Tail asymptotics for a batch service polling system with retrials and nonpersistent customers

Abstract

Perel and Yechiali 2014 [16] considered a multi-queue single-server retrial polling system with batch service of an unlimited size, i.e., the so called “Israeli queue” with retrial, where the system consists of a main queue and an orbit queue, and only the customer at the head of the orbit queue is allowed to try to access the main queue. In this present paper, we aim to give a further study on this queueing model, in which each of the retrial customers in the orbit queue independently repeatedly tries for receiving service, and customers may abandon at the arrival instant from outside or at the departure epoch from the orbit queue. By analysing this model, we find that it is difficult to obtain an explicit closed form solution for the joint stationary probability distribution of the number of retrial customers in the orbit queue and the number of groups in the main queue. Therefore, by making use of the matrix analytic approach and the censoring technique, we derive the tail asymptotics result for the stationary joint probabilities.