Bounding the Response Time of DAG Tasks Using Long Paths

TL;DR

This paper introduces a new response time bound for DAG tasks that considers multiple long paths, improving upon Graham's classic bound and enhancing schedulability analysis for complex task systems.

Contribution

The paper proposes a novel response time bound using multiple long paths in DAGs, outperforming Graham's traditional bound and extending to multi-DAG systems.

Findings

New bound outperforms Graham's bound in theory

Empirical results show improved schedulability analysis

Extension to multi-DAG systems enhances practical applicability

Abstract

In 1969, Graham developed a well-known response time bound for a DAG task using the total workload and the longest path of the DAG, which has been widely applied to solve many scheduling and analysis problems of DAG-based task systems. This paper presents a new response time bound for a DAG task using the total workload and the lengths of multiple long paths of the DAG, instead of the longest path in Graham's bound. Our new bound theoretically dominates and empirically outperforms Graham's bound. We further extend the proposed approach to multi-DAG task systems. Our schedulability test theoretically dominates federated scheduling and outperforms the state-of-the-art by a considerable margin.