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**Simulation algorithm of typical modulated Poisson-Voronoi cells and application to telecommunication network modelling.**
*(English)*
Zbl 1166.90005

This paper provides an analysis of a specialized case of modulated Poisson-Voronoi tesselations. The modulation used in the paper was generated by a Boolean germ-grain model with circular grains. This means that this model can be used to model densities or spatial densities of network devices on nationwide scales. In addition, the possible randomness of the radius of the grains allows us to minimize the observed features of the towns lying in a given area. In the stationary case, the typical cell obtained by these tessellations can be regarded as a cell chosen at random out of the pool of all cells. These tessellations may either have a deterministic or random but bounded radius.

Furthermore, the Poisson tessellation modulated in this way can provide Voronoi tessellation, as well as so-called inner city model or swiss cheese model. Several values of the mean distance from a randomly choosen location to its nearest Voronoi cell nucleus are used as the basic cost in many networks, especially for computating functionals, such as costs, prices, etc. These models are valuable for telecommunication operators and provide many useful characteristics important from a telecommunications point of view.

The important result achieved in this paper is that the estimated cost functionals from presented models are in accordance with the values computed using theoretical framework. This means that the algorithm presented in the paper can be used in modeling practice.

Furthermore, the Poisson tessellation modulated in this way can provide Voronoi tessellation, as well as so-called inner city model or swiss cheese model. Several values of the mean distance from a randomly choosen location to its nearest Voronoi cell nucleus are used as the basic cost in many networks, especially for computating functionals, such as costs, prices, etc. These models are valuable for telecommunication operators and provide many useful characteristics important from a telecommunications point of view.

The important result achieved in this paper is that the estimated cost functionals from presented models are in accordance with the values computed using theoretical framework. This means that the algorithm presented in the paper can be used in modeling practice.

Reviewer: Jerzy Martyna (Kraków)

### MSC:

90B18 | Communication networks in operations research |

60D05 | Geometric probability and stochastic geometry |

90B15 | Stochastic network models in operations research |

05C85 | Graph algorithms (graph-theoretic aspects) |

90C35 | Programming involving graphs or networks |

### Keywords:

stochastic geometry; network models, stochastic; graph algorithms; programming involving graphs in networks### References:

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