Transient Analysis of Batch Arrival Feedback Retrial Queue with Starting Failure and Bernoulli Vacation

Abstract

This paper discusses a batch arrival feedback retrial queue with Bernoulli vacation, where the server is subjected to starting failure. Any arriving batch finding the server busy, breakdown or on vacation enters an orbit. Otherwise one customer from the arriving batch enters a service immediately while the rest join the orbit. After the completion of each service, the server either goes for a vacation with probability  or may wait for serving the next customer with probability . Repair times, service times and vacation times are assumed to be arbitrarily distributed. The time dependent probability generating functions have been obtained in terms of their Laplace transforms.

Keywords: Batch arrival, Time dependent solution, Retrial queues, Starting failures, Server vacation.