The stationary behavior of ideal TCP congestion avoidance

This note derives the stationary behavior of idealized TCP congestion avoidance. More speci cally, it derives the stationary distribution of the congestion window size if loss of packets are independent events with equal probability. The mathematical derivation uses a uid ow, continuous time, approximation to the discrete time process (Wn), where Wn is the congestion window after the n-th packet. We derive explicit results for the stationary distribution and all its moments. Congestion avoidance is the algorithm used by TCP to set its window size (and indirectly its data rate) under moderate to light segment (packet) losses. The congestion avoidance mechanism we model is idealized in the sense that loss of multiple packets does not lead to time-out phenomena. Such idealized behavior can be implemented using Selective Acknowledgements (SACKs). As such, our model predicts behavior of TCP with SACKs. It also is an approximate model in other situations. Among the results are that if every packet is lost with a (small) probability p, average window size and long range throughput (when transporting a le large enough to reach stationarity) are of the order of 1= p p.