Abstract
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. [10]. Our throughput guarantee is optimal as any online algorithm must be at least 4-competitive even if the energy concern is ignored [7]. 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 = ∞ ) [4].
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References
http://www-03.ibm.com/chips/power/powerpc/newsletter/sep2004/technical2.html
Albers, S., Fujiwara, H.: Energy-efficient algorithms for flow time minimization. In: Durand, B., Thomas, W. (eds.) STACS 2006. LNCS, vol. 3884, pp. 621–633. Springer, Heidelberg (2006)
Bansal, N., Kimbrel, T., Pruhs, K.: Dynamic speed scaling to manage energy and temperature. Journal of the ACM 51(1) (2007)
Bansal, N., Pruhs, K., Stein, C.: Speed scaling for weighted flow time. In: Proc. SODA, pp. 805–813 (2007)
Bansal, N., Chan, H.L.: Weighted flow time does not have O(1) competitive algorithms (manuscript)
Bansal, N., Dhamdhere, K.: Minimizing weighted flow time. In: Proc. SODA, pp. 508–516 (2003)
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)
Becchetti, L., Leonardi, S., Marchetti-Spaccamela, A., Pruhs, K.: Online Weighted Flow Time and Deadline Scheduling. In: Proc. RANDOM-APPROX, pp. 36–47 (2001)
Brooks, D.M., Bose, P., Schuster, S.E., Jacobson, H., Kudva, P.N., Buyuktosunoglu, A., Wellman, J.D., Zyuban, V., Gupta, M., Cook, P.W.: Power-aware microarchitecture: Design and modeling challenges for next-generation microprocessors. IEEE Micro. 20(6), 26–44 (2000)
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)
Chekuri, C., Khanna, S., Zhu, A.: Algorithms for minimizing weighted flow time. In: Proc. STOC, pp. 84–93 (2001)
Dertouzos, M.L.: Control robotics: the procedural control of physical processes. In: Proc. IFIP Congress, pp. 807–813 (1974)
Grunwald, D., Levis, P., Farkas, K.I., Morrey, C.B., Neufeld, M.: Policies for dynamic clock scheduling. In: Proc. OSDI, pp. 73–86 (2000)
Hardy, G.H., Littlewood, J.E., Polya, G.: Inequalities. Cambridge University Press, Cambridge (1952)
Irani, S., Pruhs, K.: Algorithmic problems in power management. SIGACT News (2005)
Koren, G., Shasha, D.: D\(^{\it over}\): An optimal on-line scheduling algorithm for overloaded uniprocessor real-time systems. SIAM J. Comput. 24(2), 318–339 (1995)
Lam, T.W., To, K.K.: Performance Guarantee for Online Deadline Scheduling in the Presence of Overload. In: Proc. SODA, pp. 755–764 (2001)
Li, M., Liu, B.J., Yao, F.F.: Min-energy voltage allocations for tree-structured tasks. In: Wang, L. (ed.) COCOON 2005. LNCS, vol. 3595, pp. 283–296. Springer, Heidelberg (2005)
Li, M., Yao, F.: An efficient algorithm for computing optimal discrete voltage schedules. SIAM J. Comput. 35(3), 658–671 (2005)
Mudge, T.: Power: A first-class architectural design constraint. Computer 34(4), 52–58 (2001)
Pillai, P., Shin, K.G.: Real-time dynamic voltage scaling for low-power embedded operating systems. In: Proc. SOSP, pp. 89–102 (2001)
Pruhs, K., Uthaisombut, P., Woeginger, G.: Getting the best response for your erg. In: Hagerup, T., Katajainen, J. (eds.) SWAT 2004. LNCS, vol. 3111, pp. 14–25. Springer, Heidelberg (2004)
Weiser, M., Welch, B., Demers, A., Shenker, S.: Scheduling for reduced CPU energy. In: Proc. OSDI, pp. 13–23 (1994)
Yao, F., Demers, A., Shenker, S.: A scheduling model for reduced CPU energy. In: Proc. FOCS, pp. 374–382 (1995)
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Bansal, N., Chan, HL., Lam, TW., Lee, LK. (2008). Scheduling for Speed Bounded Processors. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds) Automata, Languages and Programming. ICALP 2008. Lecture Notes in Computer Science, vol 5125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70575-8_34
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