Tail distribution of the buffer occupancy in a discrete-time queue fed by general on/off sources

A statistical multiplexer with a finite number of independent, not necessarily identical, bursty traffic sources is considered in this paper. Each source stochastically alternates between on-periods, during which it generates one cell per slot, and off-periods, during which no cells are generated. The on-periods and the off-periods are assumed to be independent, but are allowed to have general distributions. The discrete-time queueing model we thus obtain is analyzed using a generating-functions approach resulting in an accurate geometric approximation for the tail distribution of the buffer contents based on the use of the dominant pole of its probability generating function. The results of the study are applied to investigate the influence of the nature of the distributions of the on-periods and the off-periods of the traffic sources on the multiplexer performance.