The Software Defined Networking (SDN) paradigm proposes to decouple the control plane (decision-making process) and the data plane (packet forwarding) to overcome the limitations of traditional network infrastructures, which are known to be difficult to manage, especially at scale. Although there are previous works focusing on the problem of Quality of Service (QoS) routing in SDN networks, only few solutions have taken into consideration the network consistency, which reflects the adequacy between the decisions made and the decisions that should be taken. Therefore, we propose a network architecture that guarantees the consistency of the decisions to be taken in an SDN network. A consistent QoS routing strategy is, then, introduced in a way to avoid any quality degradation of prioritized traffic, while optimizing resources usage. Thus, we proposed a traffic dispersion heuristic in order to achieve this goal. We compared our approach to several existing framework in terms of best-effort flows average throughput, average video bitrate and video Quality of Experience (QoE). The emulations results, which are performed using the Mininet environment, clearly demonstrate the effectiveness of the proposed approach that outperforms existing frameworks.