In this paper, we address the problem of guaranteed transmission of video flows in the context of WiMAX mesh networks for video surveillance purposes. The main design issue in such networks is to maximize the number of flows that can be accommodated in critical situations. Guaranteeing a throughput for individual flows in a multi-hop WiMAX network is a challenging task. We consider a specific dedicated architecture where communication interference can be avoided using multi- radio, multi-channel equipments where a certain latitude is offered in the configuration of video camera rates. To this end, we introduce a global utility function for the network based on the accepted video flows, their respective data rates, and the relative importance of these flows (priority). We formulate the rate assignment problem as an Integer Linear Program (ILP) that maximizes the network utility while satisfies the QoS requirements. Since the running time required to obtain the optimal solution increases exponentially with the number of nodes in the network, optimal results are only possible when the problem scale is small. Thus, the optimal solution is used for benchmarking purposes only. In this paper, we also propose new practical tree construction techniques as well as an efficient rate assignment algorithm. We compare the resulting performance of our algorithm with the optimal solution, and show that it closes a considerable portion of the gap from the theoretical optimal solution.