Improving the utilization of physical resources and reducing energy consumption in a cloud data center includes providing a plurality of virtual machines in the cloud data center; periodically reallocating resources of the plurality of virtual machines according to a current resource demand of the plurality of virtual machines in order to minimize a number of active physical servers required to handle a workload of the physical servers; maximizing a mean inter-migration time between virtual machine migrations under the quality of service requirement based on a Markov chain model; and using a multisize sliding window workload estimation process for a non-stationary workload to maximize the mean inter-migration time.