Proof of the conjecture on the stability of a multi-class retrial queue with constant retrial rates

Bara Kim, Jeongsim Kim

Research output: Contribution to journalArticlepeer-review

Abstract

This study considers a multi-class single-server retrial queue with constant retrial rates in which service times are generally distributed with different service rates for each class. Avrachenkov (Queueing Systems 100:177–179, 2022) formulated the conjecture on the stability of this queueing system. We completely resolve the conjecture by using the fluid limit approach.

Original languageEnglish
Pages (from-to)175-185
Number of pages11
JournalQueueing Systems
Volume104
Issue number3-4
DOIs
Publication statusPublished - 2023 Aug

Bibliographical note

Funding Information:
We are grateful to the reviewers for their valuable comments and suggestions. B. Kim’s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1A2B5B01001864). J. Kim’s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1F1A1A01065568).

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Keywords

  • Constant retrial rate
  • Fluid limit
  • Retrial queue
  • Stability

ASJC Scopus subject areas

  • Statistics and Probability
  • Computer Science Applications
  • Management Science and Operations Research
  • Computational Theory and Mathematics

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