On the stability of optimization-based flow control

This paper concerns optimization-based network flow control; these recently proposed algorithms select transmission rates by maximizing a utility function for the set of sources, subject to link capacity constraints. A decentralized way to carry out this optimization has been proposed recently, based on the propagation of link prices, themselves updated dynamically. In particular, the authors consider the second-order update law of S. Athuraliya et al. (2000), which includes a backlog term in the price dynamics. They adopt a deterministic, continuous-time model which enforces nonnegativity constraints in prices and backlogs. For this model, a Lyapunov function-based proof is given of global asymptotic stability, i.e. convergence to the optimal rates and prices. The paper concludes with simulation examples