Optimality, fairness, and robustness in speed scaling designs

This work examines fundamental tradeoffs incurred by a speed scaler seeking to minimize the sum of expected response time and energy use per job. We prove that a popular speed scaler is 2-competitive for this objective and no 'natural' speed scaler can do better. Additionally, we prove that energy-proportional speed scaling works well for both Shortest Remaining Processing Time (SRPT) and Processor Sharing (PS) and we show that under both SRPT and PS, gated-static speed scaling is nearly optimal when the mean workload is known, but that dynamic speed scaling provides robustness against uncertain workloads. Finally, we prove that speed scaling magnifies unfairness under SRPT but that PS remains fair under speed scaling. These results show that these speed scalers can achieve any two, but only two, of optimality, fairness, and robustness.