Asymptotic properties of a TCP model with time-outs
Niclas Carlsson, Göran Högnäs · Discrete and Continuous Dynamical Systems - B · 2005
We examine a simple discrete time Markov model of TCP congestion control, which contains congestion avoidance, fast retransmit and time-out, and we prove that it has a unique invariant measure. If the process is scaled by a factor $\sqrt{p}$, then the invariant measures converge as $p \to 0$, where $p$ is the probability of error in any given data packet. This is the $1/\sqrt{p}$-behavior of TCP throughput. If the scaled process is transformed to continuous time, we show that it converges to a piecewise linear limit process. The unique invariant measure of the limit process coincides with the limit of the invariant measures above and can be easily computed. Finally, we examine a slightly more sophisticated way of modelling time-outs.