In this paper, we undertake the problem of server consolidation in virtualized data centers from the perspective of approximation algorithms. We formulate server consolidation as a stochastic bin packing problem, where the server capacity and an allowed server overflow probability p are given, and the objective is to assign VMs to as few physical servers as possible, and the probability that the aggregated load of a physical server exceeds the server capacity is at most p.
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Chen et al. (2011) studied this question.