  We consider spatial stochastic models, which can be applied e.g. to
telecommunication networks with two hierarchy levels. In particular, we
consider two Cox processes concentrated on the edge set of a random
tessellation, where the points can describe the locations of low-level and
high-level network components, respectively, and the edge set the underlying
infrastructure of the network, like road systems, railways, etc. Furthermore,
each low-level component is marked with the shortest path along the edge set to
the nearest high-level component. We investigate the typical shortest path
length of the resulting marked point process, which is an important
characteristic e.g. in performance analysis and planning of telecommunication
networks. In particular, we show that its distribution converges to simple
parametric limit distributions if a certain scaling factor converges to zero
and infinity, respectively. This can be used to approximate the density of the
typical shortest path length by analytical formulae.
