Algorithms and complexity for periodic real-time scheduling

Abstract

We investigate the preemptive scheduling of periodic tasks with hard deadlines. We show that, even in the uniprocessor case, no polynomial time algorithm can test the feasibility of a task system within a constant speedup bound, unless P = NP. This result contrasts with recent results for sporadic task systems. For two special cases, synchronous task systems and systems with a constant number of different task types, we provide the first polynomial time constant-speedup feasibility tests for multiprocessor platforms. Furthermore, we show that the problem of testing feasibility is coNP-hard for synchronous multiprocessor task systems. The complexity of some of these problems has been open for a long time. We also propose a profit maximization variant of the feasibility problem, where every task has a non-negative profit, and the goal is to find a subset of tasks that can be scheduled feasibly with maximum profit. We give the first constant-speed, constant-approximation algorithm for the case of synchronous task systems, together with related hardness results. Copyright © by SIAM.