Abstract: “We consider an MX/G/1 queuing system with breakdown and repairs, where batches of customers are assumed to arrive in the system according to a compound poisson process. While the server is being repaired, the customer in service either remains the service position or enters a service orbit and keeps returning, after repair the server must wait for the customer to return. The server is not allowed to accepte new customers until the customer in service leaves the system. We find a stability condition for this system. In the steady state the joint distribution of the server state and queue length is obtained, and some performance mesures of the system, such as the mean number of customers in the retrial queue and waiting time, and some numerical results are presented to illustrate the effect of the system parameters on the developed performance measures.”

Keywords: batch arrival, break down, repair.