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

TL;DR

This paper analyzes switched queueing networks under maximum weight policies, demonstrating fluid approximations and multiplicative state space collapse without assuming complete resource pooling.

Contribution

It introduces a fluid model for maximum weight policies in constrained networks and proves state space collapse without requiring resource pooling.

Findings

Fluid model solutions approximate performance processes.

Invariant states solve a network-wide optimization problem.

Proves multiplicative state space collapse under critical load.

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.