Cascading Failures in Load-Dependent Finite-Size Random Geometric Networks

The problem of cascading failures in cyber-physical systems is drawing much attention in lieu of different network models for a diverse range of applications. While many analytic results have been reported for the case of large networks, very few of them are readily applicable to finite-size networks. This paper studies cascading failures in load-dependent finite-size geometric networks where the number of nodes is on the order of hundreds as in many real-life networks. In such networks, every node carries a certain amount of load in normal conditions, and maintains a load margin that enables handling a higher load up to a limit, if necessary. We investigate the impact of design parameters such as load margin, node density, and connectivity radius on network reaction to initial disturbances of different sizes. We quantify the damage imposed on the network, and derive lower and upper bounds on the size of this damage. Our finite-size analysis reveals the decisiveness and criticality of taking action within the first few stages of failure propagation in preventing a cascade. Furthermore, studying the trend of the bounds as the number of nodes increases indicates a phase transition behavior in the size of the cascade with respect to the load margin. We derive the critical value of the load margin at which such a transition occurs. The findings of this paper, in particular, shed light on how to choose the load margin appropriately such that a cascade of failures could be avoided.