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OpenFlow is a programmable network protocol and associated hardware designed to effectively manage and direct traffic by decoupling control and forwarding layers of routing. This paper presents an analytical framework for optimization of forwarding decisions at the control layer to enable dynamic Quality of Service (QoS) over OpenFlow networks and discusses application of this framework to QoS-enabled streaming of scalable encoded videos with two QoS levels. We pose and solve optimization of dynamic QoS routing as a constrained shortest path problem, where we treat the base layer of scalable encoded video as a level-1 QoS flow, while the enhancement layers can be treated as level-2 QoS or best-effort flows. We provide experimental results which show that the proposed dynamic QoS framework achieves significant improvement in overall quality of streaming of scalable encoded videos under various coding configurations and network congestion scenarios.