Refined Tail Asymptotic Properties for the $M^X/G/1$ Retrial Queue
Abstract
In the literature, retrial queues with batch arrivals and heavy service times have been studied and the so-called equivalence theorem has been established under the condition that the service time is heavier than the batch size. The equivalence theorem provides the distribution (or tail) equivalence between the total number of customers in the system for the retrial queue and the total number of customers in the corresponding standard (non-retrial) queue. In this paper, under the assumption of regularly varying tails, we eliminate this condition by allowing that the service time can be either heavier or lighter than the batch size. The main contribution made in this paper is an asymptotic characterization of the difference between two tail probabilities: the probability of the total number of customers in the system for the retrial queue and the probability of the total number of customers in the corresponding standard (non-retrial) queue. The equivalence theorem by allowing a heavier batch size is another contribution in this paper.
Keywords
Cite
@article{arxiv.1801.02525,
title = {Refined Tail Asymptotic Properties for the $M^X/G/1$ Retrial Queue},
author = {Bin Liu and Jie Min and Yiqiang Q. Zhao},
journal= {arXiv preprint arXiv:1801.02525},
year = {2020}
}
Comments
25pages. In this third version, we removed Lemma 6.1 (in the second version), and further updated Lemma 6.2 in the second version (presented now as Lemma 6.1). We did more updates on the most updated version!