A Game-Theoretic Framework for Congestion Control in General Topology Networks

We study control of congestion in general topology communication networks within a fairly general mathematical framework that utilizes noncooperative game theory. We consider a broad class of cost functions, composed of pricing and utility functions, which capture various pricing schemes along with varying behavior and preferences for individual users. We prove the existence and uniqueness of a Nash equilibrium under mild convexity assumptions on the cost function, and show that the Nash equilibrium is the optimal solution of a particular “system problem”. Furthermore, we prove the global stability of a simple gradient algorithm and its convergence to the equilibrium point. Thus, we obtain a distributed, market-based, end-to-end framework that addresses congestion control, pricing and resource allocation problems for a large class of of communication networks. As a byproduct, we obtain a congestion control scheme for combinatorially stable ad hoc networks by specializing the cost function to a specific form. Finally, we present simulation studies that explore the effect of the cost function parameters on the equilibrium point and the robustness of the gradient algorithm to variations in time delay and to link failures.