Discrete-time multiserver queues with priorities

We analyze the performance of discrete-time multiserver queues that use a priority structure in the scheduling of departures. Such systems are often encountered in the context of ATM and in voice-data multiplexing. The arrival process is iid from slot to slot with a general distribution for the batch sizes. The analysis of both system contents and delay makes extensive use of generating functions and yields simple formulas to evaluate important performance measures such as mean values, variances and tail probabilities of these random variables. A numerical example illustrates the results of the analysis and shows that using priorities and sharing resources can lead to a considerable improvement of system performance.