Simulation of typical Cox–Voronoi cells with a special regard to implementation tests |
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Authors: | C Gloaguen F Fleischer H Schmidt V Schmidt |
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Institution: | (1) France Télécom R&D TECH/LEI/MOT, 92131 Issy les Moulineaux Cedex 9, France;(2) Department of Applied Information Processing and Department of Stochastics, University of Ulm, 89069 Ulm, Germany;(3) Department of Stochastics, University of Ulm, 89069 Ulm, Germany |
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Abstract: | We consider stationary Poisson line processes in the Euclidean plane and analyze properties of Voronoi tessellations induced
by Poisson point processes on these lines. In particular, we describe and test an algorithm for the simulation of typical
cells of this class of Cox–Voronoi tessellations. Using random testing, we validate our algorithm by comparing theoretical
values of functionals of the zero cell to simulated values obtained by our algorithm. Finally, we analyze geometric properties
of the typical Cox–Voronoi cell and compare them to properties of the typical cell of other well-known classes of tessellations,
especially Poisson–Voronoi tessellations. Our results can be applied to stochastic–geometric modelling of networks in telecommunication
and life sciences, for example. The lines can then represent roads in urban road systems, blood arteries or filament structures
in biological tissues or cells, while the points can be locations of telecommunication equipment or vesicles, respectively. |
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Keywords: | Stochastic geometry Random tessellation Typical cell Shape analysis Network Random software testing |
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