Palm calculus for stationary Cox processes on iterated random tessellations

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...

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Bibliographic Details
Published in2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks pp. 1 - 6
Main Authors Voss, F., Gloaguen, C., Schmidt, V.
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.06.2009
Subjects
Algorithm design and analysis
Calculus
Cities and towns
Estimation
Geometric modeling
Geometry
Mobile communication
Monte Carlo methods
Networks
Performance analysis
Point processes
Poisson processes
Power system modeling
Random processes
Solid modeling
Stochastic processes
Strategic planning
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Summary: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 version X* of stationary Cox processes X living on random graphs that are built by the edges of an iterated random tessellation T. We derive a representation formula for the Palm version T* of T which includes the initial tessellation T 0 and the component tessellation T 1 of T as well as their Palm versions T* 0 and T* 1 . Using this formula, we are able to construct a simulation algorithm for X* if both T 0 , T 1 and their Palm versions T* 0 , T* 1 can be simulated. This algorithm for X* 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 T 0 is a Poisson-Voronoi tessellation and T 1 is a Poisson line tessellation.
ISBN:9781424449194
1424449197
DOI:10.1109/WIOPT.2009.5291572