Analysis of the waiting time distribution in M/G/1 retrial queues with two way communication

We consider an M/G/1 retrial queue in which there are two types of calls: ingoing calls made by regular customers and outgoing calls made by the server in idle time. The service times of ingoing calls and outgoing calls have different arbitrary distributions. In this paper, we are interested in the analysis of the waiting time distribution. We obtain an equation for the joint transform of the number of ingoing calls in the orbit and the waiting time of an arbitrary ingoing call. Using this result, we can obtain the moments of the waiting time distribution of an arbitrary ingoing call.