Self-similar Geometry for Ad-Hoc Wireless Networks: Hyperfractals

Philippe Jacquet 1 Dalia Popescu 1, 2
2 DYOGENE - Dynamics of Geometric Networks
DI-ENS - Département d'informatique de l'École normale supérieure, CNRS - Centre National de la Recherche Scientifique : UMR 8548, Inria de Paris
Abstract : In this work we study a Poisson patterns of fixed and mobile nodes distributed on straight lines designed for 2D urban wireless networks. The particularity of the model is that, in addition to capturing the irregularity and variability of the network topology, it exploits self-similarity, a characteristic of urban wireless networks. The pattern obeys to " Hyperfractal " measures which show scaling properties corresponding to an apparent dimension larger than 2. The hyperfractal pattern is best suitable for capturing the traffic over the streets and highways in a city. The scaling effect depends on the hyperfractal dimensions. Assuming radio propagation limited to streets, we prove results on the scaling of routing metrics and connectivity graph.
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Philippe Jacquet, Dalia Popescu. Self-similar Geometry for Ad-Hoc Wireless Networks: Hyperfractals. 3rd conference on Geometric Science of Information, Société Mathématique de France, Nov 2017, Paris, France. ⟨hal-01561828⟩

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