A Queueing Model with Multiple Types of Server Breakdowns

In this paper we consider a general queueing model in which the server may experience several different types of breakdowns. Each type of breakdown requires a finite random number of stages of repair. We obtain a necessary and sufficient condition for the stationary queue length distribution to exist. We then show how to compute the queue length distribution by matrix geometric methods, and we find an explicit expression for its mean. We also find properties of several random variables associated with the model, such as the repair time for a server breakdown, a customer’s completion time, the number of stages of repair required to restore service, and some relationships among these variables and between them and the number of breakdowns that occur during a customer’s completion time. We then discuss some interesting special cases of the model.