01.06.2015 | Ausgabe 5-6/2015
Joint distributions for total lengths of shortest-path trees in telecommunication networks
- Zeitschrift:
- Annals of Telecommunications > Ausgabe 5-6/2015
Wichtige Hinweise
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.
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.
