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

• Published in: Stochastic processes and their applications Vol. 176; p. 104435
• Main Authors: Corlin Marchand, David, Coupier, David, Henry, Benoît
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.10.2024; Elsevier
• Subjects: Continuum percolation; Cox point process; D2D network; Enhancement; Mathematics; Probability; Random environment; Stochastic geometry; secondary; Stochastic geometry; Random environment; D2D network; Cox point process; Continuum percolation; Enhancement; primary; 60D05 Secondary: 68M10; 60G55; 90B15; random environment; continuum percolation; enhancement AMS 2010 Subject Classification: Primary: 60K35; stochastic geometry; enhancement AMS 2010 Subject Classification: Primary: 60K35 60G55 60D05 Secondary: 68M10 90B15
• DOI: 10.1016/j.spa.2024.104435
• ISSN: 0304-4149

In this work, percolation properties of device-to-device (D2D) networks in urban environments are investigated. On a street system 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 (i.e. on streets) or by a Bernoulli process on the vertices of the PDT (i.e. at crossroads). We state several percolation regimes for the resulting connectivity graph according to the parameters of the model. This work completes and specifies results of Le Gall et al. (2021). 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.