Improving the energy efficiency of cloud computing systems has become an important issue because the electric energy bill for 24/7 operation of these systems can be quite large. The focus of this paper is on the virtual machine consolidation in a cloud computing system as a way of lowering daily energy consumption of the system. In contrast to the existing works that assume resource demands of virtual machines are given as scalar variables, this paper treats these demands as random variables with known means and standard deviations because the demands are not deterministic in many situations. These random variables may be correlated with one another, and there are several types of resources which can be performance bottlenecks. Therefore, both correlations and resource type heterogeneity must be considered. The virtual machine consolidation problem is thus formulated as a multi-capacity stochastic bin packing problem. This problem is NP-hard, so we present a heuristic method to efficiently solve the problem. Simulation results show that, in spite of its simplicity and scalability, the proposed method produces high quality solutions.
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