A Geo/G/1 retrial queueing system with priority services

Abstract

This paper considers a discrete-time retrial queueing system in which the arriving customers can decide to go directly to the server expelling out of the system the customer that is currently being served, if any, or to join the orbit in accordance with a FCFS discipline. An extensive analysis of the model has been carried out, and using a generating functions approach, the distributions of the number of customers in the orbit and in the system with its respective means are obtained. The stochastic decomposition law has been derived, and, as an application, bounds for the proximity between the steady-state distributions for the considered queueing system and its corresponding standard system are obtained. Also, recursive formulae for calculating the steady-state distributions of the orbit and system size have been developed. Besides, we prove that the M/G/1 retrial queue with service interruptions can be approximated by the corresponding discrete-time system. The generating function of the sojourn time of a customer in the orbit and in the system have also been provided. Finally, some numerical examples to illustrate the effect of the parameters on several performance characteristics and a section of conclusions commenting the main research contributions of this paper are presented.