We consider a stochastic model of an ECN/RED gateway with competing TCP sources sharing the capacity. As the number of competing flows becomes large, the asymptotic queue behavior at the gateway can be described by a simple recursion and the hroughput behavior of individual TCP flows becomes asymptotically independent. In addition, a Central Limit Theorem complement is presented, yielding a more accurate characterization of the asymptotic queue. These results suggest a scalable yet accurate model of the complex large-scale stochastic feedback system, and crisply reveal the sources of queue fluctuations.