This paper addresses the problem of building appropriate statistical models of the way the Internet appears from the point of view of congestion, to a transmission control protocol (TCP) sender. TCP is a mechanism for implementing full duplex, acknowledged, end-to-end transmission over an Internet protocol (IP) network. This work has been motivated by the TCP variant, the so-called Vegas implementation. TCP Vegas is really the first implementation to be based loosely on system theoretic ideas in the sense that it measures the segment round-trip times across the network to adjust its transmission rate. This paper develops a new linear system framework for TCP, and applies recursive prediction error identification techniques to specify statistical models which may be used to develop alternative control strategies. Network simulations are used to illustrate behaviour.