Asymptotic Results for the Superposition of a Large Number of Data Connections on an Atm Link Alain Dupuis, Fabrice Guillemin and Bruno Sericola

The M=PH=1 system is introduced in this paper to analyze the superposition of a large number of data connections on an ATM link. In this model, information is transmitted in bursts of data arriving at the link as a Poisson process of rate and burst durations are PH distributed with unit mean. Explicit methods of computing the distributions of some transient characteristics related to excursions by the occupation process f t g of the M=PH=1 queue above the link transmission capacity C are described. Given that such an excursion represents a congestion period for the system, the transient characteristics considered are the duration of a congestion period, the area V swept under process f t g above C in such a congestion period (V represents the volume of information lost in an overrow period), and the number N of bursts arriving in a congestion period. It is then shown that, as conjectured in earlier studies, the random variables C, CV , and N converge in distribution, as C tends to innnity while the utilization factor of the link deened by = =C is xed, towards the duration of the busy period of an M=M=1 queue with input rate and unit service rate, the area V swept under the occupation process of this M=M=1 queue in a busy period, and the number N of customers served in a busy period, respectively. Further simulation results show that after adjustment of the load of the M=M=1 queue, a similar convergence result holds for the superposition of a large number of On/OO sources with deterministic, exponential, and hyperexponential On and OO period distributions. R esultats asymptotiques pour la superposition d'un grand nombre de connexions de donn ees sur un lien ATM R esum e : La le M=PH=1 est introduite dans cet article pour analyser la superposition d'un grand nombre de connexions de donn ees sur un lien ATM. Dans ce mod ele, l'information est transmise en rafales de donn ees arrivant au lien comme un processus de Poisson de taux et les dur ees des rafales sont distribu ees selon une loi PH de moyenne 1. On d ecrit des m ethodes explicites de calcul des distributions de certaines caract eristiques transitoires en relation avec les excursions du processus d'occupation f t g de la le M=PH=1 au dessus de la capacit e C du lien de transmission. Etant donn e qu'une telle …