We consider spatial stochastic models, which can be applied to, e.g. telecommunication networks with two hierarchy levels. In particular, we consider Cox processes X
L
and X
H
concentrated on the edge set T
(1) of a random tessellation T, where the points X
L,n
and X
H,n
of X
L
and X
H
can describe the locations of low-level and high-level network components, respectively, and T
(1) the underlying infrastructure of the network, such as road systems, railways, etc. Furthermore, each point X
L,n
of X
L
is marked with the shortest path along the edges of T to the nearest (in the Euclidean sense) point of X
H
. We investigate the typical shortest path length C
* of the resulting marked point process, which is an important characteristic in, e.g. performance analysis and planning of telecommunication networks. In particular, we show that the distribution of C
* converges to simple parametric limit distributions if a scaling factor κ converges to 0 or ∞. This can be used to approximate the density of C
* by analytical formulae for a wide range of κ.