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Routing is a critical element of wireless mesh network design and serves to enhance the network's capacity as a whole and the performance of individual flows. Achieving both robustness and efficiency in mesh routing is an important, yet challenging issue due to uncertain traffic demands. To ensure routing performance while retaining robustness, we explore using knowledge of historical traffic demands. Two concepts of robustness, namely congestion robustness and performance ratio robustness are examined. We show that though a routing that is robust with respect to the interior of a convex region of traffic demands implies future robustness, the similar property does not hold for the boundaries of the region because the performance ratio is not limited by the boundaries, while the absolute congestion is. We develop a performance-ratio robust routing formulation for multi-radio, multi-channel networks that exploits traffic demands that fall into a predicted region. A linear problem transformation is presented to solve this highly complex non-linear formulation. A detailed simulation study is conducted over representative topologies with a real traffic trace to evaluate the novel algorithm. We find a strong performance improvement with little margin for further gains.