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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 probability . 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 .   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.</p

journal of mathematics research

An M[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