In this paper, we consider a resource allocation scheme for millimeter wave-based wireless personal area networks using directional antennas. This scheme involves scheduling the reservation period of medium access control for IEEE 802.15.3c. Objective functions are considered to minimize the average delay and maximize throughput; and two scheduling algorithms-namely, MInMax concurrent transmission and MAxMin concurrent transmission-are proposed to provide a suboptimal solution to each objective function. These are based on an exclusive region and two decision rules that determine the length of reservation times and the transmission order of groups. Each group consists of flows that are concurrently transmittable via spatial reuse. The algorithms appropriately apply two decision rules according to their objectives. A real video trace is used for the numerical results, which show that the proposed algorithms satisfy their objectives. They outperform other schemes on a range of measures, showing the effect of using a directional antenna. The proposed scheme efficiently supports variable bit rate traffic during the reservation period, reducing resource waste.