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Joint distributions for total lengths of shortest-path trees in telecommunication networks

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Abstract

Shortest-path trees play an important role in the field of optimising fixed-access telecommunication networks with respect to costs and capacities. Distributional properties of the corresponding two half-trees originating from the root of such a tree are of special interest for engineers. In the present paper, we derive parametric approximation formulas for the marginal density functions of the total lengths of both half-trees. Besides, a parametric copula is used in order to combine the marginal distributions of these functionals to a bivariate joint distribution as, naturally, the total lengths of the half-trees are not independent random variables. Asymptotic results for infinitely sparse and infinitely dense networks are discussed as well.

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Author information

Authors and Affiliations

  1. Ulm University, Helmholtzstraße 18, 89069, Ulm, Germany

    David Neuhäuser, Christian Hirsch & Volker Schmidt

  2. Orange Labs, 38-40 rue du Général Leclerc, 92794 Cedex 9, Issy-Moulineaux, France

    Catherine Gloaguen

Authors
  1. David Neuhäuser
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  2. Christian Hirsch
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  3. Catherine Gloaguen
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  4. Volker Schmidt
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Corresponding author

Correspondence to David Neuhäuser.

Additional information

This work was supported by Orange Labs through Research grant No. 46146063-9241. Christian Hirsch was supported by a research grant from DFG Research Training Group 1100 at Ulm University. Parts of the numerical results were obtained by the help of Jan Sommer.

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Neuhäuser, D., Hirsch, C., Gloaguen, C. et al. Joint distributions for total lengths of shortest-path trees in telecommunication networks. Ann. Telecommun. 70, 221–232 (2015). https://doi.org/10.1007/s12243-014-0440-9

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  • DOI: https://doi.org/10.1007/s12243-014-0440-9

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