Scheduling for Speed Bounded Processors

  • Nikhil Bansal
  • Ho-Leung Chan
  • Tak-Wah Lam
  • Lap-Kei Lee
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5125)


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].


Maximum Speed Competitive Ratio Online Algorithm Throughput Maximization Earliest Deadline First 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
  2. 2.
    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)CrossRefGoogle Scholar
  3. 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. 4.
    Bansal, N., Pruhs, K., Stein, C.: Speed scaling for weighted flow time. In: Proc. SODA, pp. 805–813 (2007)Google Scholar
  5. 5.
    Bansal, N., Chan, H.L.: Weighted flow time does not have O(1) competitive algorithms (manuscript)Google Scholar
  6. 6.
    Bansal, N., Dhamdhere, K.: Minimizing weighted flow time. In: Proc. SODA, pp. 508–516 (2003)Google Scholar
  7. 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. 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
  9. 9.
    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)CrossRefGoogle Scholar
  10. 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. 11.
    Chekuri, C., Khanna, S., Zhu, A.: Algorithms for minimizing weighted flow time. In: Proc. STOC, pp. 84–93 (2001)Google Scholar
  12. 12.
    Dertouzos, M.L.: Control robotics: the procedural control of physical processes. In: Proc. IFIP Congress, pp. 807–813 (1974)Google Scholar
  13. 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
  14. 14.
    Hardy, G.H., Littlewood, J.E., Polya, G.: Inequalities. Cambridge University Press, Cambridge (1952)zbMATHGoogle Scholar
  15. 15.
    Irani, S., Pruhs, K.: Algorithmic problems in power management. SIGACT News (2005)Google Scholar
  16. 16.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 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
  18. 18.
    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)CrossRefGoogle Scholar
  19. 19.
    Li, M., Yao, F.: An efficient algorithm for computing optimal discrete voltage schedules. SIAM J. Comput. 35(3), 658–671 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Mudge, T.: Power: A first-class architectural design constraint. Computer 34(4), 52–58 (2001)CrossRefGoogle Scholar
  21. 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
  22. 22.
    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)CrossRefGoogle Scholar
  23. 23.
    Weiser, M., Welch, B., Demers, A., Shenker, S.: Scheduling for reduced CPU energy. In: Proc. OSDI, pp. 13–23 (1994)Google Scholar
  24. 24.
    Yao, F., Demers, A., Shenker, S.: A scheduling model for reduced CPU energy. In: Proc. FOCS, pp. 374–382 (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Nikhil Bansal
    • 1
  • Ho-Leung Chan
    • 2
  • Tak-Wah Lam
    • 3
  • Lap-Kei Lee
    • 3
  1. 1.IBM T.J. Watson Research CenterNY
  2. 2.Computer Science DepartmentUniversity of PittsburghUSA
  3. 3.Department of Computer ScienceUniversity of Hong KongHong Kong

Personalised recommendations