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In this paper, we propose a simple algorithm to adaptively adjust the value of dupthresh, the duplicate acknowledgement threshold that triggers the transmission control protocol (TCP) fast retransmission algorithm, to improve the TCP performance in a network environment with persistent packet reordering. Our algorithm uses an exponentially weighted moving average (EWMA) and the mean deviation of the lengths of the reordering events reported by a TCP receiver with the duplicate selective acknowledgement (DSACK) extension to estimate the value of dupthresh. We also apply an adaptive upper bound on dupthresh to avoid the retransmission timeout events. In addition, our algorithm includes a mechanism to exponentially reduce dupthresh when the retransmission timer expires. With these mechanisms, our algorithm is capable of converging to and staying at a near-optimal interval of dupthresh. The simulation results show that our algorithm improves the protocol performance significantly with minimal overheads, achieving a greater throughput and fewer false fast retransmissions.