The convergence of communication and computation portrays a new vision of the services that the Internet can bring to users. There is an emerging need for isolated and protected virtual resource aggregates composed by the sharing in time and space of a set of physical entities. This paper proposes a flexible and open framework to implement this service offering a dynamic access to virtual private interconnected capacities. We develop the underlying virtual private execution infrastructure concept and propose a model to control their underlying networks. We illustrate these ideas by describing the adaptation of our HIPerNET software to the context of the experimental largescale Grid'5000 platform, thus allowing isolated and customised experiments. The goal of the designed service is to provide computer-science researchers with right-timed and right-sized experimental virtual infrastructures. Preliminary experimental results highlight the potential and challenges of this approach.