An Improved Speedup Factor for Sporadic Tasks with Constrained Deadlines under Dynamic Priority Scheduling

TL;DR

This paper improves the theoretical speedup factor bounds for partitioned-EDF scheduling of sporadic tasks with constrained deadlines on multiprocessors, bringing it closer to the lower bound.

Contribution

It introduces a novel discretization and regularization method that refines the speedup factor analysis for partitioned-EDF under constrained deadlines.

Findings

Speedup factor improved to 2.5556-1/m for constrained deadlines.

Close to the asymptotic lower bound of 2.5 for speedup factor.

Advances the theoretical understanding of schedulability analysis.

Abstract

Schedulability is a fundamental problem in real-time scheduling, but it has to be approximated due to the intrinsic computational hardness. As the most popular algorithm for deciding schedulability on multiprocess platforms, the speedup factor of partitioned-EDF is challenging to analyze and is far from been determined. Partitioned-EDF was first proposed in 2005 by Barush and Fisher [1], and was shown to have a speedup factor at most 3-1/m, meaning that if the input of sporadic tasks is feasible on m processors with speed one, partitioned-EDF will always return succeeded on m processors with speed 3-1/m. In 2011, this upper bound was improved to 2.6322-1/m by Chen and Chakraborty [2], and no more improvements have appeared ever since then. In this paper, we develop a novel method to discretize and regularize sporadic tasks, which enables us to improve, in the case of constrained deadlines, the speedup factor of partitioned-EDF to 2.5556-1/m, very close to the asymptotic lower bound 2.5 in [2].