Numerical solutions of continuum equilibria for routing in dense ad-hoc networks

We study the routing problem in massively dense static adhoc networks as the node density increases. We use a fluid approximation in which the graph providing the available routes becomes so dense that it can be approximated by a continuous area which inherits from the original problem the cost structure: a cost density is defined at each point on the limit plain; it is a function of the location and the congestion at that point. We solve numerically the routing problem for the case where the cost density is linear with respect to congestion and we obtain a result of convergence via Finite Elements Method.