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Resource allocation plays a critical role in multisession video streaming over mesh networks to maximize the overall video presentation quality under transmission delay and network resource constraints. A critical component in efficient resource allocation is to analyze and model the multihop queuing behavior along the transmission path, estimate the packet loss ratio due to delay bound violation, and predict the amount of video quality degradation after multihop video transmission. In this work, we develop a multihop packet delay bound violation model to predict the packet loss probability and end-to-end distortion for video streaming over multihop networks. To this end, we extract salient features to characterize the input source and network conditions of links along the transmission path and construct a learning-based model using artificial neural network (ANN). Based on this model, we then formulate the resource allocation into a nonconvex optimization problem which aims to minimize the overall video distortion while maintaining fairness between sessions. We solve this optimization problem using Lagrangian duality methods. Extensive experimental results demonstrate that, with this widely-used offline-training-online-estimation mechanism, the proposed model is potentially applicable to almost all network conditions and can provide fairly accurate estimation results as compared with other models with a given sample data set. The proposed optimization algorithm achieves more efficient resource allocation than existing schemes.