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

Authors:
Stephen L. Spitler;Daniel C. Lee
Affiliations:
Department of Electrical Engineering, University of Southern California, Los Angeles, USA 90089-2565;School of Engineering Science, Simon Fraser University, Burnaby, Canada V5A 1S6
Venue:
Queueing Systems: Theory and Applications
Year:
2005

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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.