Transient solution of a Markovian queuing model with heterogeneous servers and catastrophes

In this paper, we study the Markovian queuing system with heterogeneous servers and catastrophes. The customers arrive according to a Poisson process and the service times follow exponential distribution. There are a finite number of c servers with different services rates and each arriving customer requires exactly one server for its service. The queue discipline is FCFS, and the customers select the servers on fastest server first(FSF) basis. We use the generating function technique to derive the transient solution of the model in a direct way. The explicit time dependent probabilities of system size are obtained and a numerical example is presented in order to show the managerial insights of the model. Some important special cases of the model are derived and discussed. Finally, the probability that arriving customer finds system busy and average number of server busy in steady state are obtained numerically. © 2015, Operational Research Society of India.