On the higher moments of TCP

In this paper we describe the moments of a stochastic model of the Additive Increase Multiplicative Decrease (AIMD) algorithm. AIMD is the algorithm that underpins the Transmission Control Protocol (TCP), which is used extensively in the internet. We prove that the Markov chain describing TCP has the remarkable property that all moments converge to their asymptotes at exactly the same rate. Further, we illustrate how a closed form solution can be obtained from the network properties, and this formula is explicitly calculated for the case of the third moment.