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Congestion control in multi-hop infrastructure wireless mesh networks is both an important and a unique problem. It is unique because it has two prominent causes of failed transmissions which are difficult to tease apart - lossy nature of wireless medium and high extent of congestion around gateways in the network. The concurrent presence of these two causes limits applicability of already available congestion control mechanisms, proposed for wireless networks. Prior mechanisms mainly focus on the former cause, ignoring the latter one. Therefore, we address this issue to design an end-to-end congestion control mechanism for infrastructure wireless mesh networks in this paper. We formulate the congestion control problem and map that to the restless multi-armed bandit problem, a well-known decision problem in the literature. Then, we propose three myopic policies to achieve a near-optimal solution for the mapped problem since no optimal solution is known to this problem. We perform comparative evaluation through ns-2 simulation and a real testbed experiment with a wireline TCP variant and a wireless TCP protocol. The evaluation reveals that our proposed mechanism can achieve up to 52% increased network throughput and 34% decreased average energy consumption per transmitted bit in comparison to the other end-to-end congestion control variants.