Analysis of a batch retrial queue with Bernoulli vacation and starting failures

A batch arrival retrial queue with general retrial times is studied in this paper, where the server is subject to starting failures under Bernoulli vacation schedule. Any arriving batch finding the server busy, broken down or on vacation enters an orbit. Otherwise one customer from the arriving batch enters a service immediately while the rest joins the orbit. After completion of service, the server either goes for a vacation with probability p or may wait for serving the next customer with probability (1 − p). We construct the mathematical model and derive the steady-state distribution of the server state and the number of customers in the system/orbit. The effect of parameter distributions on the system performance measures is numerically presented. Such a model has potential applications in mail system and wireless network.