A Stochastic Model for Multi-Hierarchical Networks

David Neuhäuser (), Christian Hirsch, Catherine Gloaguen and Volker Schmidt
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David Neuhäuser: Ulm University, Institute of Stochastics Helmholtzstrasse
Christian Hirsch: Weierstrass Institute for Applied Analysis and Stochastics
Catherine Gloaguen: Orange Labs, 38-40 rue du General Leclerc
Volker Schmidt: Ulm University, Institute of Stochastics Helmholtzstrasse

Methodology and Computing in Applied Probability, 2016, vol. 18, issue 4, 1129-1151

Abstract: Abstract 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.

Keywords: STIT tessellation; Palm version; Multi-hierarchical networks; Typical shortest-path; Total fibre length; Limit theorem; Network planning; 60D05; 65C05; 65C50 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s11009-015-9450-y

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