Stability of node-based multipath routing and dual congestion control

This paper considers a network flow control problem where routing and input rates are controlled in a decentralized way across a network, to optimize a global welfare objective. We build on our recent work which combines ¿dual¿ congestion control for the traffic sources, with multipath routing at the router nodes, controlling the traffic split among outgoing links based on downstream congestion prices. The challenge is to obtain stabilization of the optimum point; in fact, controlling the split fractions following the price gradient has the correct equilibrium, but can lead to oscillatory instabilities. This suggests the use of derivative action to damp such oscillations. We study two alternatives in this regard; either anticipatory control of routing splits, which yields local stability in an arbitrary network topology, or anticipatory price generation, which yields a global result for the case of a network of parallel links. Proofs are based on a Lyapunov argument. Results are illustrated through simulations.