TCP Reno and queue management: Local stability and Hopf bifurcation analysis

We study local stability and the local Hopf bifurcation properties of a fluid model for TCP Reno coupled with queue management schemes in routers. We analyse models for the widely deployed Drop-Tail queue policy, over a small and an intermediate buffer regime. We also study a model for a threshold based queue policy. In small Drop-Tail buffers, stability depends crucially on the buffer size. With intermediate buffer Drop-Tail, the system can be locally unstable for large values of the feedback delay and link capacities. The threshold based policy highlights the importance of setting queue thresholds guided by stability analysis. We show that variations in system parameters can produce Hopf induced limit cycles. It is practically important to characterise the existence, uniqueness and stability of the bifurcating periodic solutions. Using the theory of normal forms and the center manifold theorem, we establish that the Hopf bifurcation is indeed supercritical. Packet-level simulations for the Drop-Tail queue policy corroborate our theoretical analysis.