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 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 .
Highlights
IntroductionQueueing systems with breakdowns have been studied by several authors including (Federgruen & So, 1990), (Aissani & Artalejo, 1998), (Wang, Cao & Li, 2001) and (Madan, Abu-Dayyeh, Gharaibeh, 2003b)
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
Summary
Queueing systems with breakdowns have been studied by several authors including (Federgruen & So, 1990), (Aissani & Artalejo, 1998), (Wang, Cao & Li, 2001) and (Madan, Abu-Dayyeh, Gharaibeh, 2003b). (Maraghi, Madan and Darby-Dowman, 2009 a) have studied some queueing systems with vacations and breakdowns. All these research papers assume no server delay in joining the system after completion of a vacation period and no delay in starting the repair process after a breakdown occurs. In this paper we add a realistic assumption that the server may have to go for an extended vacation due to many reasons which may include illness or engagement in another activity or delay in traveling etc.
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