Scheduling for Speed Bounded Processors
We consider online scheduling algorithms in the dynamic speed scaling model, where a processor can scale its speed between 0 and some maximum speed T. The processor uses energy at rate s α when run at speed s, where α> 1 is a constant. Most modern processors use dynamic speed scaling to manage their energy usage. This leads to the problem of designing execution strategies that are both energy efficient, and yet have almost optimum performance.
We consider two problems in this model and give essentially optimum possible algorithms for them. In the first problem, jobs with arbitrary sizes and deadlines arrive online and the goal is to maximize the throughput, i.e. the total size of jobs completed successfully. We give an algorithm that is 4-competitive for throughput and O(1)-competitive for the energy used. This improves upon the 14 throughput competitive algorithm of Chan et al. . Our throughput guarantee is optimal as any online algorithm must be at least 4-competitive even if the energy concern is ignored . In the second problem, we consider optimizing the trade-off between the total flow time incurred and the energy consumed by the jobs. We give a 4-competitive algorithm to minimize total flow time plus energy for unweighted unit size jobs, and a (2 + o(1)) α/ln α-competitive algorithm to minimize fractional weighted flow time plus energy. Prior to our work, these guarantees were known only when the processor speed was unbounded (T = ∞ ) .
KeywordsMaximum Speed Competitive Ratio Online Algorithm Throughput Maximization Earliest Deadline First
Unable to display preview. Download preview PDF.
- 3.Bansal, N., Kimbrel, T., Pruhs, K.: Dynamic speed scaling to manage energy and temperature. Journal of the ACM 51(1) (2007)Google Scholar
- 4.Bansal, N., Pruhs, K., Stein, C.: Speed scaling for weighted flow time. In: Proc. SODA, pp. 805–813 (2007)Google Scholar
- 5.Bansal, N., Chan, H.L.: Weighted flow time does not have O(1) competitive algorithms (manuscript)Google Scholar
- 6.Bansal, N., Dhamdhere, K.: Minimizing weighted flow time. In: Proc. SODA, pp. 508–516 (2003)Google Scholar
- 7.Baruah, S., Koren, G., Mishra, B., Raghunathan, A., Rosier, L., Shasha, D.: On-line scheduling in the presence of overload. In: Proc. FOCS, pp. 100–110 (1991)Google Scholar
- 8.Becchetti, L., Leonardi, S., Marchetti-Spaccamela, A., Pruhs, K.: Online Weighted Flow Time and Deadline Scheduling. In: Proc. RANDOM-APPROX, pp. 36–47 (2001)Google Scholar
- 10.Chan, H.L., Chan, W.T., Lam, T.W., Lee, L.K., Mak, K.S., Wong, P.: Energy efficient online deadline scheduling. In: Proc. SODA, pp. 795–804 (2007)Google Scholar
- 11.Chekuri, C., Khanna, S., Zhu, A.: Algorithms for minimizing weighted flow time. In: Proc. STOC, pp. 84–93 (2001)Google Scholar
- 12.Dertouzos, M.L.: Control robotics: the procedural control of physical processes. In: Proc. IFIP Congress, pp. 807–813 (1974)Google Scholar
- 13.Grunwald, D., Levis, P., Farkas, K.I., Morrey, C.B., Neufeld, M.: Policies for dynamic clock scheduling. In: Proc. OSDI, pp. 73–86 (2000)Google Scholar
- 15.Irani, S., Pruhs, K.: Algorithmic problems in power management. SIGACT News (2005)Google Scholar
- 17.Lam, T.W., To, K.K.: Performance Guarantee for Online Deadline Scheduling in the Presence of Overload. In: Proc. SODA, pp. 755–764 (2001)Google Scholar
- 21.Pillai, P., Shin, K.G.: Real-time dynamic voltage scaling for low-power embedded operating systems. In: Proc. SOSP, pp. 89–102 (2001)Google Scholar
- 23.Weiser, M., Welch, B., Demers, A., Shenker, S.: Scheduling for reduced CPU energy. In: Proc. OSDI, pp. 13–23 (1994)Google Scholar
- 24.Yao, F., Demers, A., Shenker, S.: A scheduling model for reduced CPU energy. In: Proc. FOCS, pp. 374–382 (1995)Google Scholar