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Stability of a Two-Pool N-Model with Preemptive-Resume Priority

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Distributed Computer and Communication Networks (DCCN 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 919))

Abstract

The regenerative methodology is applied to find stability conditions of the so-called N-model which consists of two pools of the interacting servers with two classes of external customers following a renewal input. Service times are assumed to be pool-dependent and, in each pool, are i.i.d. with a general distribution. If the queue size in pool 1 exceeds a given threshold, then a class-1 customer jumps to pool 2 and becomes class-(1,2) customer with the preemptive-resume priority. The stability analysis of this model has been developed in [5] by a modified fluid approach. In addition to the results obtained in work [5], we find the conditions when the 1st pool is stable solely, and when the 1st pool is stable, while the 2nd pool is unstable.

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Acknowledgement

The study was carried out under state order to the Karelian Research Centre of the Russian Academy of Sciences (Institute of Applied Mathematical Research KRC RAS). This research is partially supported by Russian Foundation for Basic Research, projects 18-07-00147, 18-07-00156.

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Authors and Affiliations

  1. Institute of Applied Mathematical Research of the Karelian Research Centre of the Russian Academy of Sciences, Pushkinskaya st. 11, Petrozavodsk, Russia

    Evsey Morozov

  2. Petrozavodsk State University, Lenin str. 33, Petrozavodsk, Russia

    Evsey Morozov

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  1. Evsey Morozov
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Correspondence to Evsey Morozov .

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Editors and Affiliations

  1. V.A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    Vladimir M. Vishnevskiy

  2. V.A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    Dmitry V. Kozyrev

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Morozov, E. (2018). Stability of a Two-Pool N-Model with Preemptive-Resume Priority. In: Vishnevskiy, V., Kozyrev, D. (eds) Distributed Computer and Communication Networks. DCCN 2018. Communications in Computer and Information Science, vol 919. Springer, Cham. https://doi.org/10.1007/978-3-319-99447-5_34

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  • DOI: https://doi.org/10.1007/978-3-319-99447-5_34

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-99446-8

  • Online ISBN: 978-3-319-99447-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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