Journal of Global Optimization
Geometry of information propagation in massively dense ad hoc networks
Proceedings of the 5th ACM international symposium on Mobile ad hoc networking and computing
Interperf '06 Proceedings from the 2006 workshop on Interdisciplinary systems approach in performance evaluation and design of computer & communications sytems
Balancing traffic load in wireless networks with curveball routing
Proceedings of the 8th ACM international symposium on Mobile ad hoc networking and computing
Computer Networks: The International Journal of Computer and Telecommunications Networking
On the optimality of field-line routing in massively dense wireless multi-hop networks
Performance Evaluation
Numerical solutions of continuum equilibria for routing in dense ad-hoc networks
Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools
Balancing traffic load using one-turn rectilinear routing
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Bits-per-Joule Capacity of Energy-Limited Wireless Networks
IEEE Transactions on Wireless Communications
Variational inequalities and discrete and continuum models of network equilibrium problems
Mathematical and Computer Modelling: An International Journal
The capacity of wireless networks
IEEE Transactions on Information Theory
An Aloha protocol for multihop mobile wireless networks
IEEE Transactions on Information Theory
Optimal deployment of large wireless sensor networks
IEEE Transactions on Information Theory
Gauss-seidel correction algorithm: A macroscopic model-derived routing algorithm for WSNs
ACM Transactions on Sensor Networks (TOSN)
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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 non-cooperative routing problem among a large population of users where each user seeks a path from its origin to its destination so as to minimize its individual cost. Finally, 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 and of the density of nodes. We present various solution methodologies for the problem: (1) the viscosity solution of the Hamilton-Jacobi-Bellman equation, for the global optimization problem, (2) a method based on Green's Theorem for the least cost problem of an individual, and (3) a solution of the Wardrop equilibrium problem using a transformation into an equivalent global optimization problem.