Performance analysis of a Geo[X] /GH /1 retrial queue with an unreliable server

This paper discusses a discrete-time Geo[X] /GH /1 retrial queue with an unreliable server. We study the underlying Markov process and derive the generating function of its stationary distribution. A set of generating functions regarding the orbit and the system size distributions is also derived. Hence, expressions for the main performance characteristics of the system are obtained. Moreover, we prove a stochastic decomposition property regarding the distribution of the system size. Hence, a measure of the proximity between the stationary distributions for this queueing system and its corresponding standard system is derived. Finally, a set of numerical examples is presented to illustrate the effect of different system parameters on the main performance characteristics.