Arguably, TCP is the protocol that by its feedback mechanism (increasing the congestion window when no loss occurs, halving it at packet loss events) has kept the Internet stable during the explosive growth of the last 15 years.

This talk consists of two parts. The first part presents a mathematical analysis of TCP window behavior in the face of packet loss. Among the simplifying assumptions are that the upper limits on the congestion window (TCP Window, Advertised Window) are very high, that the loss probability p is constant, and that there is independence between packets.

Let W_{n} denote the congestion window (in Maximum Segment Sizes) after the n-th good acknowledgement. With the assumptions above this is a simple stochastic process. An approximation for the stationary distribution will be derived. It will be seen that unless p is high the stationary distribution of W sqrt{p} is virtually independent of p. This is the strong form of the ''square root formula'' for TCP.

The second part of the talk presents some ideas of how TCP may need to be modified in the face of newer insights and changing technology. It is well recognized that ''halving'' the window in case of packet loss is too draconic, in particular for the much higher congestion windows now than in the late eighties. Other factors in this question are RED (Random Early Detection) and ECN (Explicit Congestion Notification), and DiffServ (Differentiated Services). In particular, the presence of high priority flows with highly variable bandwidth makes it desirable that congestion windows of low priority flows grow fast during short periods of undertilized transmission capacity. The desirability of slower decrease and faster increase clashes with the requirement of being ''TCP friendly''.


Teun Ott worked for 23 years in Bell Laboratories / Bellcore / Telcordia, as Member of Technical Staff, Supervisor, Director, and Senior Scientist. Since 2001 he is teaching in the department of Computer Science at NJIT. He has started the ''Internet Laboratory'' at NJIT, where his students do projects on Linux Routing, Linux Firewalls, etc. He has 7 patents on aspects of traffic control of TCP and ATM.