We study the performance of several TCP connections through the bottleneck of a slow network accessed via a single queue with high but finite capacity. Using mean-field asymptotic methology, we establish some asymptotical results about queue length distribution and window size distribution when the number of user increases proportionally to buffer capacity. We show that the difference between the actual queue length and its maximal capacity tends to be exponentially distributed. We give a precise determination of the window size asymptotic distribution and we prove that under our model the small window size has log-normal distribution
