Limit behavior of ECN/RED gateways under a large number of TCP flows

A stochastic model of an ECN/RED gateway with competing TCP sources sharing the capacity is considered. As the number of competing flows becomes large, the queue behavior at the gateway can be described by a two-dimensional recursion and the throughput behavior of individual TCP flows becomes asymptotically independent. The steady-state regime of the limiting behavior can be calculated from a well-known TCP throughput model with fixed loss probability. In addition, a central limit theorem is presented, yielding insight into the relationship between the queue fluctuation and the marking probability function. We confirm the results by simulations and discuss their implications for network dimensioning.