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Optimality, fairness, and robustness in speed scaling designs
"... System design must strike a balance between energy and performance by carefully selecting the speed at which the system will run. In this work, we examine fundamental tradeoffs incurred when designing a speed scaler to minimize a weighted sum of expected response time and energy use per job. We prov ..."
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Cited by 44 (14 self)
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System design must strike a balance between energy and performance by carefully selecting the speed at which the system will run. In this work, we examine fundamental tradeoffs incurred when designing a speed scaler to minimize a weighted sum of expected response time and energy use per job. We prove that a popular dynamic speed scaling algorithm is 2competitive for this objective and that no “natural” speed scaler can improve on this. Further, we prove that energyproportional speed scaling works well across two common scheduling policies: Shortest Remaining Processing Time (SRPT) and Processor Sharing (PS). Third, we show that under SRPT and PS, gatedstatic speed scaling is nearly optimal when the mean workload is known, but that dynamic speed scaling provides robustness against uncertain workloads. Finally, we prove that speed scaling magnifies unfairness, notably SRPT’s bias against large jobs and the bias against short jobs in nonpreemptive policies. However, PS remains fair under speed scaling. Together, these results show that the speed scalers studied here can achieve any two, but only two, of optimality, fairness, and robustness. 1.
Nonclairvoyant Speed Scaling for Flow and Energy
"... We study online nonclairvoyant speed scaling to minimize total flow time plus energy. We first consider the traditional model where the power function is P(s) = s α. We give a nonclairvoyant algorithm that is shown to be O(α 3)competitive. We then show an Ω(α 1/3−ǫ) lower bound on the competitive ..."
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Cited by 36 (15 self)
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We study online nonclairvoyant speed scaling to minimize total flow time plus energy. We first consider the traditional model where the power function is P(s) = s α. We give a nonclairvoyant algorithm that is shown to be O(α 3)competitive. We then show an Ω(α 1/3−ǫ) lower bound on the competitive ratio of any nonclairvoyant algorithm. We also show that there are power functions for which no nonclairvoyant algorithm can be O(1)competitive. 1
Speed Scaling of Processes with Arbitrary Speedup Curves on a Multiprocessor
"... We consider the setting of a multiprocessor where the speeds of the m processors can be individually scaled. Jobs arrive over time and have varying degrees of parallelizability. A nonclairvoyant scheduler must assign the processes to processors, and scale the speeds of the processors. We consider th ..."
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Cited by 24 (8 self)
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We consider the setting of a multiprocessor where the speeds of the m processors can be individually scaled. Jobs arrive over time and have varying degrees of parallelizability. A nonclairvoyant scheduler must assign the processes to processors, and scale the speeds of the processors. We consider the objective of energy plus flow time. We assume that a processor running at speed s uses power sα for some constant α> 1. For processes that may have side effects or that are not checkpointable, we show an Ω(m (α−1)/α2) bound on the competitive ratio of any randomized algorithm. For checkpointable processes without side effects, we give an O(logm)competitive algorithm. Thus for processes that may have side effects or that are not checkpointable, the achievable competitive ratio grows quickly with the number of processors, but for checkpointable processes without side effects, the achievable competitive ratio grows slowly with the number of processors. We then show a lower bound of Ω(log1/α m) on the competitive ratio of any randomized algorithm for checkpointable processes without side effects. 1
A.: The bell is ringing in speedscaled multiprocessor scheduling
 In: Proceedings of ACM Symposium on Parallelism in Algorithms and Architectures (SPAA
, 2009
"... This paper investigates the problem of scheduling jobs on multiple speedscaled processors without migration, i.e., we have constant α> 1 such that running a processor at speed s results in energy consumption s α per time unit. We consider the general case where each job has a monotonously increas ..."
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This paper investigates the problem of scheduling jobs on multiple speedscaled processors without migration, i.e., we have constant α> 1 such that running a processor at speed s results in energy consumption s α per time unit. We consider the general case where each job has a monotonously increasing cost function that penalizes delay. This includes the so far considered cases of deadlines and flow time. For any type of delay cost functions, we obtain the following results: Any βapproximation algorithm for a single processor yields a randomized βBαapproximation algorithm for multiple processors without migration, where Bα is the αth Bell number, that is, the number of partitions of a set of size α. Analogously, we show that any βcompetitive online algorithm for a single processor yields a βBαcompetitive online algorithm for multiple processors without migration. Finally, we show that any βapproximation algorithm for multiple processors with migration yields a deterministic βBαapproximation algorithm for multiple processors without migration. These facts improve several approximation ratios and lead to new results. For instance, we obtain the first constant factor online and offline approximation algorithm for multiple processors without migration for arbitrary release times, deadlines, and job sizes.
