. The approximate solution method proposed in this paper can be used to solve for the mean packet delay for arbitrarily large c (number of trunks) and the delay distribution when c is less than about 100. We provide easily computable error bounds for this approximation. Since brute force simulation for this problem is time consuming, we propose an efficient hybrid simulation method for the packet voice multiplexer. We also investigate the approximation based on the M/D/1 queue when c becomes large. The M/D/1 approximation works well for larger values of c with moderate levels of utilization (about 75%).