On an M^x/G/1 queue with a random set up time, random breakdowns and delayed deterministic repairs

Abstract

We study a single server queue with Poisson arrivals in batches of variable size. The server provides one by one general service to customers with a set-up time of random length before starting the first service at the start of the system as well as after every idle period of the system. The set-up time has been assumed to be general. Further, the server is subject to random breakdowns. The repair time has been assumed to be deterministic with a further delay time before starting repairs. The delay time in starting repairs has been assumed to be general. We find steady state queue length of various states of the system in terms of probability generating functions. Steady state results of a few interesting special cases have been derived.