Optimal Scheduling and Handling Potential Overload

We give a complete characterization of optimal online schedulers for preemptive hard-real-time tasks on one processor. We then use this characterization to investigate the problem of guaranteeing all critical tasks in the presence of potential overload, while at the same time guaranteeing all tasks when the load factor is below a certain value. In order to make any such guarantee, it is necessary to have an a priori bound on the load factor due to critical tasks. Given a critical load factor bound , we give a necessary and suucient condition under which a partial schedule is-critical, meaning that there is no longer a guarantee that all critical tasks, up to a critical load factor of , will meet their deadlines if overload occurs. We show that no optimal online algorithm can be guaranteed to avoid producing a-critical schedule once the load factor exceeds 1 ? 2. We then show that no optimal online algorithm produces a-critical schedule as long as the system load factor is at most 1 ? 2. Using these facts, we construct an eecient scheduling algorithm that, under the assumption that the critical load factor never exceeds , guarantees all critical tasks under any load and guarantees all tasks as long as the load factor does not exceed 1 ? 2 .