Analysis of a single server retrial queue with general retrial times, two phases of service, balking and Bernoulli vacation

In this paper, we introduce a single server retrial queue with general retrial times, two phases of service, balking and Bernoulli vacation. We assume that the arriving customers who find the server busy are queued in the orbit in accordance with an first come first served (FCFS) discipline and only the customer at the head of the queue is allowed for access to the server or balk the system. After the completion of first phase service, the customer compulsory join the second phase of service. If the orbit is empty, the server always takes a vacation. At the end of the vacation, the server waits for the customer to arrive. The steady state distribution of the server state and the number of customers in the system are obtained. The effects of various parameters on the system performance are analyzed.