# Fifth Generation (5G) Mobile Networks: Study Of Percolation Threshold On Urban Road Models

Gafur, Nila Novita (2018) Fifth Generation (5G) Mobile Networks: Study Of Percolation Threshold On Urban Road Models. Masters thesis, Institut Teknologi Sepuluh Nopember.

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06211450010019-Master_Thesis.pdf - Accepted Version

Stochastic geometry is a mathematical discipline that combines geometry and probability. In particular, it model complex systems with a large number of elements distributed over a geographical area and has numerous applications in telecommunications. Based on stochastic geometry, mathematical models are designed to represent aspects of wireless networks. Talking about stochastic geometry models of wireless networks will not be detached from the important role of the continuum percolation. That is an extension of the percolation theory at $\mathbb{R}^2$. It model a random network and analyze their behavior. We apply these theories to our model "the connectivity of multi-hop D2D (Device to Device) networks" to predict some of their characteristics, such as to estimate minimum density of devices in a territory ensuring a long-distance communication called critical percolation threshold, to model percolation probability that a given devices is in the large connected component and to find the ratio of distance of two devices who want to communicate and the number of hops necessary to establish communication. We interpret the D2D communication refers to a random graph. Using Monte-Carlo simulation, we generate the data and propose some methods to get the best representation model for both urban and rural areas. We model the street systems as a Poisson-Voronoi tessellation and Poisson-Delaunay tessellation with varying street lengths. Our results show that the estimated value of critical percolation threshold $\widehat{\lambda_c}$ with selected method is almost same to the critical value $\lambda_c$ of Poisson Boolean model (PBM) for Poisson-Voronoi tessellation (PVT) model and is quite different for Poisson-Delaunay tessellation (PDT) model, e.g for radius $0.225$ km, $\widehat{\lambda_c}$ PVT is $1.42$ users/km of street, $1.51$ users/km of street for PDT and $1.418$ users/km of street for PBM. We notice also that PVT gives a very good representation for urban areas, meanwhile PDT is good for rural areas.