A semi-partitioned approach for parallel real-time scheduling

In this paper, we consider the problem of scheduling periodic Multi-Phase Multi-Thread tasks on a set of m identical processors with Earliest Deadline First (EDF) scheduling. Each periodic task is defined by a sequence of phases with offsets that can be possibly parallelized. We use a portioned semi-partitioned approach with migrations at local deadlines assigned to each phase. We extend this approach to take into account phase parallelism. The phase parallelism we consider is an extension of the popular job parallelism. A phase, if parallelizable, can be decomposed into parallel threads run on a configurable number of processors. We only require simultaneous execution of threads inside a window equal to the local deadline of their associated phase. To decide on the schedulability of a Multi-Phase Multi-Thread task, we extend the popular uniprocessor EDF feasibility condition for periodic asynchronous tasks. We propose two new schedulability tests for EDF that significantly improve the well known Leung and Merill feasibility test based on the feasibility interval [Omin, Omax + 2P], where Omin and Omax are respectively the minimum and maximum phase offsets and P the least common multiple of the task periods. The first schedulability test is used when an EDF simulation is needed and gives, by simulation, a 44% gain in simulation speed. The second method provides a sufficient schedulability test with a time interval of length P based on the demand bound function. Finally, we study three local deadline assignment heuristics assigned to parallelizable phases. We compare and analyze the performances obtained by simulation for those three local deadline assignment heuristics.