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This article aims to present the steady-state analysis in finite-buffer M/G/1 queues with starting failures under a randomized control of N-policy. When the system empties, the server is turned off. If the system size reaches the threshold N, the server is turned on with probability p or turned off with probability 1 − p. The server needs a startup time before providing service. If the server is started successfully (with probability θ), customers are served immediately. When the server is started unsuccessfully, he is started again. It is assumed that the restart is always successful. Using the supplementary variable method, we obtain the stationary distribution of the number of customers in the system. We develop a number of performance measures. A cost model is constructed, and we then determine numerical values of the optimal service rate to minimize the average cost per unit time. Finally, numerical examples are provided to show the effects of system parameters on performance measures and the optimal service rate. [ABSTRACT FROM AUTHOR]

In this paper, we propose a machine repair problem with constant retrial policy, wherein if a failed machine finds the repairman busy upon arrival, it enters into an orbit. The machines in the orbit form a single waiting line, and only the one at the head of the orbit repeats its request for repair. The failure times of operating machines and the repair times of failed machines follow exponential distributions. It is assumed that retrial times are generally distributed. We used the supplementary variable technique to obtain explicit expressions for the steady-state probabilities of the number of failed machines in the orbit. We performed sensitivity analysis of the machine availability and operative efficiency with respect to system parameters and the number of machines in operation. The analysis of the busy period and the waiting time were also presented. Finally, we developed a cost model and formulated a cost minimization problem. [ABSTRACT FROM AUTHOR]