Partitioned Feasibility Tests For Sporadic Tasks On Heterogeneous Machines

In this paper we consider feasibility tests for partitioned scheduling sporadic tasks on a set of heterogeneous machines with different speeds. Previously a 3-approximate feasibility test was known. The feasibility test is a natural, fast and efficient algorithm which greedily assigns the tasks to machines and uses Earliest-Deadline-First (EDF) on each machine. The algorithm is 3-approximate even when compared against any schedule which need not be partitioned and therefore additionally bounds the loss due to using a partitioned scheduler. In our work, we consider the case where the adversary is required to be partitioned. We show that this natural algorithm has an improved approximate feasibility factor of 2. Building on our techniques, we further improve on the best known approximate algorithm when the adversary is partition and show the algorithm achieves a ratio better than 3. In particular, we show it is 2.98 approximate.We then consider the case where the partitioned scheduler is required to use Rate-Monotonic-Scheduling (RMS) on each of the machines. Previously, it was known that this algorithm is 3.41-approximate when compared to a non-partitioned adversary. We improve this to 2.41 when comparing to a partitioned adversary. Further, we build on these ideas to improve the best known result when compared against a partitioned adversary and show the algorithm is a 3.34 approximation.