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Stability criterion of a multiserver model with simultaneous service

Author

Listed:
  • Alexander Rumyantsev

    (Karelian Research Centre, RAS
    Petrozavodsk State University)

  • Evsey Morozov

    (Karelian Research Centre, RAS
    Petrozavodsk State University)

Abstract

In this paper, we study a multiserver system in which each customer requires a random number of servers simultaneously and a random but identical service time at all occupied servers. This model describes the dynamics of modern high performance clusters. Stability criteria of this system (under exponential assumptions) have been proved earlier for the two-server system only. Using a matrix-analytic approach, we obtain stability criteria of such a system under exponential assumptions and with an arbitrary number of servers.

Suggested Citation

  • Alexander Rumyantsev & Evsey Morozov, 2017. "Stability criterion of a multiserver model with simultaneous service," Annals of Operations Research, Springer, vol. 252(1), pages 29-39, May.
    • Handle: RePEc:spr:annopr:v:252:y:2017:i:1:d:10.1007_s10479-015-1917-2
    DOI: 10.1007/s10479-015-1917-2
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    References listed on IDEAS

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    Cited by:

    1. Isaac Grosof & Mor Harchol-Balter & Alan Scheller-Wolf, 2022. "WCFS: a new framework for analyzing multiserver systems," Queueing Systems: Theory and Applications, Springer, vol. 102(1), pages 143-174, October.
    2. Michael Dreyfuss & Yair Y. Shaki & Uri Yechiali, 2022. "The double-space parking problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(4), pages 1131-1147, December.
    3. Mor Harchol-Balter, 2022. "The multiserver job queueing model," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 201-203, April.
    4. L. G. Afanasyeva, 2020. "Asymptotic Analysis of Queueing Models Based on Synchronization Method," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1417-1438, December.
    5. Mor Harchol-Balter, 2021. "Open problems in queueing theory inspired by datacenter computing," Queueing Systems: Theory and Applications, Springer, vol. 97(1), pages 3-37, February.

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