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A transient solution to the M/M/c queuing model equation with balking and catastrophes. (English) Zbl 1392.90054
Summary: In this paper, we consider a Markovian multi-server queuing system with balking and catastrophes. The probability generating function technique along with the Bessel function properites is used to obtain a transient solution to the queuing model. The transient probabilities for the number of customers in the system are obtained explicitly. The expressions for the time-dependent expected number of customers in the system are also obtained. Finally, applications of the model are also discussed.
MSC:
90B22 Queues and service in operations research
60K25 Queueing theory (aspects of probability theory)
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