This paper studies Optimal NT policies for a two-phase service M/G/1 system with a Bernoulli vacation schedule. This system also covers an unreliable server with a breakdown period and a delaying period. While the server is serving, it may fail and the service channel may be shut for a short intermission. Then the server starts service when the number of the waiting customers approaches threshold value N, or when the waiting time of the leading customers reaches a predetermined time T. If the above policy is utilized, the server resumes its service after a startup time. The server serves the waiting customers in two consecutive phases. After the completion of the two phases of service, the server may take a short vacation or may remain in the system to serve the next unit, which is considered Bernoulli vacation schedule. Moreover, we assume the server fails according to a Poisson process whose repair time follows a general distribution. We obtain the optimal NT threshold to minimize the cost function of the system.

The purpose of this paper is to explore the multiple-server machine interference problem with standby unsuccessful switchover and Bernoulli vacation schedule. Failure times of operating and standby machines are assumed to have exponential distributions and repair times of the failed machines and vacation times of servers are also assumed to have exponential distributions. After the completion of service, the server either goes for a vacation or may continue serving for the next machine. The vacation policy we considered is a single vacation policy. In practice, the switchover may experience a significant failure. The matrix analytical method and recursive method are employed to obtain the steady-state probability vectors, and closed-form expressions of some important system characteristics are obtained. The problem of cost optimization dealt with a number of numerical examples is provided by the Quasi-Newton method, the pattern search method, and the Nelder-Mead simplex direct search method. Expressions of various system characteristics are derived. Sensitivity analysis is performed numerically for system parameters. This paper presents the first time that machine interference problem with unsuccessful switchover for a group of repairable servers with vacations has been obtained, which is quite useful for the decision makers.