A discrete-time Geo[X]/G/1 retrial queue with general retrial time and M-additional options for service

This paper concerns a discrete time Geo^[X]/G/1 retrial queue with general retrial time in which all the arriving customers require first essential service with probability ${\alpha }_0$ while only some of them demand one of other optional services: type − r (r = 1, 2, 3,…M) service with probability ${\alpha }_r$ . The system state distribution, the orbit size and the system size distributions are obtained in terms of generating functions. The stochastic decomposition law holds for the proposed model. Performance measures of the system in steady state are obtained. Finally, some numerical illustrations are presented to justify the influence of parameters on several performance characteristics.