Optimal design and operation of massively dense wireless networks: or how to solve 21st century problems using 19th century mathematics

In this overview paper, we present a few instructive examples on the optimal design and operation of massively dense wireless network. These networks contain such a large number of nodes that, in addition to the standard microscopic view, an additional macroscopic view of them emerges. The macroscopic view is not as detailed, but nevertheless preserves sufficient information to allow a meaningful network optimization and the derivation of insightful results in a wide range of settings. A prominent feature of massively dense networks is their amenability to mathematics and branches of physics that are unusual in the context of networking, for example Calculus of Variations, Electrostatics, and Optics.

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