DEPARTURE PROCESS OF SINGLE SERVER QUEUEING SYSTEM WITH MARKOV RENEWAL INPUT AND GENERAL SERVICE TIMES

Abstract

The independence of processes in queueing systems is generally assumed when developing queueing models. However,real systems often involve several process dependencies, and failure to take these into consideration can lead to seriousunderestimation of the performance measures. We consider herein a single server queueing system with a Markov renewalprocess (MRP) for its arrival process and a general service time distribution, and derive the distribution function and cor-relation coefficient of the departure process. Since the departure process also often corresponds to an arrival process indownstream queues, the results obtained here can be used to derive a better approximation of the performance measuresof a non-product form general queueing network.