STABILITY CONDITION FOR A SINGLE-SERVER RETRIAL QUEUE

A single-server retrial queue consists of a primary queue, an orbit an d a single server. Assume the primary queue capacity is 1 and the orbi t capacity is infinite. Customers can arrive at the primary queue eith er from outside the system or from the orbit. If the server is busy, t he arriving customer joins the orbit and conducts a retrial later. Oth erwise, he receives service and leaves the system. We investigate the stability condition for a single-server retrial queue. Let lambda be t he arrival rate and 1/mu be the mean service time. It has been proved that lambda/mu < 1 is a sufficient stability condition for the M/G/1/1 retrial queue with exponential retrial times. We give a counterexampl e to show that this stability condition is not valid for general singl e-server retrial queues. Next we show that lambda/mu < 1 is a sufficie nt stability condition for the stability of a single-server retrial qu eue when the interarrival times and retrial times are finite mixtures of Erlangs.