Efficient algorithms for periodic real-time tasks to optimal discrete voltage schedules

In this paper, we pay attention to the periodic task scheduling on a variable voltage processor with d discrete voltage/speed levels. We propose an intra-task DVS algorithm which constructs a minimum energy schedule for k tasks in O(d+k log k) time. We also give an inter-task DVS algorithm with O(d+n log n) time, where n denotes the number of jobs. Previous approaches solve this problem by first generating a canonical schedule and then adjusting the speed in O(dn log n) or O(n³) time. However, they do not consider that the length of a canonical schedule depends on the LCM of those of task periods and is of exponential length in general. In our approach, the tasks with arbitrary periods are first transformed into harmonic periods and then profile their key features. Afterward, the (optimal) discrete solution can be computed directly from these features.