Output process of retrial queue with two-way communication under low rate of retrials limit condition

In this paper, we consider retrial queue with MAP input and two-way communication. Upon arriving, an incoming call makes the server busy for an exponentially distributed time if it’s idle at the moment. Otherwise, the incoming call goes to the orbit and repeat its request for service after random delay. In its idle time the server also makes an outgoing calls. We use asymptotic analysis method under low rate of retrials limit condition to derive characteristic function of the number of calls in the output flow of the system