Analysis of an M/G/1 queue with N-policy, single vacation, unreliable service station and replaceable repair facility

Abstract

This paper considers an M/G/1 repairable queueing system with N-policy and single vacation, in which the service station is subject to random breakdowns. Once the service station breaks down, it is repaired by a repair facility. Moreover, the repair facility may fail during the repair period which results in repair interruptions. Failed repair facility resumes repair after a random period of time. Applying the renewal process theory and the probability decomposition technique, 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, the rate of occurrence of failures of the repair facility and the stochastic decomposition property of the reliability measures are obtained. Following the construction of the long-run expected cost function per unit time, we numerically determined the optimal threshold N ∗ for minimizing the cost function.