On the Limit Behaviour of the ATM Traffic within a Network

Abstract

The paper is concerned with the ATM traffic characterization within the network. Most of the work performed up to now has studied the effects of the traffic on the access multiplexer and the first switch of an ATM network; various source models were assumed to generate the ATM traffic. So, while the performances of a single switch node have been exhaustively examined, the statistical behaviour of the traffic modified as it crosses the network has not been thoroughly analyzed yet. The paper, through an analysis of a network of cascaded queues, shows that limit distributions exist in the statistical behaviour of the traffic streams and in the queue performances. The first modelling step consists in deriving the exact interdeparture time distribution for the cells of a reference-connection arriving to the output queue of a switch node with a general interarrival (GI) time distribution and multiplexed with a background traffic stream, then the analysis is iterated through a long sequence of cascaded output queues, until the interdeparture time distribution converges to a limit one. Simulations show that the analitycal results are more than accurate at each stage of the network under the hypothesis of independent queues. The study shows that the queue performances at the equilibrium point are always better than the M/D/1 case. The limit distributions depend only on the connection bandwidth and on the background traffic behaviour; the initial characteristics of a connection (burst length distributions and burst interarrival time distributions) do influence only the convergence speed, not the limit distributions.