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Three-level modeling of a speed-scaling supercomputer

Author

Listed:
  • Alexander Rumyantsev

    (Karelian Research Center of RAS
    Petrozavodsk State University)

  • Robert Basmadjian

    (TU Clausthal)

  • Sergey Astafiev

    (Karelian Research Center of RAS
    Petrozavodsk State University)

  • Alexander Golovin

    (Karelian Research Center of RAS
    Petrozavodsk State University)

Abstract

In this paper we study a simultaneous service multiserver system which we call speed-scaling supercomputer, where speed-scaling is used to address the performance/power demand tradeoff. We treat the system by three-level modeling approach, using matrix-analytic method, generalized semi-Markov processes and small-scale technical system as the three levels of modeling. An explicit form of stability condition is obtained for a two-server system with heterogeneous customer classes. Regenerative estimation approach is used for confidence estimation of performance measures both in simulation and technical models. We demonstrate the potential of the three-level modeling approach on a relatively sophisticated and interesting model by performing extensive experiments.

Suggested Citation

  • Alexander Rumyantsev & Robert Basmadjian & Sergey Astafiev & Alexander Golovin, 2023. "Three-level modeling of a speed-scaling supercomputer," Annals of Operations Research, Springer, vol. 331(2), pages 649-677, December.
    • Handle: RePEc:spr:annopr:v:331:y:2023:i:2:d:10.1007_s10479-022-04830-0
    DOI: 10.1007/s10479-022-04830-0
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    References listed on IDEAS

    as
    1. Mor Harchol-Balter, 2022. "The multiserver job queueing model," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 201-203, April.
    2. 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.
    3. 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.
    4. Richard V. Evans, 1964. "Queuing when Jobs Require Several Services which Need Not be Sequenced," Management Science, INFORMS, vol. 10(2), pages 298-315, January.
    5. Peter W. Glynn & Philip Heidelberger, 1992. "Experiments with Initial Transient Deletion for Parallel, Replicated Steady-State Simulations," Management Science, INFORMS, vol. 38(3), pages 400-418, March.
    6. Percy H. Brill & Linda Green, 1984. "Queues in Which Customers Receive Simultaneous Service from a Random Number of Servers: A System Point Approach," Management Science, INFORMS, vol. 30(1), pages 51-68, January.
    7. Robert Basmadjian, 2019. "Flexibility-Based Energy and Demand Management in Data Centers: A Case Study for Cloud Computing," Energies, MDPI, vol. 12(17), pages 1-22, August.
    Full references (including those not matched with items on IDEAS)

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