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In this paper, we propose a novel variable bit rate (VBR) controller for real-time H.264/scalable video coding (SVC) applications. The proposed VBR controller relies on the fact that consecutive pictures within the same scene often exhibit similar degrees of complexity, and consequently should be encoded using similar quantization parameter (QP) values for the sake of quality consistency. In order to prevent unnecessary QP fluctuations, the proposed VBR controller allows for just an incremental variation of QP with respect to that of the previous picture, focusing on the design of an effective method for estimating this QP variation. The implementation in H.264/SVC requires to locate a rate controller at each dependency layer (spatial or coarse grain scalability). In particular, the QP increment estimation at each layer is computed by means of a radial basis function (RBF) network that is specially designed for this purpose. Furthermore, the RBF network design process was conceived to provide an effective solution for a wide range of practical real-time VBR applications for scalable video content delivery. In order to assess the proposed VBR controller, two real-time application scenarios were simulated: mobile live streaming and Internet protocol television broadcast. It was compared to constant QP encoding and a recently proposed constant bit rate (CBR) controller for H.264/SVC. The experimental results show that the proposed method achieves remarkably consistent quality, outperforming the reference CBR controller in the two scenarios for all the spatio-temporal resolutions considered.