Research Article
Palm calculus for stationary Cox processes on iterated random tessellations
@INPROCEEDINGS{10.1109/WIOPT.2009.5291572, author={Florian Voss and Catherine Gloaguen and Volker Schmidt}, title={Palm calculus for stationary Cox processes on iterated random tessellations}, proceedings={5th International Workshop on Spatial Stochastic Models for Wireless Networks}, publisher={IEEE}, proceedings_a={SPASWIN}, year={2009}, month={10}, keywords={Point processes Geometric modeling Poisson processes Monte Carlo methods Estimation Mobile communication Networks}, doi={10.1109/WIOPT.2009.5291572} }- Florian Voss
Catherine Gloaguen
Volker Schmidt
Year: 2009
Palm calculus for stationary Cox processes on iterated random tessellations
SPASWIN
IEEE
DOI: 10.1109/WIOPT.2009.5291572
Abstract
We investigate Cox processes of random point patterns in the Euclidean plane, which are located on the edges of random geometric graphs. Such Cox processes have applications in the performance analysis and strategic planning of both wireless and wired telecommunication networks. They simultaneously allow to represent the underlying infrastructure of the network together with the locations of network components. In particular, we analyze the Palm distribution of stationary Cox processes living on random graphs that are built by the edges of an iterated random tessellation. We derive a representation formula for the Palm version of the underlying iterated tessellation which includes its initial tessellation and its component tessellation as well as their Palm versions. Using this formula, we are able to construct a simulation algorithm for the Palm version of such Cox processes if the initial and component tessellation as well as their Palm versions can be simulated. This algorithm extends earlier results for Cox processes on simpler (non-iterated) tessellations. It can be used, for example, in order to estimate the probability densities of various connection distances, which are important performance characteristics of telecommunication networks. In a numerical study we consider the particular case that the initial tessellation is a Poisson-Voronoi tessellation and the component tessellation is a Poisson line tessellation.