A transient solution to the M/M/c queuing model equation with balking and catastrophes.

*(English)*Zbl 1392.90054Summary: 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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\textit{R. Kumar}, Croat. Oper. Res. Rev. (CRORR) 8, No. 2, 577--591 (2017; Zbl 1392.90054)

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