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

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. Keywords Shortest-path tree · Palm calculus · parametric copula · tree length · network planning · pseudo-maximum-likelihood · stochastic geometry Mathematics Subject Classification (2000) 60D05 · 65C99 · 62E17

• Type: Journal
• Year: 2015
• Where: ADT
• Authors: David Neuhäuser, Christian Hirsch, Catherine Gloaguen, Volker Schmidt
• Keywords: ADT 2015, Programming Languages