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We study the effect of the IP router buffer size on the throughput of HighSpeed TCP (HSTCP). We are motivated by the fact that, in high speed routers, the buffer size is important, as a large buffer size might be a constraint. We first derive an analytical model for HighSpeed TCP and we show that for a small buffer size, equal to 10% of the bandwidth-delay product, HighSpeed TCP can achieve more than 90% of the bottleneck capacity. We also show that setting the buffer size equal to 20% can increase the utilization of HighSpeed TCP up to 98%. On the contrary, setting the buffer size to less than 10% of the bandwidth-delay product can decrease HighSpeed TCP's throughput significantly. We also study the performance effects under both DropTail and RED AQM (active queue management). Analytical results obtained using a fixed-point approach are compared to those obtained by simulation.