Abstract-When transport in networks follows the shortest paths, the union of all shortest path trees GuCpt can be regarded as the "transport overlay network". Overlay networks such as peer-to-peer networks or virtual private networks can be considered as a subgraph of Guspt. We construct two types of Guspt (a) GuCpt(f,) where a is the extreme value index of polynomial link weights and (b) GuCpt(p) where p is the correlation coefficient of the 2-dimensional correlated uniformly distributed link weights in QoS routing. By tuning the extreme value index ag of polynomial link weights, a phase transition occurs around a critical extreme value index ac, of the link weight distribution. If ag > oa,, transport in the network traverses many links whereas for ag < o,, all transport flows over a critical backbone: the Minimum Spanning Tree (MST). In QoS routing with 2-dimensional link weights, as we decrease the correlation coefficient p from 1 to -1, the overlay Guspt becomes denser, and is equal to the substrate when p =-1. With the Erdos-Renyi random graph as the underlying topology, we show that the overlay Gu,pt(p) is also close to an Erdos-Renyi random graph Gp (N), an observation with potential for mobile and wireless ad-hoc networks. The existence of such a controllable transition in the overlay structure may allow network operators to steer and balance flows in their network.
The construction of overlay networks, that can be regarded as "logical transport networks" in the sense defined in REF , namely composed of a fraction of the links of the underlying network, is of great importance in various areas of telecommunication network design.
Constructing the Overlay Network by Tuning Link Weights
2007 Second International Conference on Communications and Networking in China
2007 Second International Conference on Communications and Networking in China
Mathematics