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Many studies have shown that Vegas TCP has a better throughput and stability than Reno TCP in homogeneous networks with a single TCP flavor, but performs less well in heterogeneous networks in which two TCP flavors coexist. The progressive behavior of Reno TCP and the conservative behavior of Vegas TCP cause a bias when they are used simultaneously, and thus Vegas TCP fails to obtain a fair share of the bandwidth. This paper examines the origins of this bias and proposes a threshold-based congestion control mechanism designed to alleviate the resulting unfairness problem. The simulation results show that the proposed scheme achieves a higher throughput than the conventional Vegas TCP scheme and preserves the stability of the conventional scheme when used in heterogeneous wired and wireless networks.