The idea of pay-per-use computing incarnated by the cloud paradigm is gaining a lot of success, both for entertainment and business applications. As a consequence, the demand for computing, storage and communication resources to be deployed in data center infrastructures is increasing dramatically. This trend is fostering new forms of infrastructure sharing such as cloud federations, where the excess workload is smartly distributed across multiple data centers, following some kind of mutual agreement among the participating cloud providers. Federated clouds can obtain great advantages from virtualization technologies and, in particular, from multiple virtual machine live migration techniques, which allow to flexibly move bulk workload across heterogeneous computing environments with minimal service disruption. However, a quantitative characterization of the performance of the inter-data center network infrastructure underlying the cloud federation is essential to guarantee user's quality of service and optimize provider's resource utilization. The main contribution of this paper is the definition and application of an analytical model for dimensioning inter-data center network capacity in order to achieve some given performance levels, assuming some simple multiple virtual machine live migration strategies. An extensive set of results are provided that allow to understand the impact of the many parameters involved in the design of a cloud federation network.