A Stochastic Model for Multi-Hierarchical Networks

We provide a stochastic modelling approach for multi-hierarchical fixed-access telecommunication networks where cables are installed along the underlying road system. It constitutes an extension of network models consisting of only two hierarchy levels. We consider the effects of the introduction of an additional level of hierarchy on two functionals relevant in telecommunication networks, namely typical shortest-path lengths and total fibre lengths. Intuitively speaking, in the extended scenario, the typical shortest-path length gets longer whereas the total fibre length decreases. Both theoretical and numerical results are provided. The underlying infrastructure is assumed to be represented by a STIT tessellation which is particularly suitable for stochastic modelling of multi-hierarchical fixed-access telecommunication networks. In this context, we present a description of the Palm version of a planar STIT tessellation and give an appropriate simulation algorithm.