Refined tail asymptotic properties for the $$M^X/G/1$$ M X / G / 1 retrial queue

Bin Liu (), Jie Min () and Yiqiang Q. Zhao ()
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Bin Liu: Anhui Jianzhu University
Jie Min: Anhui Jianzhu University
Yiqiang Q. Zhao: Carleton University

Queueing Systems: Theory and Applications, 2023, vol. 104, issue 1, No 5, 65-105

Abstract: Abstract In the literature, retrial queues with batch arrivals and heavy-tailed 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 $$M^X/G/1$$ M X / G / 1 retrial queue and the probability of the total number of customers in the corresponding standard (non-retrial) queue.

Keywords: $$M^X/G/1$$ M X / G / 1 retrial queue; Number of customers; Tail asymptotics; Regularly varying distribution; 60K25; 60E20; 60G50 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11134-023-09874-y

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