| Summary: | 碩士 === 國立中興大學 === 統計學研究所 === 99 === This thesis studies the multiple-vacation M/M/1 machine repair problem with an unreliable repairman. We assume that failure and service times distributions of the machines are exponentially distributed. Once the system is empty, the repairman leaves the system taking a vacation of exponential length. At the end of a vacation, if there is at least one failed machines waiting for service, he must serve the machines immediately until there are no failed machines in the system; otherwise, he will take another vacation. Suppose that breakdown and repair times of the repairman are exponentially distributed. First, we apply a matrix-analytic method to derive the steady-state probabilities, and provide the numerical results of various system performance measures. Next, we construct the expected cost function per machine per unit time. We use the direct search method and the Quasi-Newton method to
determine the optimal values of operating machines, service rate, and vacation rate.
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