Random Tessellations and Cox Processes View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2013

AUTHORS

Florian Voss , Catherine Gloaguen , Volker Schmidt

ABSTRACT

We consider random tessellations T in \({\mathbb{R}}^{2}\) and Cox point processes whose driving measure is concentrated on the edges of T. In particular, we discuss several classes of Poisson-type tessellations which can describe for example the infrastructure of telecommunication networks, whereas the Cox processes on their edges can describe the locations of network components. An important quantity associated with stationary point processes is their typical Voronoi cell Z. Since the distribution of Z is usually unknown, we discuss algorithms for its Monte Carlo simulation. They are used to compute the distribution of the typical Euclidean (i.e. direct) connection length D o between pairs of network components. We show that D o converges in distribution to a Weibull distribution if the network is scaled and network components are simultaneously thinned in an appropriate way. We also consider the typical shortest path length C o to connect network components along the edges of the underlying tessellation. In particular, we explain how scaling limits and analytical approximation formulae can be derived for the distribution of C o . More... »

PAGES

151-182

References to SciGraph publications

Book

TITLE

Stochastic Geometry, Spatial Statistics and Random Fields

ISBN

978-3-642-33304-0
978-3-642-33305-7

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-642-33305-7_5

DOI

http://dx.doi.org/10.1007/978-3-642-33305-7_5

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1031688184


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