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CAPACITY DISTRIBUTIONS IN SPATIAL STOCHASTIC MODELS
FOR TELECOMMUNICATION NETWORKS
November 2009
FLORIAN VOSS, CATHERINE GLOAGUEN AND VOLKER SCHMIDT
We consider the stochastic subscriber line model as a spatial stochastic model for telecommunication networks
and we are interested in the evaluation of the required capacities at different locations of the network in order
to provide, in fine, an estimation of the cable system which has to be installed. In particular, we consider
hierarchical telecommunication networks with higher–level components (HLC) and lower–level components
(LLC) located on the road system underlying the network. The cable paths are modeled by shortest paths along
the edge set of a stationary random tessellation, whereas both HLC and LLC are modeled by Cox processes
concentrated on the edges of this tessellation. We then introduce the notion of capacity which depends on
the length of some subtree on the edge set of the underlying tessellation. Moreover, we investigate estimators
for the density and distribution function of the typical length of this subtree which can be computed based on
Monte Carlo simulations of the typical serving zone. In a numerical study, the density of the typical subtree
length is determined for different specific models.
Point Processes, Random Tessellations, Stochastic Geometry, Telecommunication Systems
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