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Wireless mesh network (WMN) is an emerging technology for last-mile broadband Internet access. Despite extensive research on and even commercial implementations of WMNs, there are still some serious performance issues in the transport layer, where the performance of Transmission Control Protocol (TCP) degrades dramatically as the number of hops increases. Improving TCP performance over WMNs is a research area that has attracted a lot of attention in recent years and the focus of this paper. We take a cross-layer design approach to improve the performance of TCP for nodes farther from the Internet gateways by giving a higher priority to the packets that have traversed a larger number of hops over the WMN. The proposal changes the way that routing and scheduling algorithms work together and can be easily implemented in IEEE 802.16d WMNs. Extensive simulation results show that the proposed method successfully improve the TCP throughput by as much as three times over a small number of hops, whereas TCP generally performs poorly when the number of hops is large.