analysis of an m/g/1 queue with multiple vacations, n-policy, unreliable service station and repair facility failures

this paper studies an m/g/1 repairable queueing system with multiple vacations and n-policy, in which the service station is subject to occasional random breakdowns. when the service station breaks down, it is repaired by a repair facility. moreover, the repair facility may fail during the repair period of the service station. the failed repair facility resumes repair after completion of its replacement. under these assumptions, applying a simple method, the probability that the service station is broken, the rate of occurrence of breakdowns of the service station, the probability that the repair facility is being replaced and the rate of occurrence of failures of the repair facility along with other performance measures are obtained. following the construction of the long-run expected cost function per unit time, the direct search method is implemented for determining the optimum threshold n* that minimises the cost function.