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Sufficient conditions for stability of longest-queue-first scheduling: second-order properties using fluid limits

Part of: Special processes Stochastic processes Operations research and management science

Published online by Cambridge University Press:  01 July 2016

Antonis Dimakis  and
Jean Walrand
Antonis Dimakis*
Affiliation:
University of California, Berkeley
Jean Walrand*
Affiliation:
University of California, Berkeley
*
∗ Postal address: Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA 94720, USA.
∗ Postal address: Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA 94720, USA.
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Abstract

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We consider the stability of the longest-queue-first scheduling policy (LQF), a natural and low-complexity scheduling policy, for a generalized switch model. Unlike that of common scheduling policies, the stability of LQF depends on the variance of the arrival processes in addition to their average intensities. We identify new sufficient conditions for LQF to be throughput optimal for independent, identically distributed arrival processes. Deterministic fluid analogs, proved to be powerful in the analysis of stability in queueing networks, do not adequately characterize the stability of LQF. We combine properties of diffusion-scaled sample path functionals and local fluid limits into a sharper characterization of stability.

Keywords

Generalized switchlongest-queue-first schedulingMaxWeight schedulingthroughput optimalitystabilitylocal poolingfluid limitlocal fluid limitsecond-order condition

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90B15: Network models, stochastic 60G17: Sample path properties
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 38 , Issue 2 , June 2006 , pp. 505 - 521
Copyright
Copyright © Applied Probability Trust 2006 

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