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

Rehab Khalaf, Kailash C. Madan, Cormac A. Lukas


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.

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Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

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