Partitioned Multiprocessor Fixed-Priority Scheduling of Sporadic Real-Time Tasks

TL;DR

This paper improves the theoretical bounds on fixed-priority partitioned multiprocessor scheduling for sporadic real-time tasks, showing better speedup factors and analyzing the impact of schedulability tests and task deadlines.

Contribution

It introduces improved speedup factors for greedy mapping strategies in fixed-priority scheduling of sporadic tasks, and analyzes the effects of schedulability tests and task deadlines.

Findings

Greedy mapping strategy has a speedup factor of 3 - 1/M for arbitrary deadlines.

Speedup factor improved to 2.84306 for constrained deadlines.

Exact schedulability tests do not improve theoretical speedup bounds for arbitrary fitting strategies.

Abstract

Partitioned multiprocessor scheduling has been widely accepted in academia and industry to statically assign and partition real-time tasks onto identical multiprocessor systems. This paper studies fixed-priority partitioned multiprocessor scheduling for sporadic real-time systems, in which deadline-monotonic scheduling is applied on each processor. Prior to this paper, the best known results are by Fisher, Baruah, and Baker with speedup factors $4-\frac{2}{M}$ and $3-\frac{1}{M}$ for arbitrary-deadline and constrained-deadline sporadic real-time task systems, respectively, where $M$ is the number of processors. We show that a greedy mapping strategy has a speedup factor $3-\frac{1}{M}$ when considering task systems with arbitrary deadlines. Such a factor holds for polynomial-time schedulability tests and exponential-time (exact) schedulability tests. Moreover, we also improve the speedup factor to $2.84306$ when considering constrained-deadline task systems. We also provide tight examples when the fitting strategy in the mapping stage is arbitrary and $M$ is sufficiently large. For both constrained- and arbitrary-deadline task systems, the analytical result surprisingly shows that using exact tests does not gain theoretical benefits (with respect to speedup factors) for an arbitrary fitting strategy.