Switched networks with maximum weight policies: Fluid approximation and multiplicative state space collapse
Name
Shah-2012-Switched networks with maxim.pdf
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526.33 KB
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Author(s)
Shah, Devavrat
Wischik, Damon
Date Issued
2012
Journal
Annals of Applied Probability
Publisher
Institute of Mathematical Statistics
Citation
Shah, Devavrat, and Damon Wischik. “Switched Networks with Maximum Weight Policies: Fluid Approximation and Multiplicative State Space Collapse.” The Annals of Applied Probability 22.1 (2012): 70–127. 2012 © Institute of Mathematical Statistics
Version
Final published version
Abstract
We consider a queueing network in which there are constraints on which queues may be served simultaneously; such networks may be used to model input-queued switches and wireless networks. The scheduling policy for such a network specifies which queues to serve at any point in time. We consider a family of scheduling policies, related to the maximum-weight policy of Tassiulas and Ephremides [IEEE Trans. Automat. Control 37 (1992) 1936–1948], for single-hop and multihop networks. We specify a fluid model and show that fluid-scaled performance processes can be approximated by fluid model solutions. We study the behavior of fluid model solutions under critical load, and characterize invariant states as those states which solve a certain network-wide optimization problem. We use fluid model results to prove multiplicative state space collapse. A notable feature of our results is that they do not assume complete resource pooling.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1214/11-aap759
