Narrowing the speedup factor gap of partitioned EDF

Abstract Schedulability is a fundamental problem in analyzing real-time systems, but it often has to be approximated due to the intrinsic computational hardness. As the most popular polynomial-time and practical algorithm for deciding schedulability on multiprocessor platforms, the speedup factor of Partitioned-EDF is challenging to analyze and is far from being determined. Partitioned-EDF was first proposed in 2005 by Barush and Fisher and was shown to have a speedup factor at most 3 − 1 / m , i.e., if the input set of sporadic tasks is schedulable on m unit-speed processors, partitioned-EDF will always succeed on m processors with speed 3 − 1 / m . For the constrained deadline case where the relative deadline of each task is at most its period, this upper bound was improved to 2.6322 − 1 / m by Chen and Chakraborty in 2011. No improvement has appeared since then. In this paper, we further improve the factor to 2.5556 − 1 / m for both constrained- and arbitrary-deadline cases, which is very close to the lower bound 2.5 − 1 / m [1] . The key ideas are that: we develop a novel method to discretize and regularize sporadic task sets which are schedulable on uniprocessors, and obtain that the ratio (ρ) of the approximate demand bound value to machine capacity is upper bounded by 1.5556 for the arbitrary deadline case, which plays an important role in estimating the speed factor of Partitioned-EDF.