Stability and Instability of the MaxWeight Policy

TL;DR

This paper investigates the stability properties of the MaxWeight scheduling policy in switched queueing networks, showing it is not always maximally stable but can be stable under certain conditions or with modifications.

Contribution

It proves that MaxWeight is not generally maximally stable and introduces a weighted version that guarantees stability across broader scenarios.

Findings

MaxWeight is not always maximally stable.

MaxWeight is stable in a restricted setting.

Weighted MaxWeight ensures stability regardless of traffic conditions.

Abstract

Consider a switched queueing network with general routing among its queues. The MaxWeight policy assigns available service by maximizing the objective function $\sum_j Q_j \sigma_j$ among the different feasible service options, where $Q_j$ denotes queue size and $\sigma_j$ denotes the amount of service to be executed at queue $j$. MaxWeight is a greedy policy that does not depend on knowledge of arrival rates and is straightforward to implement. These properties, as well as its simple formulation, suggest MaxWeight as a serious candidate for implementation in the setting of switched queueing networks; MaxWeight has been extensively studied in the context of communication networks. However, a fluid model variant of MaxWeight was shown by Andrews--Zhang (2003) not to be maximally stable. Here, we prove that MaxWeight itself is not in general maximally stable. We also prove MaxWeight is maximally stable in a much more restrictive setting, and that a weighted version of MaxWeight, where the weighting depends on the traffic intensity, is always stable.