page_title: Stochastic geometry models of wireless networks
section_title: Node positioning model
hierarchical_section_title: Stochastic geometry models of wireless networks / Model fundamentals / Node positioning model
caption_attribution_description: English: A panoramic view of the Sydney skyline as viewed across Sydney Harbour from Kirribilli. Taken by myself with a Canon 5D and 100mm f/2.8 lens. This is an exposure blended image. Français&#160;: Vue panoramique de Sydney depuis Kirribilli avec le bassin de Port Jackson au premier plan. Photo prise avec un appareil Canon EOS 5D et un objectif 100mm f/2.8. Español: Vista panorámica de Sydney desde Kirribilli con la Bahía de Sídney en primer plano. Fotografía tomada con una Canon EOS 5D y un lente 100mm f/2.8.
context_page_description: In mathematics and telecommunications, stochastic geometry models of wireless networks refer to mathematical models based on stochastic geometry that are designed to represent aspects of wireless networks. The related research consists of analyzing these models with the aim of better understanding wireless communication networks in order to predict and control various network performance metrics. The models require using techniques from stochastic geometry and related fields including point processes, spatial statistics, geometric probability, percolation theory, as well as methods from more general mathematical disciplines such as geometry, probability theory, stochastic processes, queueing theory, information theory, and Fourier analysis.
  In the early 1960s a stochastic geometry model was developed to study wireless networks. This model is considered to be pioneering and the origin of continuum percolation. Network models based on geometric probability were later proposed and used in the late 1970s and continued throughout the 1980s for examining packet radio networks.
context_section_description: An important task in stochastic geometry network models is choosing a mathematical model for the location of the network nodes. The standard assumption is that the nodes are represented by (idealized) points in some space (often Euclidean Rⁿ, and even more often in the plane R²), which means they form a stochastic or random structure known as a (spatial) point process.
caption: According to one statistical study, the locations of cellular or mobile phone base stations in the Australian city of Sydney resemble a realization of a Poisson point process.[34]
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