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Stability Analysis of a MAP/M/s Cluster Model by Matrix-Analytic Method

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Computer Performance Engineering (EPEW 2016)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9951))

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Abstract

In this paper, we study the stability conditions of the multiserver system in which each customer requires a random number of servers simultaneously and a random service time, identical at all occupied servers. We call it cluster model since it describes the dynamics of the modern multicore high performance clusters (HPC). Stability criterion of an M/M/s cluster model has been proved by the authors earlier. In this work we, again using the matrix-analytic approach, prove that the stability criterion of a more general MAP/M/s cluster model (with Markov Arrival Process) has the same form as for M/M/s system. We verify by simulation that this criterion (in an appropriate form) allows to delimit stability region of a MAP/PH/s cluster model with phase-type (PH) service time distribution. Finally, we discuss asymptotic results related to accelerated stability verification, as well as to the new method of accelerated regenerative estimation of the performance metrics.

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Acknowledgments

This research is partially supported by Russian Foundation for Basic Research, grants 15-07-02341, 15-07-02354, 15-07-02360, 15-29-07974, 16-07-00622 and the Program of Strategic Development of Petrozavodsk State University. The authors thank Udo Krieger for a few useful comments.

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Authors and Affiliations

  1. Institute of Applied Mathematical Research, Karelian Research Centre of RAS, 11 Pushkinskaya Str., Petrozavodsk, 185910, Russia

    Evsey Morozov & Alexander Rumyantsev

  2. Petrozavodsk State University, Petrozavodsk, Russia

    Evsey Morozov & Alexander Rumyantsev

Authors
  1. Evsey Morozov
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  2. Alexander Rumyantsev
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Correspondence to Alexander Rumyantsev .

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Editors and Affiliations

  1. Ghent University, Gent, Belgium

    Dieter Fiems

  2. University of Florence, Firenze, Italy

    Marco Paolieri

  3. University of the Aegean, Chios, Greece

    Agapios N. Platis

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Morozov, E., Rumyantsev, A. (2016). Stability Analysis of a MAP/M/s Cluster Model by Matrix-Analytic Method. In: Fiems, D., Paolieri, M., Platis, A. (eds) Computer Performance Engineering. EPEW 2016. Lecture Notes in Computer Science(), vol 9951. Springer, Cham. https://doi.org/10.1007/978-3-319-46433-6_5

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  • DOI: https://doi.org/10.1007/978-3-319-46433-6_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-46432-9

  • Online ISBN: 978-3-319-46433-6

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