M/D/1 QUEUE WITH COMPULSORY VACATION AND RANDOM BREAKDOWNS

We analyze a single server vacation queue with Poisson arrivals, deterministic service of constant duration ????????(> 0) subject to vacation and random breakdowns. As soon as the service of a customer is complete, the server will go for compulsory vacation. The vacation times are also assumed to be general while we consider exponential distribution for repair time. The supplementary variable technique is used to find explicitly the probability generating function of the number in the system and the mean number in the system.