Improved Bounds for Speed Scaling in Devices Obeying the Cube-Root Rule
Speed scaling is a power management technique that involves dynamically changing the speed of a processor. This gives rise to dual-objective scheduling problems, where the operating system both wants to conserve energy and optimize some Quality of Service (QoS) measure of the resulting schedule. In the most investigated speed scaling problem in the literature, the QoS constraint is deadline feasibility, and the objective is to minimize the energy used. The standard assumption is that the power consumption is the speed to some constant power α. We give the first non-trivial lower bound, namely eα− 1/α, on the competitive ratio for this problem. This comes close to the best upper bound which is about 2eα + 1.
We analyze a natural class of algorithms called qOA, where at any time, the processor works at q ≥ 1 times the minimum speed required to ensure feasibility assuming no new jobs arrive. For CMOS based processors, and many other types of devices, α= 3, that is, they satisfy the cube-root rule. When α= 3, we show that qOA is 6.7-competitive, improving upon the previous best guarantee of 27 achieved by the algorithm Optimal Available (OA). So when the cube-root rule holds, our results reduce the range for the optimal competitive ratio from [1.2, 27] to [2.4, 6.7]. We also analyze qOA for general α and give almost matching upper and lower bounds.
Unable to display preview. Download preview PDF.
- 1.Albers, S., Müller, F., Schmelzer, S.: Speed scaling on parallel processors. In: Proc. ACM Symposium on Parallel Algorithms and Architectures (SPAA), pp. 289–298 (2007)Google Scholar
- 2.Bansal, N., Bunde, D., Chan, H.L., Pruhs, K.: Average rate speed scaling. In: Latin American Theoretical Informatics Symposium (2008)Google Scholar
- 3.Bansal, N., Chan, H., Pruhs, K.: Speed scaling with a solar cell. In: International Conference on Algorithmic Aspects in Information and Management (submitted, 2008)Google Scholar
- 4.Bansal, N., Kimbrel, T., Pruhs, K.: Dynamic speed scaling to manage energy and temperature. In: Proc. IEEE Symp. on Foundations of Computer Science, pp. 520–529 (2004)Google Scholar
- 5.Bansal, N., Kimbrel, T., Pruhs, K.: Speed scaling to manage energy and temperature. JACM 54(1) (2007)Google Scholar
- 7.Bansal, N., Pruhs, K., Stein, C.: Speed scaling for weighted flow time. In: SODA 2007: Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms, pp. 805–813 (2007)Google Scholar
- 9.Chan, H.L., Chan, W.-T., Lam, T.-W., Lee, L.-K., Mak, K.-S., Wong, P.W.H.: Energy efficient online deadline scheduling. In: SODA 2007: Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms, pp. 795–804 (2007)Google Scholar
- 10.Chan, H.-L., Edmonds, J., Lam, T.-W., Lee, L.-K., Marchetti-Spaccamela, A., Pruhs, K.: Nonclairvoyant speed scaling for flow and energy. In: STACS (2009)Google Scholar
- 11.Kwon, W.-C., Kim, T.: Optimal voltage allocation techniques for dynamically variable voltage processors. In: Proc. ACM-IEEE Design Automation Conf., pp. 125–130 (2003)Google Scholar
- 16.Yao, F., Demers, A., Shenker, S.: A scheduling model for reduced CPU energy. In: Proc. IEEE Symp. Foundations of Computer Science, pp. 374–382 (1995)Google Scholar