This document summarizes a research paper on dynamic consolidation of virtual machines in cloud data centers to manage overloaded hosts while maintaining quality of service constraints. It proposes using a Markov chain model and control algorithm to optimally detect host overloads by maximizing the average time between VM migrations, while meeting a specified QoS goal. The algorithm handles unknown workloads using a multisize sliding window approach. Evaluation shows the algorithm efficiently solves the problem of host overload detection as part of dynamic VM consolidation in cloud computing systems.