Abstract
This paper is concerned with online scheduling algorithms that aim at minimizing the total flow time plus energy usage. The results are divided into two parts. First, we consider the well-studied “simple” speed scaling model and show how to analyze a speed scaling algorithm (called AJC) that changes speed discretely. This is in contrast to the previous algorithms which change the speed continuously. More interestingly, AJC admits a better competitive ratio, and without using extra speed. In the second part, we extend the study to a more general speed scaling model where the processor can enter a sleep state to further save energy. A new sleep management algorithm called IdleLonger is presented. This algorithm, when coupled with AJC, gives the first competitive algorithm for minimizing total flow time plus energy in the general model.
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Notes
Static power is dissipated due to leakage current and is independent of processor speed, and dynamic power is due to dynamic switching loss and increases with the speed.
Young’s Inequality is stated as follows. Let f be a real-valued, continuous and strictly increasing function such that f(0)=0. Then, for all g,h≥0, \(\int _{0}^{g}\!f(x)\,\textup {d}x + \int _{0}^{h}\!f^{-1}(x)\,\textup {d}x \ge gh\), where f −1 is the inverse function of f. When using Young’s inequality to adapt the bound of \(\frac {\textup {d}\Phi_{2}}{\textup {d}t}\), we set f(x)=x α−1, f −1(x)=x 1/(α−1), g=s o/μ, and h=(n a+σ)1−1/α μ.
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T.W. Lam is partially supported by HKU Grant 201007176149.
I.K.K. To and P.W.H. Wong are partially supported by EPSRC Grant EP/E028276/1.
The results in this paper have appeared in preliminary form in the proceedings of the 16th Annual European Symposium on Algorithms, 2008 and the proceedings of the 36th International Colloquium on Automata, Languages and Programming, 2009.
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Lam, TW., Lee, LK., To, I.K.K. et al. Online Speed Scaling Based on Active Job Count to Minimize Flow Plus Energy. Algorithmica 65, 605–633 (2013). https://doi.org/10.1007/s00453-012-9613-y
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DOI: https://doi.org/10.1007/s00453-012-9613-y