Using SDE to achieve the stable and statistical analyses for TCP/RED flows

In this paper, we show how to make a complete analysis of the performance of TCP/RED (Transmission Control Protocol / Random Early Detection) flows in a single bottleneck network with Stochastic Differential Equation (SDE). We start from deducing the SDE for the aggregate TCP flow. Using this SDE model, we calculate the exact stable range of the TCP connection number and the variance of the queue length in router under a configured RED algorithm. Our deductive results are explicit formulas which are shown to be consistent with our simulations. We use TCP/RED as an example of the application of SDE method here, but such SDE method can be applied to many other protocols as well.