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We consider massively dense ad hoc networks and study their continuum limitsas the node density increases and as the graph providing the available routesbecomes a continuous area with location and congestion dependent costs. Westudy both the global optimal solution as well as the non-cooperative routingproblem among a large population of users where each user seeks a path from itsorigin to its destination so as to minimize its individual cost. Finally, weseek for a (continuum version of the) Wardrop equilibrium. We first show how toderive meaningful cost models as a function of the scaling properties of thecapacity of the network and of the density of nodes. We present varioussolution methodologies for the problem: (1) the viscosity solution of theHamilton-Jacobi-Bellman equation, for the global optimization problem, (2) amethod based on Green's Theorem for the least cost problem of an individual,and (3) a solution of the Wardrop equilibrium problem using a transformationinto an equivalent global optimization problem.

Continuum Equilibria and Global Optimization for Routing in Dense Static Ad Hoc Networks