Abstract
We consider a situation where jobs arrive over time at a data center, consisting of identical speed-scalable processors. For each job, the scheduler knows how much income is lost as a function of how long the job is delayed. The scheduler also knows the fixed cost of a unit of energy. The online scheduler determines which jobs to run on which processors, and at what speed to run the processors. The scheduler’s objective is to maximize profit, which is the income obtained from jobs minus the energy costs. We give a (1 + ε)-speed O(1)-competitive algorithm, and show that resource augmentation is necessary to achieve O(1)-competitiveness.
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References
Albers, S., Fujiwara, H.: Energy-efficient algorithms for flow time minimization. ACM Transactions on Algorithms 3(4) (2007)
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)
Bansal, N., Chan, H.L., Pruhs, K.: Speed scaling with a solar cell. In: International Conference on Algorithmic Aspects in Information and Management (2008)
Bansal, N., Kimbrel, T., Pruhs, K.: Speed scaling to manage energy and temperature. JACM 54(1) (2007)
Bansal, N., Bunde, D., Chan, H.L., Pruhs, K.: Average rate speed scaling. In: Latin American Theoretical Informatics Symposium (2008)
Bansal, N., Chan, H.-L., Lam, T.W., Lee, L.-K.: Scheduling for speed bounded processors. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 409–420. Springer, Heidelberg (2008)
Bansal, N., Chan, H.-L., Pruhs, K.: Competitive algorithms for due date scheduling. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 28–39. Springer, Heidelberg (2007)
Bansal, N., Chan, H.-L., Pruhs, K.: Speed scaling with an arbitrary power function. In: SODA, pp. 693–701 (2009)
Bansal, N., Chan, H.-L., Pruhs, K., Katz, D.: Improved bounds for speed scaling in devices obeying the cube-root rule. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5556, pp. 144–155. Springer, Heidelberg (2009)
Bansal, N., Pruhs, K., Stein, C.: Speed scaling for weighted flow time. In: ACM-SIAM Symposium on Discrete Algorithms, pp. 805–813 (2007)
Barroso, L.A.: The price of performance. ACM Queue 3(7), 48–53 (2005)
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)
Bunde, D.P.: Power-aware scheduling for makespan and flow. J. Scheduling 12(5), 489–500 (2009)
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: ACM-SIAM Symposium on Discrete Algorithms, pp. 795–804 (2007)
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, pp. 795–804 (2007)
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, pp. 255–264 (2009)
Chan, H.-L., Edmonds, J., Pruhs, K.: Speed scaling of processes with arbitrary speedup curves on a multiprocessor. In: SPAA, pp. 1–10 (2009)
Chan, H.-L., Lam, T.W., To, K.-K.: Nonmigratory online deadline scheduling on multiprocessors. SIAM J. Comput. 34(3), 669–682 (2005)
Fan, X., Weber, W.-D., Barroso, L.A.: Power provisioning for a warehouse-sized computer. In: International Symposium on Computer Architecture, pp. 13–23 (2007)
Kalyanasundaram, B., Pruhs, K.: Speed is as powerful as clairvoyance. J. ACM 47(4), 617–643 (2000)
Kalyanasundaram, B., Pruhs, K.: Eliminating migration in multi-processor scheduling. J. Algorithms 38(1), 2–24 (2001)
Li, M., Liu, B.J., Yao, F.F.: Min-energy voltage allocation for tree-structured tasks. Journal of Combinatorial Optimization 11(3), 305–319 (2006)
Li, M., Yao, F.F.: An efficient algorithm for computing optimal discrete voltage schedules. SIAM J. on Computing 35, 658–671 (2005)
Markoff, J., Lohr, S.: Intel’s huge bet turns iffy. New York Times (September 29, 2002)
Mudge, T.: Power: A first-class architectural design constraint. Computer 34(4), 52–58 (2001)
Phillips, C.A., Stein, C., Torng, E., Wein, J.: Optimal time-critical scheduling via resource augmentation. Algorithmica 32(2), 163–200 (2002)
Pruhs, K.: Competitive online scheduling for server systems. SIGMETRICS Performance Evaluation Review 34(4), 52–58 (2007)
Pruhs, K., Sgall, J., Torng, E.: Online scheduling. In: Handbook on Scheduling. CRC Press, Boca Raton (2004)
Pruhs, K., Uthaisombut, P., Woeginger, G.: Getting the best response for your erg. In: Scandanavian Workshop on Algorithms and Theory (2004)
Pruhs, K., van Stee, R., Uthaisombut, P.: Speed scaling of tasks with precedence constraints. Theory Comput. Syst. 43(1), 67–80 (2008)
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)
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Pruhs, K., Stein, C. (2010). How to Schedule When You Have to Buy Your Energy. In: Serna, M., Shaltiel, R., Jansen, K., Rolim, J. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. RANDOM APPROX 2010 2010. Lecture Notes in Computer Science, vol 6302. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15369-3_27
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DOI: https://doi.org/10.1007/978-3-642-15369-3_27
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