Emerging network paradigms, such as Software Defined Networking and Network Function Virtualization, represent the key enablers for efficient and cost-effective deployment and management of cloud-based edge networks, where a number of cooperating virtual machines can implement the tasks traditionally performed by expensive and disrupting network middleboxes. A key feature in such a scenario is the capability of live migrating a group of correlated virtual machines as a single entity representing a customer's profile. Multiple VM live migration is a topic that has not been thoroughly studied in the literature. This manuscript presents a relatively simple model that can be used to derive some performance indicators, such as the whole service downtime and the total migration time, and allows to properly design the cloud-based edge network. The model is used to compare some simple scheduling strategies for the VM migration and to provide guidelines to such implementation.