Proof of Monotone Loss Rate of Fluid Priority-Queue with Finite Buffer |
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Authors: | Stephen L Spitler Daniel C Lee |
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Institution: | (1) Department of Electrical Engineering, University of Southern California, 3740 McClintock Avenue, Los Angeles, CA 90089-2565, USA;(2) School of Engineering Science, Simon Fraser University, 8888 University Drive, Burnaby, BC, V5A 1S6, Canada |
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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.
AMS subject classification: 60K25, 68M20 |
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Keywords: | priority queueing monotone loss rate finite buffer fluid queueing system |
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