AnM[X]/G/1 Queue with Bernoulli Schedule General Vacation Times, General Extended Vacations, Random Breakdowns, General Delay Times for Repairs to Start and General Repair Times

Abstract This paper studies a batch arrival queueing system in which the server may face occasional random breakdowns. The repair process does not start immediately after a breakdown and there is a delay time waiting for repairs to start. Further, after every service completion the server has the option to leave for a vacation with probability p or continue serving with probability1 − p. The main new assumption in this paper is that the server has the option to go on extended vacation after the original vacation completion with probability r or rejoins the system to provide service directly after the original vacation with probability 1 − r. The service times, vacation times, extended vacation times, delay times and repair times are all assumed to follow general arbitrary distributions, while only the breakdown times are exponentially distributed.