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Transient analysis of a single server queue with catastrophes, failures and repairs. (English) Zbl 1124.60073
Summary: A transient solution is obtained analytically using continued fractions for the system size in an M/M/1 queueing system with catastrophes, server failures and non-zero repair time. The steady state probability of the system size is present. Some key performance measures, namely, throughput, loss probability and response time for the system under consideration are investigated. Further, reliability and availability of the system are analysed. Finally, numerical illustrations are used to discuss the system performance measures.

MSC:
60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
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