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Simulation of typical Cox–Voronoi cells with a special regard to implementation tests

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  • C. Gloaguen
  • F. Fleischer
  • H. Schmidt
  • V. Schmidt

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. Copyright Springer-Verlag 2005

Suggested Citation

  • C. Gloaguen & F. Fleischer & H. Schmidt & V. Schmidt, 2005. "Simulation of typical Cox–Voronoi cells with a special regard to implementation tests," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(3), pages 357-373, December.
    • Handle: RePEc:spr:mathme:v:62:y:2005:i:3:p:357-373
    DOI: 10.1007/s00186-005-0036-2
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    References listed on IDEAS

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    1. Roland Maier & Johannes Mayer & Volker Schmidt, 2004. "Distributional properties of the typical cell of stationary iterated tessellations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(2), pages 287-302, June.
    2. Alexander Shapiro & Jos Berge, 2002. "Statistical inference of minimum rank factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 79-94, March.
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    Cited by:

    1. David Neuhäuser & Christian Hirsch & Catherine Gloaguen & Volker Schmidt, 2016. "A Stochastic Model for Multi-Hierarchical Networks," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 1129-1151, December.
    2. C. Gloaguen & F. Fleischer & H. Schmidt & V. Schmidt, 2010. "Analysis of Shortest Paths and Subscriber Line Lengths in Telecommunication Access Networks," Networks and Spatial Economics, Springer, vol. 10(1), pages 15-47, March.

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