To achieve an efficient and adapted network usage during video content distribution, bandwidth is classically controlled by limiting the outgoing server traffic with a token bucket policy. In this paper, we propose a predictive hull-based token bucket parameter setting in the specific context of a closed domestic network. Hull is an abstraction of the bitrate, dynamically following the bandwidth requirement evolution. The hull mechanism guarantees a maximal quality of service (QoS) for the streaming of variable bitrate encoded videos and a minimal over-reservation according to the implementation constraints. In the case of multiple simultaneous video streaming, we propose a shifting technique to reduce the impact of peaks. Postponing the streaming starting time of a video helps to decrease the maximal required bandwidth. Simulations and experiments show the effectiveness of the combined approaches to optimize online bandwidth usage, guaranteeing the best QoS (reduced delay) and quality of experience for multiple video streaming applications.