This paper presents a channel reservation and preemption (CRP) model using overlapping regions in a cellular network with multiple sectors. To fully exploit and reuse the frequencies, directional antennas are installed on base stations (BSs) to divide the coverage into a number of equal-sized sectors. When traffic is unevenly distributed across the sectors in a BS, channel utilization in every sector may become very different; low-traffic sectors may be underutilized while high-traffic sectors may be overutilized. A CRP scheme is thus proposed to more efficiently utilize free channels among sectors. CRP aims at reducing the dropping probabilities of handoff calls. Specifically, when free channels in a sector are not available, a handoff call, instead of being dropped, is allowed to preempt an ongoing call residing in the overlapping region of two adjacent sectors or two neighbor cells. Under CRP, the preempted ongoing call will not be disconnected, because it can switch over its service to the BS of a neighbor cell or to another directional antenna of an adjacent sector. For the purpose of evaluation, we build an analytical model for the proposed CRP using six-tuple Markov chains. Analytical results show that the proposed CRP can significantly reduce the dropping probabilities of inter-sector handoff calls, particularly when traffic between two sectors is not evenly distributed.