Optimal Control for a kind of Repairable Queuing System with Regular Repairman Vacation

This article studies the problem about optimizing replacement policy for a repairable queuing system where the repairman takes multiple vacations. We assume that the service station after a repair is not “as good as new” and the duration of repairman vacation is either random variational or regular constant. We optimize the number N of the customers that have been served at the service station to achieve the maximum long-run profit per unit time. Both working time and repair time are assumed to be geometric processes. The explicit expressions of the objective function is derived in this article, and a detailed and in-depth discussion is offered.