Evaluating the limit behavior of the ATM traffic within a network

This paper is concerned with the ATM traffic characterization within the network. Most of the work performed up to now has studied the effects of 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 performance of a single switch node has been exhaustively examined, the statistical behavior of the traffic modified as it crosses the network has not been thoroughly analyzed yet. This paper, through an analysis of a network of cascaded queues, indicates that limit distributions exist in the statistical behavior of the traffic streams and in the queue performance, although a formal proof is believed to be very hard to obtain. The first modelling step consists of 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 time distribution and multiplexed with a background traffic stream. The analysis is iterated through a long sequence of cascaded output queues, until the interdeparture time distribution converges. Simulations show that the analytical results are accurate at each stage of the network under the hypothesis of independent queues, and are also good approximations in the case of correlated queues. This study shows that the queue performance at the limit point is always better than the M/D/1 case. The distributions found in this way depend only on the connection bandwidth and on the background traffic behavior. The initial characteristics of a connection (burst length distributions and burst interarrival time distributions) only influence the convergence speed, not the limit distribution.