An Optimal Semi-Partitioned Scheduler Assuming Arbitrary Affinity Masks

Modern operating systems allow task migrations to be restricted by specifying per-task processor affinity masks. Such a mask specifies the set of processor cores upon which a task can be scheduled. In this paper, a semi-partitioned scheduler, AM-Red (affinity mask reduction), is presented for scheduling implicit-deadline sporadic tasks with arbitrary affinity masks on an identical multiprocessor. AM-Red is obtained by applying an affinity-mask-reduction method that produces affinities in accordance with those specified, without compromising feasibility, but with only a linear number of migrating tasks. It functions by employing a tunable frame of size |F|. For any choice of |F|, AM-Red is soft-real-time optimal, with tardiness bounded by |F|, but the frequency of task migrations is proportional to |F|. If |F| divides all task periods, then AM-Red is also hard-real-time-optimal (tardiness is zero). AM-Red is the first optimal scheduler proposed for arbitrary affinity masks without future knowledge of all job releases. Experiments are presented that show that AM-Red is implementable with low overhead and yields reasonable tardiness and task-migration frequency.