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Volume 10
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10.3390/math10152799
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Article

Tail Asymptotics for a Retrial Queue with Bernoulli Schedule

by
Bin Liu
1 and
Yiqiang Q. Zhao
2,*
1
School of Mathematics & Physics, Anhui Jianzhu University, Hefei 230601, China
2
School of Mathematics and Statistics, Carleton University, Ottawa, ON K1S 5B6, Canada
*
Author to whom correspondence should be addressed.
Mathematics 2022, 10(15), 2799; https://doi.org/10.3390/math10152799
Submission received: 8 July 2022 / Revised: 2 August 2022 / Accepted: 5 August 2022 / Published: 7 August 2022
(This article belongs to the Special Issue Advances in Queueing Theory)
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Abstract

In this paper, we study the asymptotic behaviour of the tail probability of the number of customers in the steady-state M/G/1 retrial queue with Bernoulli schedule, under the assumption that the service time distribution has a regularly varying tail. Detailed tail asymptotic properties are obtained for the conditional probability of the number of customers in the (priority) queue and orbit, respectively, in terms of the recently proposed exhaustive stochastic decomposition approach. Numerical examples are presented to show the impacts of system parameters on the tail asymptotic probabilities.
Keywords: M/G/1 retrial queue; Bernoulli schedule; number of customers; asymptotic tail probability; regularly varying distribution M/G/1 retrial queue; Bernoulli schedule; number of customers; asymptotic tail probability; regularly varying distribution

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MDPI and ACS Style

Liu, B.; Zhao, Y.Q. Tail Asymptotics for a Retrial Queue with Bernoulli Schedule. Mathematics 2022, 10, 2799. https://doi.org/10.3390/math10152799

AMA Style

Liu B, Zhao YQ. Tail Asymptotics for a Retrial Queue with Bernoulli Schedule. Mathematics. 2022; 10(15):2799. https://doi.org/10.3390/math10152799

Chicago/Turabian Style

Liu, Bin, and Yiqiang Q. Zhao. 2022. "Tail Asymptotics for a Retrial Queue with Bernoulli Schedule" Mathematics 10, no. 15: 2799. https://doi.org/10.3390/math10152799

APA Style

Liu, B., & Zhao, Y. Q. (2022). Tail Asymptotics for a Retrial Queue with Bernoulli Schedule. Mathematics, 10(15), 2799. https://doi.org/10.3390/math10152799

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