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Assessing an intuitive condition for stability under a range of traffic conditions via a generalised Lu-Kumar network

Author

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  • Kevin D. Glazebrook
  • José Niño-Mora

Abstract

We argue the importance both of developing simple sufficient conditions for the stability of general multiclass queueing networks and also of assessing such conditions under a range of assumptions on the weight of the traffic flowing between service stations. To achieve the former, we review a peak-rate stability condition and extend its range of application and for the latter, we introduce a generalisation of the Lu-Kumar network on which the stability condition may be tested for a range of traffic configurations. The peak-rate condition is close to exact when the between-station traffic is light, but degrades as this traffic increases.

Suggested Citation

  • Kevin D. Glazebrook & José Niño-Mora, 1997. "Assessing an intuitive condition for stability under a range of traffic conditions via a generalised Lu-Kumar network," Economics Working Papers 429, Department of Economics and Business, Universitat Pompeu Fabra, revised Jan 2000.
    • Handle: RePEc:upf:upfgen:429
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    References listed on IDEAS

    as
    1. J. G. Dai & G. Weiss, 1996. "Stability and Instability of Fluid Models for Reentrant Lines," Mathematics of Operations Research, INFORMS, vol. 21(1), pages 115-134, February.
    2. K.D. Glazebrook & J. Niño‐Mora, 1999. "A linear programming approach to stability, optimisationand performance analysis for Markovian multiclassqueueing networks," Annals of Operations Research, Springer, vol. 92(0), pages 1-18, January.
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    Cited by:

    1. I. M. MacPhee & L. J. Müller, 2007. "Stability Criteria for Multi-class Queueing Networks with Re-entrant Lines," Methodology and Computing in Applied Probability, Springer, vol. 9(3), pages 377-388, September.

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    More about this item

    Keywords

    Multiclass queueing networks; stability; fluid model; Lu-Kumar network;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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