New approximation for analyzing the multiplexing of bursty sources in ATM networks

The paper is concerned with the analysis of an ATM multiplexer serving bursty applications such as voice, image, and high-speed data. The model used is a ΣGI_i/D/1 discrete-time single-server queueing system: the arrival process is a superposition of several random processes, and the departure process is a deterministic with a FCFS discipline. The difficulty in solving such a queueing system depends on the model chosen for the individual traffic sources. For the case in which the cell arrival stream from the individual sources is modeled as a Bernouli process, an exact solution is possible. The problem with such a model is that it does not incorporate the effect of burst length. A more realistic model that takes into consideration the impact of the burst length is considered in the study. In particular, an alternating-state Markov process is chosen to model the individual arrival stream. The solution of a ΣGI_i/D/1 queueing system with the arrival process being a superposition of several renewal processes is in general intractable. The paper obtains a new approximation which the authors refer to as the three-parameters approximation (TPA). This approximation is based on the asymptotic properties of the aggregate traffic and the congestion estimates from the simulation experiments. The TPA solution is found to be dependent on three parameters: number of sources, overall traffic intensity at the queue, and multiplexing factor. The TPA is an improvement of a previous approximation developed in analyzing packet voice system