This paper addresses the problem of mobility management in Content Delivery Networks (CDN). We introduce a CDN architecture where admission control is performed at mobility aware access routers. We formulate a Markov Modulated Poisson Decision Process for access control that captures the bursty nature of data and packetized traffic together with the heterogeneity of multimedia services. The optimization of performance parameters, like the blocking probabilities and the overall utilization, is conducted and the structural properties of the optimal solutions are also studied. Heuristics are proposed to encompass the computational difficulties of the optimal solution when several classes of multimedia traffic are considered.