Speed Scaling with an Arbitrary Power Function

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

doi:10.1137/1.9781611973068.76

Cited by 100 publications

(147 citation statements)

References 7 publications

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“…In this paper we consider the more general model (see for example [9]) in which the power P (s(t)) of a processor is any differentiable convex function of the speed s(t). Then the energy consumption is equal to the power integrated over time.…”

Section: Preliminariesmentioning

confidence: 99%

Green scheduling, flows and matchings

Bampis

Letsios

Lucarelli

2015

Theoretical Computer Science

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International audienceRecently, optimal combinatorial algorithms have been presented for the energy minimization multiprocessor speed-scaling problem with migrations [5] and [7]. These algorithms use repeated maximum-flow computations that allow the partition of the set of jobs into subsets in which all the jobs are executed at the same speed. The optimality of these algorithms is based on a series of technical lemmas showing that this partition and the corresponding speeds lead to the minimization of the energy consumption. In this paper, we show that both the algorithms and their analysis can be greatly simplified. In order to do this, we formulate the problem as a convex cost flow problem in an appropriate flow network. Furthermore, we show that our approach is useful to solve other problems in the dynamic speed-scaling setting. As an example, we consider the preemptive open-shop speed-scaling problem and we propose a polynomial-time algorithm for finding an optimal solution based on the computation of convex cost flows. We also propose a polynomial-time algorithm for minimizing a linear combination of the sum of the completion times of the jobs and the total energy consumption, for the non-preemptive multiprocessor speed-scaling problem. Instead of using convex cost flows, our algorithm is based on the computation of a minimum weighted maximum matching in an appropriate bipartite graph

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Section: Preliminariesmentioning

confidence: 99%

Green scheduling, flows and matchings

Bampis

Letsios

Lucarelli

2015

Theoretical Computer Science

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“…Bansal, Chan, and Pruhs minimize arbitrary power functions for speed scaling in job scheduling [8]. The problem is to schedule the execution of n computational jobs on a single processor, whose speed may vary within a countable collection of intervals.…”

Section: Related Workmentioning

confidence: 99%

“…This is commonly known as VM consolidation [6,7]. However, despite the static power, the dynamic power consumption of a server, which has been shown to be superlinear on the load of a given computational resource [8,9], is also significant and cannot be ignored. Since the definition of load is not precise, we borrow the definition in [4] and define the load of a server as the amount of active cycles per second a task requires, an absolute metric independent of the operating frequency or the number of cores of a PM.…”

Section: Introductionmentioning

confidence: 99%

Power-efficient assignment of virtual machines to physical machines

Aroca

Anta

Mosteiro

et al. 2016

Future Generation Computer Systems

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h i g h l i g h t s • Formal definition of 4 versions of the Virtual Machine Assignment problem (VMA). • Study of hardness of the offline version. • Study of competitiveness of the online version. • Proposal of algorithms for the online version. a b s t r a c tMotivated 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 criterion 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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“…At processing rates higher than a base rate the PR function is convex increasing, whereas in the lower portion of the rate range the PR function is at best linear [5]- [7], [13]- [15]. Since packet processing times increase linearly as the rate decreases, scaling the processing rate below yields no tangible energy savings per packet.…”

Section: Optimum Power-rate Functionmentioning

confidence: 99%

Performance bounds of rate-adaptation schemes for energy-efficient routers

Francini¹,

Stiliadis²

2010

2010 International Conference on High Performance Switching and Routing

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To maximize the energy efficiency of packet networks, energy use in network equipment should scale rigorously with the traffic load. Rate adaptation is gaining popularity as a promising framework for achieving energy proportionality in the data-path components of routers and switches, but a thorough characterization of its energy-saving capabilities and impact on network performance is still lacking. In this paper, we present novel rate-adaptation schemes that are easy to implement, amenable to incremental deployment in packet switches and routers, and whose negative effect on end-toend packet delays is bounded. We derive tight lower and upper bounds on energy consumption that we use to further refine the design of our schemes. Our analysis indicates that large-scale deployments of rate adaptation can enable substantial energy savings, as large gains can be attained in individual data-path devices under parametric configurations that do not compromise the end-to-end delay performance of the network.

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Speed Scaling with an Arbitrary Power Function

Cited by 100 publications

References 7 publications

Green scheduling, flows and matchings

Green scheduling, flows and matchings

Power-efficient assignment of virtual machines to physical machines

Performance bounds of rate-adaptation schemes for energy-efficient routers

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