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