Limiting model of ECN/RED under a large number of heterogeneous TCP flows

We introduce a stochastic model of a bottleneck ECN/RED gateway under a large number of competing heterogeneous TCP flows. Our main result shows that as the number of flows becomes large, the queue dynamics and the aggregate traffic are simplified and can be accurately described by simple statistical recursions. These recursions can be evaluated independently of the number of flows, and hence the resulting traffic model is scalable. We also present a simple analysis on the buffer utilization and window size at the steady-state.