Optimal Improvement of Communication Network Congestion via Nonlinear Programming with Generalized Nash Equilibrium Constraints

We consider a popular model of congestion control in communication networks within the theory of generalized Nash equilibrium problems with shared constraints, where each player is a user who has to send his/her flow over a path in the network. The cost function of each player consists of two parts: a pricing and a utility term. Within this framework we assume that the network system manager can invest a given amount of money to improve the network by enhancing the capacity of its links and, because of limited financial resources, has to make a choice as to which of the links to improve. This choice is made with the help of a performance function which is computed for each set of improvements under consideration and has the property that, once the equilibrium has been reached, maximizes the aggregate utility and minimizes the sum of delays at the links. We model this problem as a nonlinear knapsack problem with generalized Nash equilibrium constraints and show some preliminary numerical experiments.