Analytic derivation of tail probabilities for queue lengths and waiting times in ATM multiserver queues

In this paper the authors consider a discrete-time queueing model, useful for the design and the performance evaluation of many slotted communication systems in general, and ATM-based networks in particular. The model assumes a general independent packet arrival process, an infinite waiting room, an an arbitrary number of servers. By means of an approximation technique, explicit closed-form expressions are derived for the tail probabilities of both the buffer contents (queue length) and the delay (or the waiting time). These formulas are very easy to evaluate. They are applied in the performance analysis of an ATM switching element with output queueing, in order to obtain predictions for such quantities as the cell loss ratio and the delay jitter. Also, an application with more bursty arrivals is discussed. In both cases, very good agreement between actual (numerical) and approximate (analytic) results is observed.