Performance analysis of the system contents in a discrete–time non-preemptive priority queue with general service times

We consider a discrete-time queueing system with non-preemptive priority scheduling. Two classes of traffic will be considered, i.e., high priority and low priority traffic, which both generate variable length packets. We will derive an expression for the joint Probability Generating Function (pgf) of the steady-state system contents of the high and the low priority traffic. From these, some performance measures (such as the mean value of steady-state system contents and packet delay of high and low priority packets) will be derived. These will be used to illustrate the significance of priority scheduling. Our results can be used to analyse performance of buffers in voice/data networks.