Optimal Scheduling of Periodic Tasks in Soft Real-Time Systems Using Language Measure

In soft real-time systems, if a task completes after its deadline, its utility degrades gradually as its completion is delayed. So it is necessary to schedule tasks in consideration of the degradation. In this paper, we model execution of each task by a timed discrete event system (DES) and introduce a signed language measure proposed by Wang and Ray to evaluate performance of the completed tasks quantitatively. To model behaviors of the multi-tasking real-time systems, interactions among active tasks are described by the composition of their timed DES models. We propose a design method of the optimal scheduler using the language measure-based optimal supervisor control with reinforcement learning