Sharp utilization thresholds for some real-time scheduling problems

TL;DR

This paper investigates sharp utilization thresholds in real-time scheduling policies, showing that workload below a certain threshold is almost surely schedulable, providing a simple test and insights for balancing power and deadlines.

Contribution

It introduces the concept of sharp utilization thresholds for real-time scheduling, extending understanding to both periodic and aperiodic tasks, and offers practical schedulability tests.

Findings

Threshold behavior is sharp for most policies.

Workload below threshold is almost surely schedulable.

Application to power management in web servers.

Abstract

Scheduling policies for real-time systems exhibit threshold behavior that is related to the utilization of the task set they schedule, and in some cases this threshold is sharp. For the rate monotonic scheduling policy, we show that periodic workload with utilization less than a threshold $U_{RM}^{*}$ can be scheduled almost surely and that all workload with utilization greater than $U_{RM}^{*}$ is almost surely not schedulable. We study such sharp threshold behavior in the context of processor scheduling using static task priorities, not only for periodic real-time tasks but for aperiodic real-time tasks as well. The notion of a utilization threshold provides a simple schedulability test for most real-time applications. These results improve our understanding of scheduling policies and provide an interesting characterization of the typical behavior of policies. The threshold is sharp (small deviations around the threshold cause schedulability, as a property, to appear or disappear) for most policies; this is a happy consequence that can be used to address the limitations of existing utilization-based tests for schedulability. We demonstrate the use of such an approach for balancing power consumption with the need to meet deadlines in web servers.