A note on resilience of telecommunication networks
Rogerio J. M. Alves, Marcos M. Rodrigues, Marcia Helena Moreira Paiva, Marcelo E. V. Segatto · 2017
In telecommunication networks resilience intuitively refers to cycles and their lengths. More specifically, considering that the shortest cycle involving each pair of nodes in the network can be disassembled into two disjoint paths, a working path and a backup path, the average of the shortest cycles involving each pair of nodes in the network can be considered as an indicative of resilience. In turn, the residual mean distances (RMDs) measure the resilience of a telecommunication network from the difference between the average hop distances in the network before and after each possible node or link failure on the network. This indirectly takes into account the differences between the lengths of the working and backup paths defined for each pair of nodes. In this work, we investigate the relationship between the RMDs and two structural properties intrinsically related to the concept of resilience: the average length of the shortest cycles involving each node, and the average length of the shortest cycles involving each pair of nodes of the network. The results of these analyses are presented for all 2-connected networks on 8 nodes. We also present the results of the RMDs for a set of 40 real-world optical backbone networks, and illustrate for a couple of topologies how the values of the edge residual mean distances respond to the lengths of the cycles in each of them.