Mathematics – Probability
Scientific paper
2010-04-12
Annals of Applied Probability 2012, Vol. 22, No. 1, 70-127
Mathematics
Probability
Published in at http://dx.doi.org/10.1214/11-AAP759 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst
Scientific paper
10.1214/11-AAP759
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.
Shah Devavrat
Wischik Damon
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