Switched networks with maximum weight policies: Fluid approximation and multiplicative state space collapse

• Main Authors: Shah, Devavrat (Contributor), Wischik, Damon (Author)
• Other Authors: Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science (Contributor)
• Format: Article
• Language: English
• Published: Institute of Mathematical Statistics, 2012-09-28T15:23:22Z.
• Subjects: Article
• Online Access: Get fulltext

 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.