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.
© 2010 ACM. This work was supported by NSF CCF 0830511 and CNS 0435520, Microsoft Research, the Lee Center for Advanced Networking and ARC grant FT0991594. We thank Jeremy Hurwitz for comments on the proof of Theorem 4.