Modeling TCP throughput: An elaborated large-deviations-based model and its empirical validation

In today's Internet, a large part of the traffic is carried using the TCP transport protocol. Characterization of the variations of TCP traffic is thus an important issue, both for resource provisioning and Quality of Service purposes. However, most existing models are limited to the prediction of the (almost-sure) mean TCP throughput and are unable to characterize deviations from this value. In this paper, we propose a method to describe the deviations of a long TCP flow's throughput from its almost-sure mean value. This method relies on an ergodic large-deviations result, which was recently proved to hold on almost every single realization for a large class of stochastic processes. Applying this result to a Markov chain modeling the congestion window's evolution of a long-lived TCP flow, we show that it is practically possible to quantify and to statistically bound the throughput's variations at different scales of interest for applications. Our Markov-chain model can take into account various network conditions and we demonstrate the accuracy of our method's prediction in different situations using simulations, experiments and real-world Internet traffic. In particular, in the classical case of Bernoulli losses, we demonstrate: (i) the consistency of our method with the widely-used square-root formula predicting the almost-sure mean throughput, and (ii) its ability to additionally predict finer properties reflecting the traffic's variability at different scales.