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Three collision-avoidance protocols are analyzed that use omni-directional packet reception together with omni-directional transmissions, directional transmissions, or a combination of both. A simple model is introduced to analyze the performance of these collision avoidance protocols in multi-hop networks with arbitrary topologies. The numerical results of this analysis show that collision avoidance using a narrow antenna beamwidth for the transmission of all control and data packets achieves the highest throughput among the three collision avoidance schemes considered. Simulation experiments of the popular IEEE 802.11 MAC protocol and its variants based on directional transmissions and omni-directional packet reception validate the results predicted in the analysis. The results further show that narrow-beamwidth transmissions can also reduce the average delay experienced by nodes. It is concluded that the advantage of spatial reuse achieved by narrow-beamwidth transmissions outweighs that of conservative collision avoidance schemes featured by the omnidirectional transmission of some control packets. This is due to the fact that the latter requires far more stringent coordination of nodes with their neighbors and hidden terminals, which can lead to much more channel resource wasted due to nodes' excessive waiting time.