The holy grail for Infrastructure as a Service (IaaS) providers is to maximize the utilization of their infrastructure while ensuring the quality of service (QoS) for the virtual machines they host. Although the frameworks in charge of managing virtual machines (VM) on pools of physical ones (PM) have been significantly improved, enabling to manage large- scale infrastructures composed of hundreds of PMs, most of them do not efficiently handle the aforementioned objective. The main reason is that advanced scheduling policies are subject to important and hard scalability problems, that become even worse when VM image transfers have to be considered. In this article, we provide a new validation of the Distributed VM Scheduler approach (DVMS) in a twofold manner. First, we provide a formal proof of the algorithm based on temporal logic. Second, we discuss large-scale evaluations involving up to 4.7K VMs distributed over 467 nodes of the Grid'5000 testbed. As far as we know, these experiments constitute the largest in vivo validation that has been performed so far with decentralized VM schedulers. These results show that a cooperative approach such as ours permits to fix overload problems in a reactive and scalable way.