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A Stochastic Model for Multi-Hierarchical Networks

Author

Listed:
  • 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)

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.

Suggested Citation

  • David Neuhäuser & Christian Hirsch & Catherine Gloaguen & Volker Schmidt, 2016. "A Stochastic Model for Multi-Hierarchical Networks," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 1129-1151, December.
    • Handle: RePEc:spr:metcap:v:18:y:2016:i:4:d:10.1007_s11009-015-9450-y
    DOI: 10.1007/s11009-015-9450-y
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    References listed on IDEAS

    as
    1. C. Gloaguen & F. Fleischer & H. Schmidt & V. Schmidt, 2005. "Simulation of typical Cox–Voronoi cells with a special regard to implementation tests," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(3), pages 357-373, December.
    2. Roland Maier & Johannes Mayer & Volker Schmidt, 2004. "Distributional properties of the typical cell of stationary iterated tessellations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(2), pages 287-302, June.
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    1. C. Gloaguen & F. Fleischer & H. Schmidt & V. Schmidt, 2010. "Analysis of Shortest Paths and Subscriber Line Lengths in Telecommunication Access Networks," Networks and Spatial Economics, Springer, vol. 10(1), pages 15-47, March.
    2. C. Gloaguen & F. Fleischer & H. Schmidt & V. Schmidt, 2005. "Simulation of typical Cox–Voronoi cells with a special regard to implementation tests," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(3), pages 357-373, December.

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