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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 thedoi:10.1109/infcom.2002.1019264 dblp:conf/infocom/BaccelliH02 fatcat:wq2lrxxwyzebljm47xmavbsor4