Discrete-time GeoX/G/1 queue with preemptive resume priority

This paper considers a GeoX/G/1 queue with preemptive resume priority. Service times of messages of each priority class are i.i.d. according to a general distribution function that may differ between two classes. The analysis is based on the generating function technique and the supplementary variable method. We derive the joint system occupancy distributions at various observation instant and provide the analysis of the system time and the busy period.