The AIMD Model for TCP Sessions Sharing a Common Router

We propose a natural and simple model for the joint throughpu t evolution of a set of TCP sessions sharing a single bottleneck router, via prod ucts of random matrices. This model leads to several results on TCP such as the quantificati on of throughput fluctuations, that of fairness, the characterization of the autocorrelat ion function of inter-loss periods, or the evaluation of the performance degradation due to sync hro ization of losses in the shared router. Surprisingly enough, even when based on the a ssumption of i.i.d losses, this model yields a fractal scaling of aggregates of traffic a t short time scales, as recently identified on real traces by a statistical analysis based on w avelets.