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 because of the intrinsic computational hardness. Partitioned earliest deadline first (EDF) is one of the most popular polynomial-time and practical scheduler on multiprocessor platforms, and it was shown to have a speedup factor of at most 2.6322−1/m. This paper further improves the factor to 2.5556−1/m for both the constrained-deadline case and the arbitrary-deadline case, and it is very close to the known (non-tight) lower bound of 2.5−1/m. The key ideas are that we develop a novel method to discretize and regularize sporadic task sets that are schedulable on uniprocessors, and we find that the ratio (ρ) of the approximate demand bound value to the 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.