Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-27T08:36:35.426Z Has data issue: false hasContentIssue false
  • English
  • Français

PATHS IN THE SIMPLE RANDOM GRAPH AND THE WAXMAN GRAPH

Published online by Cambridge University Press:  11 January 2002

Piet Van Mieghem
Piet Van Mieghem
Affiliation:
Information Technology and Systems, Delft University of Technology, Delft, The Netherlands, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The Waxman graphs are frequently chosen in simulations as topologies resembling communications networks. For the Waxman graphs, we present analytic, exact expressions for the link density (average number of links) and the average number of paths between two nodes. These results show the similarity of Waxman graphs to the simpler class G>p(N). The first result enables one to compare simulations performed on the Waxman graph with those on other graphs with same link density. The average number of paths in Waxman graphs can be useful to dimension (or estimate) routing paths in networks. Although higher-order moments of the number of paths in Gp(N) are difficult to compute analytically, the probability distribution of the hopcount of a path between two arbitrary nodes seems well approximated by a Poisson law.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 15 , Issue 4 , October 2001 , pp. 535 - 555
Copyright
© 2001 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)