Stability and Cost Optimization in Controlled Random Walks Using Scheduling Fields

TL;DR

This paper introduces a novel scheduling field approach for controlling large queueing networks, ensuring stability and cost efficiency without extensive parameter tuning, and demonstrates its effectiveness through simulations.

Contribution

It develops a new technique for stability in queueing networks using scheduling fields, improving upon the h-MaxWeight framework with direct perturbation implementation.

Findings

Guarantees universal stability in queueing networks.

Achieves higher cost optimization gains in simulations.

Operates effectively without extensive parameter tuning.

Abstract

The control of large queueing networks is a notoriously difficult problem. Recently, an interesting new policy design framework for the control problem called h-MaxWeight has been proposed: h-MaxWeight is a natural generalization of the famous MaxWeight policy where instead of the quadratic any other surrogate value function can be applied. Stability of the policy is then achieved through a perturbation technique. However, stability crucially depends on parameter choice which has to be adapted in simulations. In this paper we use a different technique where the required perturbations can be directly implemented in the weight domain, which we call a scheduling field then. Specifically, we derive the theoretical arsenal that guarantees universal stability while still operating close to the underlying cost criterion. Simulation examples suggest that the new approach to policy synthesis can even provide significantly higher gains irrespective of any further assumptions on the network model or parameter choice.