Abstract
In this paper, we study a geometric process model for M/ M/1 queueing system with a repairable service station. By introducing a supplementary variable, some queueing characteristics of the system and reliability indices of the service station are derived. Then a replacement policy N for the service station by which the service station will be replaced following the Nth failure is applied. An optimal replacement policy N ∗ for minimizing the long-run average cost per unit time for the service station is then determined.
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