An Optimal Semi-Partitioned Scheduler Assuming Arbitrary Affinity Masks∗

Modern operating systems like Linux allow task migrations to be restricted by specifying pertask 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 F 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 assess its practical viability. 1998 ACM Subject Classification C.1.2 [Processor Architectures]: Multiple Data Stream Architectures (Multiprocessors); C.3 [Special-Purpose and Application-Based Systems]— real-time and embedded systems; D.4.1 [Operating Systems]: Process Management—scheduling; D.4.7 [Operating Systems]: Organization and Design—real-time systems and embedded systems; J.7 [Computer Applications]: Computers in Other Systems—real time