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This paper presents a novel framework for streaming video over a Differentiated Services (DiffServ) network that jointly considers video source coding, packet classification and error concealment within the scope of cost-distortion optimization. Our formulation incorporates the random network delay for each packet into the calculation of the probability of packet loss and manages the end-to-end packet delay by selecting the encoding parameters and packet priority. We formulate two approaches to evaluate the performance of the proposed framework: a minimum distortion approach and a minimum cost approach, in which the encoding mode and priority class for each packet are optimally selected so as to minimize the total distortion subject to cost constraints, or to minimize the total cost subject to end-to-end distortion constraints. Simulation results demonstrate the advantage of jointly adapting the source coding and packet classification.