Unreliable Mx/G/1 Queueing System with Two Types of Repair

Abstract

This paper deals with a Single Server non-Markovian batch arrival queueing system (M^X/G/1) in which the breakdowns occur during busy period, according to a Poison process and the server is sent for repair immediately. The breakdown server is facilitated with two types of repair, according as the customer just being served stays in the service facility (with probability 1-q) to complete the remaining service or joins the head of the queue and opts for a new service (with probability q). Immediately after the server is fixed, the customer waiting for the completion of the remaining service is considered for service if exists, otherwise the customer in the head of the queue is taken for service. Further, it is assumed that the server is as good as new after repair. The expressions for the steady state system size probabilities when the system is in different states and the corresponding expected system size are derived in a closed form.. The results of some particular cases of interest are discussed in order to verify the results. Moreover, some numerical examples are also presented.