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In this paper, we propose an analytic approach of modeling a closed-loop network with multiple feedback loops using fluid-flow approximation. Specifically, we model building blocks of a network (i.e., the congestion control mechanism of TCP, propagation delay of a transmission link, and the buffer of a router) as independent continuous-time systems. By interconnecting these systems, we obtain the model for a complex closed-loop network. We improve the accuracy of analytic models for TCP congestion control and RED router by extending existing fluid-flow models. First, we obtain a block diagram for each continuous-time system using a standard CAD tool widely used in control engineering. Second, we evaluate the performance of a closed-loop network with multiple feedback loops by connecting these block diagrams. We also validate the effectiveness of our analytic approach by comparing our analytic results with simulation results. Unlike other fluid-based modeling approaches, our analytic approach is scalable and accurate; our analytic approach is scalable in terms of the number of TCP connections and routers since both input/output of all continuous-time systems are uniformly defined as a packet transmission rate. Our analytic approach is accurate since the timeout mechanism of TCP and the packet dropping algorithm of RED router are rigorously modeled in our continuous-time systems.