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Data centres and similar server clusters consume a large amount of energy. However, not all consumed energy produces useful work. Servers consume a disproportional amount of energy when they are idle, underutilised, or overloaded. The effect of these conditions can be minimised by attempting to balance the demand for and the supply of resources through a careful prediction of future workloads and their efficient consolidation. In this paper we extend the cutting stock problem for consolidating workloads having stochastic characteristics. Hence, we employ the aggregate probability density function of co-located and simultaneously executing services to establish valid patterns. A valid pattern is one yielding an overall resource utilisation below a set threshold. We tested the scope and usefulness of our approach on a 16-core server with 29 different benchmarks. The workloads of these benchmarks have been generated based on the CPU utilisation traces of 100 real-world virtual machines which we obtained from a Google data centre hosting more than 32000 virtual machines. Altogether, we considered 600 different consolidation scenarios during our experiment. We compared the performance of our approach-system overload probability, job completion time, and energy consumption-with four existing/proposed scheduling strategies. In each category, our approach incurred a modest penalty with respect to the best performing approach in that category, but overall resulted in a remarkable performance clearly demonstrating its capacity to achieve the best trade-off between resource consumption and performance.

The energy consumption of large-scale data centers or server clusters is expected to grow significantly in the next couple of years contributing to up to 13% of the worldwide energy demand in 2030. As the involved processing units require a disproportional amount of energy when they are idle, underutilized, or overloaded, balancing the supply of and the demand for computing resources is a key issue to obtain energy-efficient server consolidations. Whereas traditional concepts mostly consider deterministic predictions of the future workloads or only aim at finding approximate solutions, in this article, we propose an exact approach to tackle the problem of assigning jobs with (not necessarily independent) stochastic characteristics to a minimal amount of servers subject to further practically relevant constraints. As a main contribution, the problem under consideration is reformulated as a stochastic bin packing problem with conflicts and modeled by an integer linear program. Finally, this new approach is tested on real-world instances obtained from a Google data center.

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