Optimal Algorithms for Right-Sizing Data Centers- Extended Version

Albers, Susanne; Quedenfeld, Jens

doi:10.48550/arxiv.1807.05112

Cited by 3 publications

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“…Proof. (Sketch) The proof is similar to the ones in [4] and [5]. First, the expected cost of an arbitrary algorithm A is not smaller than a converted deterministic algorithm A * in the continuous setting.…”

Section: Randomized Online Algorithmmentioning

confidence: 82%

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Zhai

Chau

Chen

2019

Proceedings of the Tenth ACM International Conference on Future Energy Systems

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Energy markets with retail choice enable customers to switch energy plans among competitive retail suppliers. Despite the promising benefits of more affordable prices and better savings to customers, there appears subsided participation in energy retail markets from residential customers. One major reason is the complex online decision-making process for selecting the best energy plan from a multitude of options that hinders average consumers. In this paper, we shed light on the online energy plan selection problem by providing effective competitive online algorithms. We first formulate the online energy plan selection problem as a metrical task system problem with temporally dependent switching costs. For the case of constant cancellation fee, we present a 3-competitive deterministic online algorithm and a 2-competitive randomized online algorithm for solving the energy plan selection problem. We show that the two competitive ratios are the best possible among deterministic and randomized online algorithms, respectively. We further extend our online algorithms to the case where the cancellation fee is linearly proportional to the residual contract duration. Through empirical evaluations using real-world household and energy plan data, we show that our deterministic online algorithm can produce on average 14.6% cost saving, as compared to 16.2% by the offline optimal algorithm, while our randomized online algorithm can further improve cost saving by up to 0.5%. CCS CONCEPTS• Theory of computation → Online algorithms.

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Section: Randomized Online Algorithmmentioning

confidence: 82%

“…Moreover, [3] and [4] show that by applying proper randomization, a 2-competitive online algorithm can be constructed based on [5]. In this paper, we combine these two papers and construct an uniform version of algorithms, which is more practical and easier to be implemented.…”

Section: Related Workmentioning

confidence: 99%

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Zhai

Chau

Chen

2019

Proceedings of the Tenth ACM International Conference on Future Energy Systems

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“…Already for the 1-dimensional case (i.e. identical machines), it is not trivial to round a fractional schedule without increasing the competitive ratio (see [26] and [2]). In d-dimensional space, it is completely unclear, if continuous solutions can be rounded without arbitrarily increasing the total cost.…”

Section: Introductionmentioning

confidence: 99%

“…Simply rounding up can lead to arbitrarily large switching costs, for example if the fractional solution rapidly switches between 1 and 1 + ǫ. Using a randomized rounding scheme like in [2] (that was used for homogeneous data centers) independently for each dimension can result in an infeasible schedule (for example, if λ t = 1 and x t = (1/d, . .…”

Section: Introductionmentioning

confidence: 99%

Algorithms for Energy Conservation in Heterogeneous Data Centers

Albers¹,

Quedenfeld²

2021

Preprint

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Power consumption is the major cost factor in data centers. It can be reduced by dynamically right-sizing the data center according to the currently arriving jobs. If there is a long period with low load, servers can be powered down to save energy. For identical machines, the problem has already been solved optimally by and .In this paper, we study how a data-center with heterogeneous servers can dynamically be right-sized to minimize the energy consumption. There are d different server types with various operating and switching costs. We present a deterministic online algorithm that achieves a competitive ratio of 2d as well as a randomized version that is 1.58d-competitive. Furthermore, we show that there is no deterministic online algorithm that attains a competitive ratio smaller than 2d. Hence our deterministic algorithm is optimal. In contrast to related problems like convex body chasing and convex function chasing, we investigate the discrete setting where the number of active servers must be integral, so we gain truly feasible solutions.

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“…Thereby, we seek truly feasible solutions. For homogeneous data centers (d = 1), both the offline and the online problem were solved optimally in [3,4].In this paper, we study heterogeneous data centers with general time-dependent operating cost functions. We develop an online algorithm based on a work function approach which achieves a competitive ratio of 2d + 1 + ǫ for any ǫ > 0.…”

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confidence: 99%

Algorithms for Right-Sizing Heterogeneous Data Centers

Albers¹,

Quedenfeld²

2021

Preprint

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Power consumption is a dominant and still growing cost factor in data centers. In time periods with low load, the energy consumption can be reduced by powering down unused servers. We resort to a model introduced by Lin, Wierman, Andrew and Thereska [23,24] that considers data centers with identical machines, and generalize it to heterogeneous data centers with d different server types. The operating cost of a server depends on its load and is modeled by an increasing, convex function for each server type. In contrast to earlier work, we consider the discrete setting, where the number of active servers must be integral. Thereby, we seek truly feasible solutions. For homogeneous data centers (d = 1), both the offline and the online problem were solved optimally in [3,4].In this paper, we study heterogeneous data centers with general time-dependent operating cost functions. We develop an online algorithm based on a work function approach which achieves a competitive ratio of 2d + 1 + ǫ for any ǫ > 0. For time-independent operating cost functions, the competitive ratio can be reduced to 2d + 1. There is a lower bound of 2d shown in [5], so our algorithm is nearly optimal. For the offline version, we give a graph-based (1 + ǫ)-approximation algorithm. Additionally, our offline algorithm is able to handle time-variable data-center sizes.

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Optimal Algorithms for Right-Sizing Data Centers- Extended Version

Cited by 3 publications

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Algorithms for Energy Conservation in Heterogeneous Data Centers

Algorithms for Right-Sizing Heterogeneous Data Centers

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