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Stability Criterion of a General Multiserver Multiclass Queueing System

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Information Sciences and Systems 2014

Abstract

We consider a FCFS multiclass, multiserver queueing system with class-dependent and server-dependent service times. We find stability criterion of such a system using the regenerative approach. The key idea is to consider the basic queue-size process in the saturated system. Then we use renewal theory and a characterization of the limiting remaining regeneration time to establish that the basic regenerative process is positive recurrent. First we prove a sufficient condition, and then show that the system is unstable when this condition is violated. Some generalizations of this system are discussed as well.

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Acknowledgments

The author cordially thanks S. Foss and N. Chernova for their useful comments and pointing out the papers [4, 6, 11]. The research is partially supported by the Program of Strategy Development of Petrozavodsk State University in the framework of the research activity and the Polish project NCN nr 4796/B/T02/2011/40 “Models for transmissions dynamics, congestion control and quality of service in Internet”.

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Authors and Affiliations

  1. Institute of Applied Mathematical Research, Karelian Research Center and Petrozavodsk State University, 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. Polish Academy of Sciences, Gliwice, Poland

    Tadeusz Czachórski

  2. Imperial College London, London, United Kingdom

    Erol Gelenbe

  3. Imperial College London, London, United Kingdom

    Ricardo Lent

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© 2014 Springer International Publishing Switzerland

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Morozov, E. (2014). Stability Criterion of a General Multiserver Multiclass Queueing System. In: Czachórski, T., Gelenbe, E., Lent, R. (eds) Information Sciences and Systems 2014. Springer, Cham. https://doi.org/10.1007/978-3-319-09465-6_24

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  • DOI: https://doi.org/10.1007/978-3-319-09465-6_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09464-9

  • Online ISBN: 978-3-319-09465-6

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