  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].
