A Batch Arrival Retrial Queue with Two Phases of Service, Feedback and K Optional Vacations

Abstract

We consider a batch arrival queueing system with two phases of service, feedback and K optional vacations under a classical retrial policy. At the arrival epoch, if the server is busy the whole batch joins the orbit. Whereas if the server is free, then one of the arriving customer starts its service immediately and the rest joins the orbit. For each customer, the server provides two phases of service. After the completion of two phases of service, the customer may rejoin the orbit as a feedback customer for receiving another regular service with probability p. If the system is empty, then the server become inactive and begins the first essential vacation. After the completion of first essential vacation, the server may either wait idle for a customer or may take one of K additional vacations. The steady state distribution of the server state and the number of customers in the orbit are obtained. Also the effects of various parameters on the system performance are analyzed numerically.