Speed Scaling with an Arbitrary Power Function

Bansal, Nikhil; Chan, Ho-Leung; Pruhs, Kirk

doi:10.1145/2438645.2438650

Cited by 37 publications

(60 citation statements)

References 12 publications

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“…To the best of our knowledge there is no other algorithmic work directly related to the results in this paper. [4] showed that a natural online algorithm is 2-competitive for the objective of a linear combination of energy and weighted fractional delay. [4], [5] showed that a natural online algorithm is 2-competitive for the objective of a linear combination of energy and total (unweighted) (integer) delay.…”

Section: Related Resultsmentioning

confidence: 99%

“…[4] showed that a natural online algorithm is 2-competitive for the objective of a linear combination of energy and weighted fractional delay. [4], [5] showed that a natural online algorithm is 2-competitive for the objective of a linear combination of energy and total (unweighted) (integer) delay. Previously, [3], [6], [7], [8], [9], [10], [11] gave online algorithms with competitive analyses in the case that the power function was of the form s α .…”

Section: Related Resultsmentioning

confidence: 99%

“…We adopt the speed scaling model, originally proposed in [4], that essentially allows the speed to power function to be arbitrary. In particular the power function may have a maximum power, and hence maximum speed.…”

Section: Preliminariesmentioning

confidence: 99%

See 2 more Smart Citations

Optimal energy trade-off schedules

Barcelo

Cole

Letsios

et al. 2013

Sustainable Computing: Informatics and Systems

Self Cite

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Abstract-We consider scheduling tasks that arrive over time on a speed scalable processor. At each time a schedule specifies a job to be run and the speed at which the processor is run. Processors are generally less energy efficient at higher speeds. We seek to understand the structure of schedules that optimally trade-off the energy used by the processor with a common scheduling quality of service measure, fractional weighted delay. We assume that there is some user defined parameter β specifying the user's desired additive trade-off between energy efficiency and quality of service. We prove that the optimal energy trade-off schedule is essentially unique, and has a simple structure. Thus it is easy to check the optimality of a schedule. We further prove that the optimal energy trade-off schedule changes continuously as a function of the parameter β. Thus it is possible to compute the optimal energy trade-off schedule using a natural homotopic optimization algorithm. We further show that multiplicative trade-off schedules have fewer desirable properties.

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Section: Related Resultsmentioning

confidence: 99%

Section: Related Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Optimal energy trade-off schedules

Barcelo

Cole

Letsios

et al. 2013

Sustainable Computing: Informatics and Systems

Self Cite

View full text Add to dashboard Cite

show abstract

“…Several studies on this metric suggest that the optimal dynamic speed scaling function should be a function of n, the number of jobs in the system. Later, Bansal, Chan and Pruhs [8] showed that SRPT with the speed scaling function P −1 (n+1) is 3-competitive for an arbitrary power function P . Andrew, Lin and Wierman [10] show that SRPT with speed scaling function P −1 (nβ) is 2-competitive, and is optimal among the class of "natural" speed scaling functions.…”

Section: B Speed Scaling Systemsmentioning

confidence: 99%

“…This work pre-dated the widely-cited Yao, Demers, and Shenker (YDS) paper [3] on speed scaling in 1995, which provided the first formal treatment of the speed scaling problem, including several heuristic algorithms, as well as proofs that they were within a constant factor of optimal. The latter paper triggered substantial follow-on work by Albers [4], [5], Bansal [6], [7], [8], and others on improved algorithms, tighter bounds, and alternative metrics for evaluating speed scaling designs.…”

Section: Introductionmentioning

confidence: 99%

Decoupled speed scaling: Analysis and evaluation

Elahi¹,

Williamson²,

Woelfel³

2014

Performance Evaluation

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Abstract-In this paper, we introduce the notion of decoupled speed scaling, wherein the speed scaling function is completely decoupled from the scheduling policy used in a simple singleserver computer system. As an initial result, we first demonstrate that the Fair Sojourn Protocol (FSP) scheduling policy does not work properly with coupled (native) speed scaling, but that it can and does work well with decoupled speed scaling. We then compare the performance of PS, SRPT, and FSP scheduling policies under decoupled speed scaling, and demonstrate significant advantages for FSP. Our simulation results suggest that it might be possible to simultaneously achieve fairness, robustness, and near optimality with decoupled speed scaling.

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Power-Efficient Assignment of Virtual Machines to Physical Machines

Aroca

Anta

Mosteiro

et al. 2014

Adaptive Resource Management and Scheduling for Cloud Computing

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Abstract. Motivated by current trends in cloud computing, we study a version of the generalized assignment problem where a set of virtual processors has to be implemented by a set of identical processors. For literature consistency, we say that a set of virtual machines (VMs) is assigned to a set of physical machines (PMs). The optimization criteria is to minimize the power consumed by all the PMs. We term the problem Virtual Machine Assignment (VMA). Crucial differences with previous work include a variable number of PMs, that each VM must be assigned to exactly one PM (i.e., VMs cannot be implemented fractionally), and a minimum power consumption for each active PM. Such infrastructure may be strictly constrained in the number of PMs or in the PMs' capacity, depending on how costly (in terms of power consumption) it is to add a new PM to the system or to heavily load some of the existing PMs. Low usage or ample budget yields models where PM capacity and/or the number of PMs may be assumed unbounded for all practical purposes. We study four VMA problems depending on whether the capacity or the number of PMs is bounded or not. Specifically, we study hardness and online competitiveness for a variety of cases. To the best of our knowledge, this is the first comprehensive study of the VMA problem for this cost function.

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Speed Scaling with an Arbitrary Power Function

Cited by 37 publications

References 12 publications

Optimal energy trade-off schedules

Optimal energy trade-off schedules

Decoupled speed scaling: Analysis and evaluation

Power-Efficient Assignment of Virtual Machines to Physical Machines

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