Fixed Point Approximations for TCP Behavior in Networks of Routers

In this paper we use fixed point methods to model the behavior of a population of TCP flows traversing a network of routers implementing either Drop Tail or the RED queue management policies. We formulate a non-linear problem with the router average queue lengths as unknowns. Once the average queue lengths are obtained, other metrics such as router loss probability, TCP flow throughput, TCP flow end-to-end loss rates, and average round trip time can be easily obtained. Comparison with simulation for a variety of scenarios shows that the model is quite accurate in its predictions.