A Performance Model for Statistical Multiplexing of correlated ATM Traffic Superpositions

Models for ATM statistical multiplexing must involve bursty (i.e. several cell arrivals are possible at a time instant) and correlated input processes. Correlation is important, since ATM networks will carry VBR video sources, the cell streams of which are typically correlated. In addition, the superposition of individual sources (e.g. in an ATM multiplexer), which are renewal (and non-Poisson), shows correlations. This paper extends recent results on queues with deterministic service times (greater or equal to the time-unit) and Semi-Markovian input processes (SMPs) to the SMP[x]/V/l/s queue. The SMP generates arrival instants, and the independent process X of i.i.d. random variables “modulates” the batch size. The solution provides the probability functions of the number of cells in the system and of the waiting time of a test-cell, the loss probability of a test-cell and the conditional cell loss probability. A possible extension allowing one batch input stream and one single cell stream is outlined; it can serve as a model for Connection Admission Control (CAC) in ATM.