Continuum Equilibria for Routing in Dense Ad-hoc Networks

Publication Type:

Conference Paper


45th Annual Allerton Conference on Communication, Control and Computing, Monticello, Illinois (2007)


We consider massively dense ad-hoc networks and study their continuum limits as the node density increases and as the graph providing the available routes becomes a continuous area with location and congestion dependent costs. We study both the global optimal solution as well as the noncooperative routing problem among a large population of users. Each user seeks a path from its source to its destination so as to minimize its individual cost. We seek for a (continuum version of the) Wardrop equilibrium. We first show how to derive meaningful cost models as a function of the scaling properties of the capacity of the network as a function of the density of nodes. We present various solution methodologies for the problem: (1) the viscosity solution of the Hamilton-Jacobi-Bellman equation, (2) a transformation into an equivalent global optimization problem that is obtained by identifying some potential related to the costs. We finally study the problem in which the routing decisions are taken by a finite number of competing service providers.

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