Cost optimisation analysis of retrial queue with K optional phases of service under multiple working vacations and random breakdowns

Abstract

In this paper, we consider a cost optimisation analysis of M/G/1 retrial queue with k optional phases of service under multiple working vacations and vacation interruption, where each phase consists of an optional re-service. An arriving customer may balk the system at some particular times. When the orbit becomes empty at regular service completion instant, the server goes for a working vacation. During a working vacation period, the server works in lower service rate. The normal busy server may get to breakdown and the service channel will fail for a short interval of time. We analyse the steady state probability generating function for the system size by using the supplementary variable method. Some important system performance measures are obtained. Finally, some numerical examples and cost optimisation analysis are presented.