Asymptotic Analysis of M/M/1/1 Retrial Queue with Two-Way Communication

In this paper, we consider M/M/1/1 retrial queue where incoming fresh calls arrive at the server according to a Poisson process. Upon arrival, an incoming call either occupies the server if it is idle or joins a virtual waiting room called orbit if the server is busy. From the orbit, incoming calls retry to occupy the server and behaves the same as a fresh incoming call. The server makes an outgoing call. Our contribution is to derive the asymptotics of the number of calls in retrial queue under the conditions that the high rate of making outgoing calls and the low rate of service time of outgoing calls.