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Optimising for energy or robustness? Trade-offs for VM consolidation in virtualized datacenters under uncertainty

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Abstract

Reducing the energy consumption of virtualized datacenters and the Cloud is very important in order to lower CO\( _2 \) footprint and operational cost of a Cloud operator. However, there is a trade-off between energy consumption and perceived application performance. In order to save energy, Cloud operators want to consolidate as many Virtual Machines (VM) on the fewest possible physical servers, possibly involving overbooking of resources. However, that may involve SLA violations when many VMs run on peak load. Such consolidation is typically done using VM migration techniques, which stress the network. As a consequence, it is important to find the right balance between the energy consumption and the number of migrations to perform. Unfortunately, the resources that a VM requires are not precisely known in advance, which makes it very difficult to optimise the VM migration schedule. In this paper, we therefore propose a novel approach based on the theory of robust optimisation. We model the VM consolidation problem as a robust Mixed Integer Linear Program and allow to specify bounds for e.g. resource requirements of the VMs. We show that, by using our model, Cloud operators can effectively trade-off uncertainty of resource requirements with total energy consumption. Also, our model allows us to quantify the price of the robustness in terms of energy saving against resource requirement violations.

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Notes

  1. http://www.datacenterdynamics.com/news/facebook-data-centers-energy-use-up-in-2012/80642.fullarticle.

  2. We explicitly acknowledge the fact that the power model used is simple but the model can be easily extended to a more complex one.

  3. Please note that Bertsimas and Thiele in [5] show how to reformulate problem (1) in the case that uncertainty also affects the cost vector \( \mathbf {c} \) and the right-hand side \( \mathbf {b} \) of problem (1).

  4. For simplicity, we refer to it as \( \Gamma \) in this section.

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Acknowledgments

This research was partially supported by the Spanish Government and ERDF through CICYT project TEC2013-48099-C2-1-P and by the Knowledge Foundation of Sweden through the project READY. The authors would like to thank Dr. Igor Buchberger for useful discussion on the robust counterpart formulation.

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Authors and Affiliations

  1. Universitat Politècnica de Catalunya (UPC), Barcelona, Spain

    Enrica Zola

  2. Karlstad University (KAU), Karlstad, Sweden

    Andreas J. Kassler

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  1. Enrica Zola
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  2. Andreas J. Kassler
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Correspondence to Enrica Zola.

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Zola, E., Kassler, A.J. Optimising for energy or robustness? Trade-offs for VM consolidation in virtualized datacenters under uncertainty. Optim Lett 11, 1571–1592 (2017). https://doi.org/10.1007/s11590-016-1065-x

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