Multiprocessor Real-Time Scheduling with Hierarchical Processor Affinities

Many multiprocessor real-time operating systems offer the possibility to restrict the migrations of any task to a specified subset of processors by setting affinity masks. A notion of “strong arbitrary processor affinity scheduling” (strong APA scheduling) has been proposed; this notion avoids schedulability losses due to overly simple implementations of processor affinities. Due to potential overheads, strong APA has not been implemented so far in a real-time operating system. We show that, in the special but highly relevant case of hierarchical processor affinities (HPA), strong APA scheduling can be implemented with a vastly improved runtime complexity. In particular, we present a strong HPA scheduler with a runtime complexity of O(m) per task arrival and O(log n+m²) per task departure, where mis the number of processors and n is the number of tasks, thus improving on the previous bounds of O(m²) and O(mn). The improved runtime algorithms allowed us to implement support for strong hierarchical processor affinities in LITMUSRT. We benchmarked this implementation on a 24-core platform and observed nonnegligible, but still viable runtime overheads. Additionally, in the case of a bilevel affinity hierarchy and when job priorities are based on deadlines, we argue that the performance of our strong HPA scheduler, HPA-EDF, can be related to system optimality in the following way: any collection of jobs that is schedulable (under any policy) on m unit-speed processors subject to hierarchical affinity constraints is correctly scheduled by HPA-EDF on m processors of speed 2.415.