Abstract
In this paper, we consider an M/G/1 queueing system with removable server subject to failure interruptions, where the failure occurs only during operating busy period. More precisely, jobs arrive according to an identical and independent Poisson stream, and are processed with identically and independently distributed general service times. Two kinds of recovery functions for a system failure are analyzed. One is the retry function, the other is the repair function. In the retry model, after a system failure the system undergoes instantly the corrective repair and the interrupted job is processed again after the system becomes as good as new. On the other hand, in the repair model, the minimal-repair is executed for each failure. In the both models, the preventive maintenance is carried out at the termination of the process of a job. In the framework of the N-policy for the M/G/1 queue, we formulate the relevant expected costs under two recovery functions, respectively, and derive the optimal control-limit policies minimizing them.
