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Proof of Monotone Loss Rate of Fluid Priority-Queue with Finite Buffer

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Abstract

This paper studies a fluid queueing system that has a single server, a single finite buffer, and which applies a strict priority discipline to multiple arriving streams of different classes. The arriving streams are modeled by statistically independent, identically distributed random processes. A proof is presented for the highly intuitive result that, in such a queueing system, a higher priority class stream has a lower average fluid loss rate than a lower priority class stream. The proof exploits the fact that for a work-conserving queue, the fluid loss rate for a given class is invariant of what queueing discipline is applied to all arriving fluid of this particular class.

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Authors and Affiliations

  1. Department of Electrical Engineering, University of Southern California, 3740 McClintock Avenue, Los Angeles, CA, 90089-2565, USA

    Stephen L. Spitler

  2. School of Engineering Science, Simon Fraser University, 8888 University Drive, Burnaby, BC, V5A 1S6, Canada

    Daniel C. Lee

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  1. Stephen L. Spitler
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Correspondence to Stephen L. Spitler.

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AMS subject classification: 60K25, 68M20

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Spitler, S.L., Lee, D.C. Proof of Monotone Loss Rate of Fluid Priority-Queue with Finite Buffer. Queueing Syst 51, 77–87 (2005). https://doi.org/10.1007/s11134-005-3749-2

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  • DOI: https://doi.org/10.1007/s11134-005-3749-2

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