Modified T vacation policy for an M/G/1 queueing system with an unreliable server and startup

This paper studies the vacation policy of an M/G/1 queueing system with an unreliable server and startup. After all the customers are served in the queue exhaustively, the server deactivates and takes at most J vacations of constant time length T repeatedly until at least one customer is found waiting in the queue upon returning from a vacation. If at least one customer presents in the system when the server returns from a vacation, then the server reactivates and requires a startup time before providing the service. On the other hand, if no customers arrive by the end of the Jth vacation, the server remains dormant in the system until at least one customer arrives. We will call the policy modified T vacation policy. Furthermore, it is assumed that the server breaks down according to a Poisson process and his repair time has a general distribution. We analyze the system characteristics for this model.