Algorithms and Complexity for Periodic Real-Time Scheduling

We investigate the preemptive scheduling of pet iodic tasks with lend deadlines We show that, even in the umprocessor case, no polynomial tune algorithm can test the feasibility of a task system within a constant speedup bound, unless P = NP This result contrasts with recent minks 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 tune 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.