Discrete-time Geo1, Geo2/G/1 retrial queueing systems with two types of calls

We consider a discrete-time Geo1, Geo2/G/1 retrial queue with two types of calls. When arriving calls are blocked due to the server being busy, Type I calls are queued in the priority queue with infinite capacity whereas, Type II calls enter the retrial group in order to try service again after a random amount of time. We find the joint generating function of the number of calls in the priority queue and the number of calls in the retrial group in a closed form. It is shown that our results are consistent with those already known for special cases.