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Due to a continued increase in the speed and capacities of computing devices, combined with our society's growing need for mobile communication capabilities, multihop wireless networks (MWNs), such as wireless mesh networks (WMNs), have gained a lot of interest from the research community. Quality of service (QoS) provisioning in these networks is an essential component that is needed to support multimedia and real-time applications. On the other hand, directional antenna technology provides the capability for considerable increases in spatial reuse, which is essential in the wireless medium. In this paper, a bandwidth reservation protocol for QoS routing in TDMA-based MWNs using directional antennas is presented. The routing algorithm allows a source node to reserve a path to a particular destination with the needed bandwidth, which is represented by the number of slots in the data phase of the TDMA frame. Further optimizations to improve the efficiency and resource utilization of the network are also provided.