Fitting of stochastic telecommunication network models via distance measures and Monte–Carlo tests

Abstract

We explore real telecommunication data describing the spatial geometrical structure of an urban region and we propose a model fitting procedure, where a given choice of different non-iterated and iterated tessellation models is considered and fitted to real data.This model fitting procedure is based on a comparison of distances between characteristics of sample data sets and characteristics of different tessellation models by utilizing a chosen metric. Examples of such characteristics are the mean length of the edge-set or the mean number of vertices per unit area. In particular, after a short review of a stochastic-geometric telecommunication model and a detailed description of the model fitting algorithm, we verify the algorithm by using simulated test data and subsequently apply the procedure to infrastructure data of Paris.

Random Laguerre tessellations

“…Similar approaches are discussed for example in Gloaguen et al (2006) and in Kühn (2005). Both are based on optimization with respect to distance measures defined on vectors of cell characteristics of the tessellations.…”

“…Letĉ be the vector of characteristics estimated from the input structure and c the vector of the same characteristics for one of the model structures under consideration. For measuring the distance betweenĉ and c we adopt the approach of Gloaguen et al (2006) who define relative distance measures based on the Euclidean, the absolute, and the maximum metric via…”

“…In the application discussed in Gloaguen et al (2006), all three measures performed similarly. Since we do not see any reasons why one of them should be preferred, we will run the optimization procedure with all three measures and compare the results.…”

Simulation of the typical Poisson–Voronoi–Cox–Voronoi cell

“…In [5] and [6] a similar effect for PLCVT is used to reduce the number of parameters in the numerical experiments. Namely, using scaling invariance, it is sufficient to do computations for each κ only for one parameter pair (λ l , λ p ).…”

“…The comparison with previous simulation studies for the PLCVT ( [5]) is especially interesting, since both can represent possible models for telecom-munication networks ( [6]). …”