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Geo/G/1 queues with disasters and general repair times. (English) Zbl 1217.90073
Summary: This paper discusses discrete-time single server Geo/G/1 queues that are subject to failure due to a disaster arrival. Upon a disaster arrival, all present customers leave the system. At a failure epoch, the server is turned off and the repair period immediately begins. The repair times are commonly distributed random variables. We derive the probability generating functions of the queue length distribution and the FCFS sojourn time distribution. Finally, some numerical examples are given.

MSC:
90B22 Queues and service in operations research
90B25 Reliability, availability, maintenance, inspection in operations research
60K25 Queueing theory (aspects of probability theory)
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