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FAST TCP is a promising new transfer control protocol developed for high-speed long-latency networks, whose performance has previously only been studied for data traffic sent in one direction. In this study, the authors propose a mathematical model for bi-directional connections using the FAST TCP protocol, which captures the asymmetric bandwidth dynamics in duplex dumbbell networks, prevalent in ADSL, satellite and other high-speed technologies. Using this model, the authors obtain a powerful result that the queue delays observed by opposite FAST TCP flows only have a time difference in a dumbbell network. Furthermore, the authors establish the conditions under which the bi-directional FAST TCP flows achieve stability, and on this basis the throughput rates of the forward and backward flows at steady-state are deduced. The authors find that, in the case of bandwidth asymmetry and one flow in each direction, in equilibrium the throughput of the bi-directional FAST TCP flows can only achieve the smaller link capacity of the duplex links, and the link with larger capacity is not fully occupied. These theoretical findings are corroborated by NS2 simulations.