Local stability analysis of TCP with a queue management policy: Single bottleneck link with two delays

We analyze a non-linear fluid model of TCP coupled with a queue management policy. For our analysis, we consider a topology in which two sets of TCP flows, each having different round-trip times, uses a single bottleneck link. We first conduct a local stability analysis and determine the necessary and sufficient condition for local asymptotic stability. We then show, with the help of transversality condition of Hopf spectrum, that the underlying system would loose local stability as system parameters are varied. Employing the Nyquist stability criteria, we then derive a simple sufficient condition for local stability of the system. Following the analytical results we perform some numerical computations and stability charts are also presented. The analytical results can help to provide design guidelines for the choice of protocol and queue management parameters.