P-YDS algorithm: An optimal extension of YDS algorithm to minimize expected energy for real-time jobs

The YDS algorithm computes a schedule on a DVS-enabled resource to meet deadlines of all jobs and optimally minimize the total energy consumption. The algorithm requires that an exact execution time of each job be known. For settings where execution times are variable or uncertain, stochastic scheduling has been proposed to preferentially accelerate less probable phases of jobs to reduce the expected energy consumption. However, an analogue to the YDS algorithm for the stochastic setting has not been optimally solved. In this paper, we propose the p-YDS algorithm to minimize the expected energy consumption for a set of jobs with arbitrary arrival times, deadlines, and execution times. We then derive the competitive ratio of the YDS algorithm w.r.t. the p-YDS algorithm, for the metric of expected energy consumption. By comparing two optimal algorithms, this ratio specifies the worst-case energy cost of being agnostic to the variability in the execution time of jobs.