Synchronisation in TCP networks with Drop-Tail Queues

The design of transport protocols, embedded in end-systems, and the choice of buffer sizing strategies, within network routers, play an important role in performance analysis of the Internet. In this paper, we take a dynamical systems perspective on the interplay between fluid models for transport protocols and some router buffer sizing regimes. Among the flavours of TCP, we analyse Compound, as well as Reno and Illinois. The models for these TCP variants are coupled with a Drop-Tail policy, currently deployed in routers, in two limiting regimes: a small and an intermediate buffer regime. The topology we consider has two sets of long-lived TCP flows, each passing through separate edge routers, which merge at a common core router. Our analysis is inspired by time delayed coupled oscillators, where we obtain analytical conditions under which the sets of TCP flows synchronise. These conditions are made explicit in terms of coupling strengths, which depend on protocol parameters, and on network parameters like feedback delay, link capacity and buffer sizes. We find that variations in the coupling strengths can lead to limit cycles in the queue size. Packet-level simulations corroborate the analytical insights. For design, small Drop-Tail buffers are preferable over intermediate buffers as they can ensure both low latency and stable queues.