Virtual machine (VM) placement problem has been active research area over the past decade. The research community needs an open simulation framework that can accurately and scalably simulate virtual machine operations including live migrations. However, existing cloud simulation frameworks cannot reproduce live migration behaviors correctly. A naive migration model, not considering memory update operations nor resource sharing contention, can drastically underestimate the duration of a live migration and the size of migration traffic. In this paper, we propose a simulation framework of virtualized distributed systems with the first class support of live migration operations. We developed a resource share calculation mechanism for VMs and a live migration model implementing the precopy migration algorithm of Qemu/KVM. We extended a widely-used simulation toolkits, SimGrid, which allows users to simulate large-scale distributed systems by using user friendly programming API. Through experiments, we confirmed that our simulation framework correctly reproduced live migration behaviors of the real world under various conditions. Through a first use case, we also confirmed that it is possible to conduct large scale simulations of complex virtualized workloads upon hundred thousands of VMs upon thousands of physical machines (PMs).