ANALYSIS OF M/G/1 QUEUE WITH OPTIONAL SERVICES AND DETERMINISTIC REPAIR

We analyze an M/G/1 queue with Poisson arrivals, three optional services, random breakdowns and deterministic repair. The first service is essential and other three services are optional. All arriving customers demand first essential service and after completion of first service, the customer has the option of choosing any one of the three optional services with probability Otherwise the customer can leave the system without choosing any of the three optional services with probability . The server is subject to random breakdowns and just after a breakdown the server undergoes repairs of fixed (constant) duration ( ) 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.