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The Internet is witnessing a rapid increase in video traffic. Due to the scalability and the cost-savings offered by cloud-computing, Internet video service providers are increasingly delivering their content from multi-tenant cloud data centers. One of the major challenges faced by such a video service provider is the management of the Quality-of-Experience (QoE) of the end-users in the presence of Variable Bit Rate (VBR) video flows, time varying network conditions in the Internet, and the bounded egress bandwidth provided by the data center. To this end, we present InSite, a light-weight and easy-to-deploy solution for managing the QoE of a set of video flows of a service provider, which are served from a data center. InSite is deployed at the egress of a data center, between the video servers and the clients, and manages the video flows that are transmitted over TCP. The solution uses a novel generalized binary search technique to concurrently search for the appropriate flow rates for a set of flows, with the goal of maximizing the QoE-fairness across the flows, as opposed to TCP-fairness. The search takes into account the total egress bandwidth allocated for the set of video flows at the data center, the unknown and possibly time-varying capacities of any remote bottleneck links, and the playout buffer sizes of the video flows. The solution is also designed to operate with minimal modifications to the video servers and the clients. In our evaluations using extensive ns-3 simulations and a testbed implementation for serving videos over TCP, we observe that deploying InSite achieves several folds reduction in playout stalls over a system without InSite.