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To efficiently provide a video streaming service in home networks, a network node should support QoS (Quality of Service) for the streaming videos. In order to guarantee QoS, it is necessary to allocate the high bandwidth for the video stream flow when multiple flows compete for the scarce bandwidth resource. In this paper, we propose a novel bandwidth sharing scheme, called W-BS (Weighed Bandwidth Sharing), for video streaming service in home networks. To provide network stability in a congested network, the W-BS scheme shares the bandwidth according to the target utilization of bottleneck link. It also adaptively applies weighting factor to service traffics. Through the simulation results, we prove that the proposed scheme guarantees the quality of the video streaming service in home networks.