Stochastic analysis of an M/G/1 retrial queue subject to working vacation and starting failure

This paper deals with the analysis of an M/G/1 retrial queue with starting failure and working vacation which arise in many industries. The single server provides service in both a normal busy period and in a vacation period, which turn as working vacations. We assume that, during the normal busy period, the server faces unreliability due to starting failure. In working vacation period the server will provide service lower rate rather than completely stopping the service. After the vacation completion instant, the server will come back to the normal working and starts serving the customers. The necessary and suffcient condition for the system to be stable have been derived. Using supplementary variable method, we obtain the stationary probability distribution and some performance measures. To validate the proposed model some numerical examples are illustrated. Further, we carry out some special cases for the proposed model.