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arXiv · 2402.07544

Line-of-sight Cox percolation on Poisson-Delaunay triangulation

David Corlin Marchand·David Coupier·Benoît Henry
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Abstract

In this work, percolation properties of device-to-device (D2D) networks in urban environments are investigated. The street system is modeled by a Poisson-Delaunay triangulation (PDT). Users are of two types: given either by a Cox process supported by the edges of the PDT or by a Bernoulli process on the vertices of the PDT (i.e. on streets and at crossroads). Percolation of the resulting connectivity graph G p,$λ$,r is interpreted as long-range connection in the D2D network. According to the parameters p, $λ$, r of the model, we state several percolation regimes in Theorem 1 (see also Fig. 3). This work completes and specifies results of Le Gall et al [23]. To do it, we take advantage of a percolation tool, inspired by enhancement techniques, used to our knowledge for the first time in the context of communication networks.

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David Corlin Marchand, David Coupier, Benoît Henry. 2024-02-12. Line-of-sight Cox percolation on Poisson-Delaunay triangulation. https://arxiv.org/abs/2402.07544

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