Video is expected to be the dominant application by traffic volume over mobile networks in the near future. Mobile network operators are deploying video optimization techniques to enhance the user experience and network utilization for video delivery. Video optimization is typically “out‐of‐network” and includes techniques such as transcoding, transrating, time shifting and pacing that are implemented outside of mobile radio access and core networks. However, such techniques cannot easily exploit information about real time cell congestion and radio conditions for the video terminals because it is difficult to obtain such information from the radio access network. We propose a novel “in‐network” video optimization technique, named Adaptive Guaranteed Bit Rate (AGBR), for HTTP‐based Adaptive Streaming (HAS) video. This optimization technique is implemented at the base station and can thus exploit knowledge of the radio and congestion conditions. With only limited knowledge of the video stream properties or content, AGBR works by adjusting the throughput delivered to the different HAS clients that in turn adjust the video quality they request. The optimization algorithm maximizes aggregate quality across multiple video flows served by the base station without starving data clients, thereby improving the overall quality of experience. We demonstrate through extensive analytical modeling and simulations that AGBR can adapt to changing network conditions to support more video sessions at an acceptable quality than alternative algorithms, while enforcing fairness among all users competing for resources within a sector. © 2013 Alcatel‐Lucent.