Rate of convergence for the .square root formula. in the Internet transmission control protocol

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.