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In this paper, we study the issues of medium access control (MAC) for multihop wireless networks with directional antennas. Existing solutions to directional antenna MAC problems rarely account for the impact of minor lobes and typically assume that the neighboring nodes' locations are known a priori. As a result, they are not applicable to practical systems or mobile nodes. In this paper, we propose a reservation-based directional medium access control (RDMAC) protocol for multihop wireless networks based on the IEEE 802.11 distributed coordination function. The design objective of RDMAC is to increase the network throughput by reducing interference among neighboring nodes. We then develop an analytical model for RDMAC to investigate the throughput performance of RDMAC under arbitrary node density. The analytical model provides insights into RDMAC parameter settings. We also evaluate the performance of the proposed RDMAC through ns-2 simulations. The results validate the accuracy of our analytical model and show that our mechanism outperforms existing solutions, in terms of higher throughput.