$\text{D}^{\textit{over}}$: An Optimal On-Line Scheduling Algorithm for Overloaded Uniprocessor Real-Time Systems

Abstract

Consider a real-time system in which every task has a value that it obtains only if it completes by its deadline. The problem is to design an on-line scheduling algorithm (i.e., the scheduler has no knowledge of a task until it is released) that maximizes the guaranteed value obtained by the system. When such a system is underloaded (i.e., there exists a schedule for which all tasks meet their deadlines), Dertouzos [Proceedings IFIF Congress, 1974, pp. 807--813] showed that the earliest deadline first algorithm will achieve 100% of the possible value. Locke [Ph. D. thesis, Computer Science Dept., Carnegie-Mellon Univ., Pittsburgh, PA] showed that earliest deadline first performs very badly, however, when the system is overloaded, and he proposed heuristics to deal with overload. This paper presents an optimal on-line scheduling algorithm for overloaded uniprocessor systems. It is optimal in the sense that it gives the best competitive ratio possible relative to an off-line scheduler.