Rate of convergence for the `square root formula' in the Internet transmission control protocol
Teunis J. Ott · Advances in Applied Probability · 2006
The `square root formula' in the Internet transmission control protocol (TCP) states that if the probability p of packet loss becomes small and there is independence between packets, then the stationary distribution of the congestion window W is such that the distribution of W√p is almost independent of p and is completely characterizable. This paper gives an elementary proof of the convergence of the stationary distributions for a much wider class of processes that includes classical TCP as well as T. Kelly's `scalable TCP'. This paper also gives stochastic dominance results that translate to a rate of convergence.