Fixed point approximations for TCP behavior in an AQM network

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Abstract
In this paper, we explore the use of fixed point methods to evaluate the performance of a large population of TCP flows traversing a network of routers implementing active queue management (AQM) such as RED (random early detection). Both AQM routers that drop and that mark packets are considered along with infinite and finite duration TCP flows. In the case of finite duration flows, we restrict ourselves to networks containing one congested router. In all cases, we formulate a fixed point problem with the router average queue lengths as unknowns. Once these are obtained, other metrics such as router loss probability, TCP flow throughput, TCP flow end-to-end loss rates, average round trip time, and average session duration are easily obtained. Comparison with simulation for a variety of scenarios shows that the model is accurate in its predictions (mean errors less than 5%). Last, we establish monotonicity properties exhibited by the solution for a single congested router that explains several interesting observations, such as TCP SACK suffers higher loss than TCP Reno.

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