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Transient analysis for state-dependent queues with catastrophes. (English) Zbl 1153.60394
Summary: Queueing systems with catastrophes and state-dependent arrival and service rates are considered. For two types of queueing systems, namely, queues with discouraged arrivals and infinite server queue, explicit expressions for the transient probabilities of system size are obtained by using the continued fractions technique. Some system performance measures and steady-state probabilities are studied. The effect of system parameters on system size probabilities are also illustrated numerically. It is observed that the steady-state probabilities differ when catastrophes are present, while they are identical in the absence of catastrophes.

MSC:
60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
60G10 Stationary stochastic processes
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