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This paper presents a semi-Markov model that evaluates the performance of TCP connections with asymmetric Additive Increase and Multiplicative Decrease (AIMD) congestion control settings involved in sharing of a common drop-tail router. We study the fairness of the connections and their individual bandwidth utilizations as well as packet loss rates. We confirm that certain asymmetric AIMD settings may achieve fairness in bandwidth sharing. We also found that while connections with asymmetric AIMD settings operate at different bandwidth utilizations, they generally experience similar packet loss rate.