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To ensure probabilistic guarantees on quality of service in content delivery networks (CDN), an access control support is needed that takes into account a proper differentiation of requests and performs session based decisions, managing different types of services and different service phases. In this paper we introduce a CDN architecture with access control capabilities at session aware access routers. We formulate a Markov modulated Poisson decision process for access control that captures the heterogeneity of multimedia services and the variable availability of resources due to the network congestions that characterize a non-dedicated network environment. The structural properties of the optimal solutions are studied and considered as the basis for the formulation of heuristics that perform close to the optimal policy.