Geo[X]/G/1 retrial queue with non-preemptive priority

A retrial queue accepting two types of customers with batch arrival and non-preemptive priority is studied. It is assumed that time is slotted and the service times follow arbitrary distributions. We derive the joint generating function for the number of individual customers in the priority queue and in the retrial group at an arbitrary time by the supplementary variable technique. Then the mean number of customers in the system is obtained by these results. Furthermore, we consider the relation between the discrete-time retrial queue and the continuous-time one. Finally, we present numerical examples.