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As an evolution of peer-to-peer (p2p) file-sharing applications, overlay-based networks are also adopted to efficiently distribute content with real-time constraints to a wide user population. In addition, they can be utilized to exploit application level strategies to overcome limitations imposed by the underlying network infrastructure, e.g., the lack of multicast support. In this perspective, the paper introduces an overlay content distribution network (CDN) able to sustain the real-time delivery of data streams. To better use resources, and to face the churn affecting users, the control and optimization of the CDN are performed through a model predictive control scheme. Simulations are provided to show the effectiveness of the proposed solution.