K-robust network design using resistance distance: Case of RocketFuel and power grids

Abstract

This paper reconsiders the problem of robust network design form a different point of view using the concept of resistance distance from network science. It has been shown that some important network performance metrics, such as average utilization in a communication network or total power dissipation in an electrical grid, can be expressed in terms of linear combination of point-to-point resistance distances of a graph. In this paper we choose to have a weighted linear combination of resistance distances, referred to as weighted network criticality (WNC), as the objective and we investigate the vulnerability of different network types. In particular, we formulate a min-max convex optimization problem to design k-robust networks and we provide extension to account for joint optimization of resources and flows. We study the solution of the optimization problem in two different networks. First we consider RocketFuel topologies and Abilene as representatives for service provider networks, and we show gains that can be achieved by optimizing link capacities and flows in RocketFuel topologies and Abilene. In the second experience, we show the application of the proposed optimization problem in designing robust electrical grids.