A Tutorial on Amortized Local Competitiveness in Online Scheduling
, 2011
"... potential functions are used to show that a particular online algorithm is locally competitive in an amortized sense. Algorithm analyses using potential functions are sometimes criticized as seeming to be black magic ..."
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potential functions are used to show that a particular online algorithm is locally competitive in an amortized sense. Algorithm analyses using potential functions are sometimes criticized as seeming to be black magic
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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Cited by 16 (3 self)
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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
Scalably Scheduling PowerHeterogeneous Processors
"... Abstract. We show that a natural online algorithm for scheduling jobs on a heterogeneous multiprocessor, with arbitrary power functions, is scalable for the objective function of weighted flow plus energy. 1 ..."
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Abstract. We show that a natural online algorithm for scheduling jobs on a heterogeneous multiprocessor, with arbitrary power functions, is scalable for the objective function of weighted flow plus energy. 1
Algorithms for dynamic speed scaling
 In STACS 2011, volume 9 of LIPIcs. Schloss Dagstuhl  LeibnizZentrum fuer Informatik
, 2011
"... Many modern microprocessors allow the speed/frequency to be set dynamically. The general goal is to execute a sequence of jobs on a variablespeed processor so as to minimize energy consumption. This paper surveys algorithmic results on dynamic speed scaling. We address settings where (1) jobs have ..."
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Cited by 13 (0 self)
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Many modern microprocessors allow the speed/frequency to be set dynamically. The general goal is to execute a sequence of jobs on a variablespeed processor so as to minimize energy consumption. This paper surveys algorithmic results on dynamic speed scaling. We address settings where (1) jobs have strict deadlines and (2) job flow times are to be minimized.
Deadline Scheduling and Power Management for Speed Bounded Processors
"... Energy consumption has become an important issue in the study of processor scheduling. Energy reduction can be achieved by allowing a processor to vary the speed dynamically (dynamic speed scaling) [2–4, 7, 10] or to enter a sleep state [1, 5, 8]. In the past, these two mechanisms are often studied ..."
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Cited by 13 (1 self)
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Energy consumption has become an important issue in the study of processor scheduling. Energy reduction can be achieved by allowing a processor to vary the speed dynamically (dynamic speed scaling) [2–4, 7, 10] or to enter a sleep state [1, 5, 8]. In the past, these two mechanisms are often studied separately. It is indeed natural to consider an integrated model in which a
Sleep with Guilt and Work Faster to Minimize Flow plus Energy
"... Abstract. In this paper we extend the study of flowenergy scheduling to a model that allows both sleep management and speed scaling. Our main result is a sleep management algorithm called IdleLonger, which works online for a processor with one or multiple levels of sleep states. The design of IdleL ..."
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Cited by 9 (6 self)
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Abstract. In this paper we extend the study of flowenergy scheduling to a model that allows both sleep management and speed scaling. Our main result is a sleep management algorithm called IdleLonger, which works online for a processor with one or multiple levels of sleep states. The design of IdleLonger is interesting; among others, it may force the processor to idle or even sleep even though new jobs have already arrived. IdleLonger works in both clairvoyant and nonclairvoyant settings. We show how to adapt two existing speed scaling algorithms AJC [15] (clairvoyant) and LAPS [9] (nonclairvoyant) to the new model. The adapted algorithms, when coupled with IdleLonger, are shown to be O(1)competitive clairvoyant and nonclairvoyant algorithms for minimizing flow plus energy on a processor that allows sleep management and speed scaling. The above results are based on the traditional model with no limit on processor speed. If the processor has a maximum speed, the problem becomes more difficult as the processor, once overslept, cannot rely on unlimited extra speed to catch up the delay. Nevertheless, we are able to enhance IdleLonger and AJC so that they remain O(1)competitive for flow plus energy under the bounded speed model. Nonclairvoyant scheduling in the bounded speed model is left as an open problem. 1