Optimal Policies for a K-Phase Service System with Bernoulli Vacation Schedule

This paper studies Optimal NT policies for a k-phase service M/G/1 system with Bernoulli vacation schedule. The system contains an unreliable server with a breakdown period and delaying period. The server determines to start service by the policy: the server reactivates as soon as the number of arrivals in the queue reaches to a predetermined threshold N or T time units have elapsed since the end of the completion period. There are k phases of service in the system. After the completion of k phases service, the server may take a short vacation or may remain in the system to serve the next unit, which is defined by Bernoulli vacation schedule. Moreover, we assume the server fails according to a Poisson process whose repair time follows a general distribution. In final, we analyze the system characteristics for each scheme and obtained the optimal NT threshold to minimize the cost function.