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This paper proposes a priority-based contention period allocation scheme for devices using a directional antenna in smart home. The use of directional antenna in contention period causes many collisions due to deafness problem. To mitigate this obstacle with small changes of the current IEEE 802.11ad standard, we introduce the scheme limiting the access to contention period according to traffic type. Numerical results show the proposed scheme outperforms more than twice compared to that of the IEEE 802.11ad. Various beamwidths and radiation efficiencies are considered. The results show that the narrower beamwidth deliver more throughputs.