A discrete-time Geo/G/1 retrial queue with preemptive resume and collisions

We consider a discrete-time Geo/G/1 retrial queue with preemptive resume, collisions of customers and general retrial times. We analyze the Markov chain underlying the considered queueing system and derive its ergodicity condition. Using generating function technique, the system state distribution as well as the orbit size and the system size distributions are studied. Some interesting and important performance measures are obtained. Besides, the stochastic decomposition property is investigated. Finally, some numerical examples are provided.