Title: Fifth Generation (5G) Mobile Networks: Study Of Percolation Threshold On Urban Road Models
Abstract: 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 will not be detached from important role of continuum percolation. That is an extension of 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 large connected component and to find ratio of distance of two devices who want to communicate and number of hops necessary to establish communication. We interpret D2D communication refers to a random graph. Using Monte-Carlo simulation, we generate data and propose some methods to get best representation model for both urban and rural areas. We model street systems as a Poisson-Voronoi tessellation and Poisson-Delaunay tessellation with varying street lengths.
Our results show that estimated value of critical percolation threshold $\widehat{\lambda_c}$ with selected method is almost same to 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.
Publication Year: 2018
Publication Date: 2018-09-01
Language: en
Type: dissertation
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