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Steady-State Convergence of the Continuous-Time JSQ System with General Distributions in Heavy Traffic

Published: 06 September 2024 Publication History

Abstract

This paper studies the continuous-time join-the-shortestqueue (JSQ) system with general interarrival and service distributions.

References

[1]
M. Bramson. Stability of join the shortest queue networks. The Annals of Applied Probability, 21(4):1568--1625, 2011.
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A. Braverman, J. G. Dai, and M. Miyazawa. Heavy traffic approximation for the stationary distribution of a generalized Jackson network: the BAR approach. Stochastic Systems, 7(1):143--196, 2017.
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A. Braverman, J. G. Dai, and M. Miyazawa. The BAR approach for multiclass queueing networks with SBP service policies. Stochastic Systems, 2024.
[4]
J. G. Dai, P. Glynn, and Y. Xu. Asymptotic product-form steady-state for generalized Jackson networks in multi-scale heavy traffic. arXiv preprint arXiv:2304.01499, 2023.
[5]
J. G. Dai, J. Guang, and Y. Xu. Steady-state convergence of the continuous-time JSQ system with general distributions in heavy traffic. arXiv preprint arXiv:2405.10876, 2024.
[6]
A. Eryilmaz and R. Srikant. Asymptotically tight steady-state queue length bounds implied by drift conditions. Queueing Systems, 72(3--4):311--359, 2012.
[7]
J. Guang, X. Chen, and J. G. Dai. Uniform moment bounds for generalized Jackson networks in multi-scale heavy traffic. arXiv preprint arXiv:2401.14647, 2024.
[8]
D. Hurtado-Lange and S. T. Maguluri. Transform methods for heavy-traffic analysis. Stochastic Systems, 10(4):275--309, 2020.
[9]
X. Zhou and N. Shroff. A note on Stein?s method for heavy-traffic analysis. arXiv preprint arXiv:2003.06454, 2020.

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Published In

cover image ACM SIGMETRICS Performance Evaluation Review
ACM SIGMETRICS Performance Evaluation Review  Volume 52, Issue 2
September 2024
61 pages
DOI:10.1145/3695411
  • Editor:
  • Bo Ji
Issue’s Table of Contents
Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 06 September 2024
Published in SIGMETRICS Volume 52, Issue 2

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