Performance analysis of discrete-time GeoX/G/1 retrial queue with various vacation policies and impatient customers

Abstract

This paper studies the behavior of a batch arrival single server retrial queueing model under three different vacation policies. Three types of vacation policies, single vacation, multiple vacations, and atmost J-vacations with impatient customers in general retrial times are considered. The probability generating function and marginal generating function of orbit size are obtained in a steady state. The stability condition for each vacation model is derived. Performance measures such as mean orbit size, mean system size, mean waiting time of a customer, and the probabilities of the server being in different states have also been determined. Based on performance characteristics, a comparative analysis is performed among the three vacations. Numerical illustrations are displayed to establish the consistency of the theory developed.