Two-Way Communication M/M/1/ /N Retrial Queue

We consider in this paper retrial queue with one server that serves a finite number of customers, each one producing a Poisson flow of incoming calls. In addition, after some exponentially distributed idle time the server makes outgoing calls of two types - to the customers in orbit and to the customers outside it. The outgoing calls of both types follow the same exponential distribution, different from the exponential service time distribution of the incoming calls. We derive formulas for computing the steady state distribution of the system state as well as formulas expressing the main performance macro characteristics in terms of the server utilization. Numerical examples are presented.