Optimal task execution speed setting and lower bound for delay and energy minimization

Abstract

The current technology trend reveals that static power consumption is growing at a faster rate than dynamic power consumption. In this paper, energy-efficient task scheduling is studied when static power consumption is a significant part of energy consumption which cannot be ignored. The problems of scheduling a set of independent sequential tasks on identical processors so that the schedule length is minimized for a given energy consumption constraint or the energy consumption is minimized for a given schedule length constraint are investigated. For a given schedule, the optimal task execution speed setting for delay and energy minimization is found analytically. Lower bounds for the minimum schedule length of a set of tasks with a given energy consumption constraint and the minimum energy consumption of a set of tasks with a given schedule length constraint are established. Our lower bounds are applicable to sequential or parallel, and independent or precedence constrained tasks, on processors with discrete or continuous speed levels, and bounded or unbounded speed ranges. The significance of these lower bounds is that they can be used to evaluate the performance of any heuristic algorithms when compared with optimal algorithms. Experimental study on the performance of list scheduling algorithms is performed and it is shown that their performance is very close to the optimal. To the best of the author’s knowledge, this is the first paper that provides such analytical results for energy-efficient task scheduling with both dynamic and static power consumptions.