Stability of TCP Dynamics in Large Data Networks
Russell D. Halper, Eric J. Harder, Brian R. Hunt, James A. Yorke · SIAM Journal on Applied Dynamical Systems · 2009
We study the stability of the dynamics of a deterministic model of Transmission Control Protocol (TCP) traffic in a multiple flow, multiple router data network. In this model, flow rates increase continuously until network congestion causes them to decrease discontinuously. In computer simulations of small networks, trajectories appear to approach periodic orbits for most but not all parameter values. We prove that if all the data flows are coupled, periodic orbits must be exponentially attracting and thus persist under parameter changes, regardless of network size. Furthermore, we describe the model as a discontinuous but piecewise affine map and show that trajectories must either approach a periodic orbit or come arbitrarily close to map discontinuities.