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Nonclairvoyant Speed Scaling for Weighted Flow Time
"... Abstract. We study online job scheduling on a processor that can vary its speed dynamically to manage its power. We attempt to extend the recent success in analyzing total unweighted flow time plus energy to total weighted flow time plus energy. We first consider the nonclairvoyant setting where th ..."
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Abstract. We study online job scheduling on a processor that can vary its speed dynamically to manage its power. We attempt to extend the recent success in analyzing total unweighted flow time plus energy to total weighted flow time plus energy. We first consider the nonclairvoyant setting where the size of a job is only known when the job finishes. We show an online algorithm WLAPS that is 8α 2competitive for weighted flow time plus energy under the traditional power model, which assumes the power P (s) toruntheprocessoratspeeds to be s α for some α>1. More interestingly, for any arbitrary power function P (s), WLAPS remains competitive when given a more energyefficient processor; precisely, WLAPS is 16(1 + 1 ɛ)2competitive when using a processor that, given the power P (s), can run at speed (1 + ɛ)s for some ɛ>0. Without such speedup, no nonclairvoyant algorithm can be O(1)competitive for an arbitrary power function [8]. For the clairvoyant setting (where the size of a job is known at release time), previous results on minimizing weighted flow time plus energy rely on scaling the speed continuously over time [5–7]. The analysis of WLAPS has inspired us to devise a clairvoyant algorithm LLB which can transform any continuous speed scaling algorithm to one that scales the speed at discrete times only. Under an arbitrary power function, LLB can give an 4(1 + 1 ɛ)competitive algorithm using a processor with (1 + ɛ)speedup. 1
Speed scaling: An algorithmic perspective
"... Speed scaling has long been used as a powersaving mechanism at a chip level. However, in recent years, speed scaling has begun to be used as an approach for trading off energy usage and performance throughout all levels of computer systems. This widespread use of speed scaling has motivated signif ..."
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Speed scaling has long been used as a powersaving mechanism at a chip level. However, in recent years, speed scaling has begun to be used as an approach for trading off energy usage and performance throughout all levels of computer systems. This widespread use of speed scaling has motivated significant research on the topic, but many fundamental questions about speed scaling are only beginning to be understood. In this chapter, we focus on a simple, but general, model of speed scaling and provide an algorithmic perspective on four fundamental questions: (i) What is the structure of the optimal speed scaling algorithm? (ii) How does speed scaling interact with scheduling? (iii) What is the impact of the sophistication of speed scaling algorithms? and (iv) Does speed scaling have any unintended consequences? For each question we provide a summary of insights from recent work on the topic in both worstcase and stochastic analysis as well as a discussion of interesting open questions that remain. 1
SPECIAL ISSUE FOR CATS 2010 Nonclairvoyant Scheduling for Weighted Flow Time and Energy on Speed Bounded Processors∗
, 2010
"... Abstract: We consider the online scheduling problem of minimizing total weighted flow time plus energy in the dynamic speed scaling model, where a processor can scale its speed dynamically between 0 and some maximum speed T. In the past few years this problem has been studied extensively under the c ..."
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Abstract: We consider the online scheduling problem of minimizing total weighted flow time plus energy in the dynamic speed scaling model, where a processor can scale its speed dynamically between 0 and some maximum speed T. In the past few years this problem has been studied extensively under the clairvoyant setting, which requires the size of a job to be known at release time [1, 4, 5, 8, 15, 18–20]. For the nonclairvoyant setting, despite its practical importance, the progress is relatively limited. Only recently an online algorithm LAPS is known to be O(1)competitive for minimizing (unweighted) flow time plus energy in the infinite speed model (i.e., T = ∞) [11, 12]. This paper makes two contributions to the nonclairvoyant scheduling. First, we resolve the open problem that the unweighted result of LAPS can be extended to the more realistic model with bounded maximum speed. Second, we show that another nonclairvoyant algorithm WRR is O(1)competitive when weighted flow time is concerned. Note that WRR is not as efficient as LAPS for scheduling unweighted jobs as WRR has a much bigger constant hidden in its competitive ratio. ∗This is a corrected version of a paper with the same title in CATS 2010 [14]; in particular, Lemmas 2 and 4 of Section 3 and the ordering of jobs in the potential analysis of Section 4 were given incorrectly before and are fixed in this version. On the other hand, the conjecture, given in Section 5, about the generalization of LAPS to the weighted setting has recently been resolved [13].