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Video streaming over mesh networks operates under stringent network resource constraints, with a large number of video sessions competing for limited network resources. In this work, we aim to establish so-called resource-distortion models to characterize the inherent relationship between the allocated network resources to each video session and its end-to-end video distortion or presentation quality at the receiver end. We observed that priority-based packet scheduling has significant impact on such resource-distortion relationship. Using ANN-based learning methods, we develop an end-to-end packet delay bound violation (PDBV) probability model for video streaming over multi-hop networks with priority-based packet scheduling. We then derive a quadratic video transmission distortion model to capture the unique behavior of priority-based packet scheduling and its impact on the end-to-end video distortion. Based on these resource-distortion models, we are able to predict the end-to-end distortion for video streaming over multi-hop networks with priority-based packet scheduling. Our extensive experimental results demonstrate that the proposed method is very accurate.