Calculation of output characteristics of a priority queue through a busy period analysis

In this paper, we analyze some output characteristics of a discrete-time two-class priority queue by means of probability generating functions. Therefore, we construct a Markov chain which – after analysis – provides a.o. the probability generating functions of the lengths of the busy periods of both classes. It is furthermore shown how performance measures, related to the output process, are calculated from these functions. The queueing model is kept fairly simple to explain the method of analysis of the busy periods and the output characteristics of priority queues as clearly as possible.