We study the interaction of a large number of connections over the Internet, sharing the same local loop and controlled by TCP. We focus on the case when the connections are homogeneous and the access router has a Fair-Queueing scheduling discipline, whereas the Internet is represented by a set of First-In-First-Out (FIFO) routers. We use both simulation and analytical results to determine the characteristics of the throughput obtained by each connection under a realistic description of the traffic offered to the network. The key idea for the analysis consists in a fixed point method which is based on the exact description of one TCP connection and a simplified description of the interaction with the other connections. The convergence of this fixed point method is substantiated by extensive simulations. The validation of the approach is carried out using NS simulation in cases where both methods can be used. We show that the goodput obtained by each connection and its fluctuations can be accurately evaluated from this approach.