Discrete-time GeoX/G/1 que with non-preemptive priority

This paper considers a discrete-time two-class queueing system with non-preemptive priority. Service times of messages of each priority class are i.i.d. according to a general discrete distribution function that may differ between two classes. Using the supplementary variable method and the generating function technique, we derive the joint system occupancy distribution at an arbitrary slot, and also compute the probability distributions for the system time and the busy period.