We consider an
retrial queue with two types of calls: incoming calls (regular one’s) and outgoing calls (which are made when the server is free). A blocked incoming call joins the orbit and retries for service after some random time while an outgoing call is made by the server after some random idle time. We assume that incoming and outgoing calls have random amount of works which are processed by the server at two distinct speeds. This assumption is suitable for evaluating the power consumption that depends on the speed of the server. We obtain the joint probability distribution of the server state and the number of requests in the orbit in terms of Laplace and
- transforms. From these transforms, we obtain some performance metrics of interest such as the probability that the server is idle or busy by an incoming (outgoing) call and the mean number of requests in orbit. We propose two optimization problems to find the optimal outgoing call rate and service speeds.