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AIMD, fairness and fractal scaling of TCP traffic

We propose a natural and simple model for the joint throughput evolution of a set of TCP sessions sharing a common tail drop bottleneck router, via products of random matrices. This model allows one to predict the fluctuations of the throughput of each session, as a function of the synchronization rate in the bottleneck router; several other and more refined properties of the protocol are analyzed such as the instantaneous imbalance between sessions, the autocorrelation function or the performance degradation due to synchronization of losses. When aggregating traffic obtained from this model, one obtains, for certain ranges of the parameters, short time scale statistical properties that are consistent with a fractal scaling similar to what was identified on real traces using wavelets.