Controlled Queueing Systems with Recovery Functions

Consider the 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 the identical and independent Poisson stream and are processed with an identical and independent general service distribution. Two kinds of recovery functions from failures are analyzed in this paper. 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 reprocessed 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 and at the termination of the process of a job, the preventive repair is carried out again. In the framework of the T-policy for the M/G/1 queue, we formulate the relevant expected costs under two recovery functions, respectively, and derive the optimal timing strategies minimizing them. In numerical examples, we compare two strategies under respective recovery functions in terms of cost effectiveness and examine the dependence of model parameters in the recovery functions.