Global Stability of Nonlinear Congestion Control with Time-Delay

Abstract

In recent years large strides have been taken in analytical approaches to network congestion control. These methods, originating in the academic community [1, 2, 3, 4, 5, 6, 7] are quickly evolving into viable alternatives to correct deficiencies of current Internet protocols [8, 9]. Using a framework proposed in [1, 2] based on fluid-flow models and utility functions, tools from convex optimization and control theory have come into play to propose new control laws that achieve equilibrium objectives of efficient network utilization, fair resource allocation and low delay, and local stability. Control can be included in a decentralized way either at network sources or at links; following [1], it has become customary to denote by “primal” control laws those that contain dynamics at sources, but static functions at links, and “dual” laws those where the opposite holds. In this vein, the case where both control laws are dynamic is named “primal-dual”.