Dynamics of Compound TCP with small buffer Drop-Tail queues

Abstract

Compound TCP is widely deployed in the Windows operating system, and the Drop-Tail queue policy is commonly used in Internet routers. We study models for Compound and Drop-Tail in the limiting regime of small router buffers, with smooth and with bursty traffic. We conduct a systematic local stability and local Hopf bifurcation analysis of the underlying non-linear, time-delayed, fluid models. The stability analysis allows us to capture relationships between protocol and network parameters to ensure stability in high bandwidth-delay environments. In particular, we exhibit that even minor variations in router buffer sizes, in a small buffer regime, can lead to Hopf induced limit cycles in the queue size. Limit cycles in the queue size may hurt end-to-end network performance and should, if possible, be avoided. Applying Poincaré normal forms and the center manifold analysis, we explicitly show that the Hopf bifurcation is supercritical. Thus loss of local stability would give rise to limit cycles, which are also proved to be asymptotically orbitally stable. The analytical results are corroborated by packet-level simulations which are conducted in a network simulator. Some design guidelines to ensure the stability of, and low-latency in, highspeed communication networks are also provided.