Effect of the on-period distribution on the performance of an ATM multiplexer fed by on/off sources: an analytical study

In this paper, we consider a statistical multiplexer in an ATM network, which is fed by a finite number of independent bursty on/off traffic sources. Most of the previous work assumes a two-state on/off source model, where both the on-periods and the off-periods are geometrically distributed. We assume a general distribution for the on-period lengths, and we study the effect of the on-period distribution on the multiplexer performance. Both the homogeneous and the heterogeneous traffic case are considered. An analytical method is presented to analyze the system, which basically is a generating-functions approach and uses an infinite-dimensional state description. Exact closed-form expressions are obtained for the mean and the tail distribution of the system contents. The numerical evaluation of the derived formulas is simple and not CPU time and/or memory space consuming, whatever the on-period distribution is. Numerical results indicate that, for a given fixed on-period length, the multiplexer performance strongly depends on the actual distribution of the on-period.