A study on M/G/1 feedback retrial queue with subject to server breakdown and repair under multiple working vacation policy

TLDR: In this article, a single server feedback retrial queueing system with multiple working vacations and vacation interruption is considered and the steady state probability generating function for the system size is obtained by using the supplementary variable method.

Abstract: In this paper, we consider a single server feedback retrial queueing system with multiple working vacations and vacation interruption. An arriving customer may balk the system at some particular times. As soon as orbit becomes empty at regular service completion instant, the server goes for a working vacation. The server works at a lower service rate during working vacation (WV) period. After completion of regular service, the unsatisfied customer may rejoin into the orbit to get another service as feedback customer. The normal busy server may get to breakdown and the service channel will fail for a short interval of time. The steady state probability generating function for the system size is obtained by using the supplementary variable method. Some important system performance measures are obtained. Finally, some numerical examples and cost optimization analysis are presented.