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In this paper we investigate the effect of introducing TCP Westwood+ on regular TCP New Reno. By means of analytical modeling and ns-2 simulations, we demonstrate that the two protocols get different shares of the available bandwidth in the network. Our main result is that the bandwidth sharing between the two protocols depends on one crucial parameter: the ratio between the bottleneck router buffer size and the bandwidth delay product. If the ratio is smaller than one, TCP Westwood+ takes more bandwidth. On the contrary, if the ratio is greater than one, it is TCP New Reno which gets the larger part. Inspired by our results, we propose a simple modification to the window decrease algorithm in TCP Westwood+ that solves the unfairness problem for large buffer sizes. For small buffers, the unfairness problem is still open.