© 2016 IEEE.In anticipatory networking, channel prediction is used to improve communication performance. This paper describes a new approach for allocating resources to video streaming traffic while accounting for quality of service. The proposed method is based on integrating a model of the user's local play-out buffer into the radio access network. The linearity of this model allows to formulate a Linear Programming problem that optimizes the trade-off between the allocated resources and the stalling time of the media stream. Our simulation results demonstrate the full power of anticipatory optimization in a simple, yet representative, scenario. Compared to instantaneous adaptation, our anticipatory solution shows impressive gains in spectral efficiency and stalling duration at feasible computation time while being robust against prediction errors.