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This paper proposes an adaptive slot allocation mechanism to improve the performance of Transmission Control Protocol (TCP) in DOCSIS-based hybrid fiber coaxial (HFC) networks. The proposed mechanism is comprised of two parts: fast request transmission (FRT) and long packet deferment (LPD). FRT is designed to handle one-way TCP transfers, while LDP targets two-way transfers. Here "one-way transfers" means all active cable modems perform downloading; while "two-way transfers" indicates some perform downloading and some perform uploading. We analyze the proposed mechanism and conduct simulations using network simulator ns-2 to evaluate the performance of our mechanism. The results show that the proposed mechanism has better performance in terms of aggregate downstream throughput, access delay, and required buffer size, as compared to the original control mechanism of DOCSIS.