Limitations Concerning On-Line Scheduling Algorithms for Overloaded Real-Time Systems

Abstract

With respect to on-line scheduling algorithms that must direct the service of sporadic task requests we quantify the benefit of possessing knowledge concerning the timing of future events. Consider the problem of preemptively scheduling sporadic task requests in a uniprocessor environment. If a task request is successfully scheduled to completion, a value equal to the request’s execution time is obtained; otherwise a value of zero is obtained. We prove that no on-line scheduling algorithm can guarantee a cumulative value greater than (√2—1) times the value obtainable by a clairvoyant scheduler, i.e., we prove a performance guarantee limitation of 41.4%. Over intervals where the loading factor does not exceed one the performance guarantee limitation is 100%. As the loading factor exceeds one we show that the performance guarantee limitation immediately drops to 61.8%. and as the loading factor increases from one to two, we show that the performance guarantee limitation falls from 61.8%; to 41.4%. Beyond two the performance guarantee limitation remains at 41.4%.