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
Computer Networks: The International Journal of Computer and Telecommunications Networking
Numerical solutions of continuum equilibria for routing in dense ad-hoc networks
Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools
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
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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In this paper we study the optimal placement and optimal number of active relay nodes through the traffic density in mobile sensor ad hoc networks. We consider a setting in which a set of mobile sensor sources is creating data and a set of mobile sensor destinations is receiving that data through multihop wireless paths. We make the assumption that the network is massively dense, i.e., there are so many sources, destinations, and relay nodes, that it is best to describe the network in terms of macroscopic parameters rather than in terms of microscopic parameters. A simple one-dimensional scenario is used to introduce the problem. We solve the two-dimensional scenario where the mobility of the nodes is deterministic and when it follows the brownian mobility model.