DENSITIES OF SHORTEST PATH LENGTHS IN SPATIAL STOCHASTIC NETWORKS

We consider a spatial stochastic model for telecommunication networks, the stochastic subscriber line model, and we investigate the distribution of the typical shortest path length between network components. Therefore, we derive a representation formula for the probability density of this distribution which is based on functionals of the so-called typical serving zone. Using this formula, we construct an estimator for the density of the typical shortest path length and we analyze the statistical properties of this estimator. Moreover, we introduce new simulation algorithms for the typical serving zone which are used in a numerical study in order to estimate the density and moments of the typical shortest path length for different specific models.