Abnormal dynamics induced by congestion effect in cascading failures

Robustness of infrastructure networks is essential for our modern society. Cascading failures are the cause of most large-scale network outages. We study the cascading failure of networks due to overload, using the betweenness centrality of an edge as the measure of its initial load. Taking into account the congestion effect of a slightly overloading edge, we define two capacities (the basic capacity and the removal capacity) of every edge and give three possible states (the free state, the congestion state, and the removal state) of every edge according to its current load. We propose a new method to dynamically adjust two capacities of the slightly overloading edge and study the dynamical features of cascading propagation induced by removing the edge with the highest load in two artificial networks, two traffic networks, and two power grids. We mainly focus on the relationship between the capacity parameters and two robust metrics. By simulations, we find two interesting and counterintuitive results, i.e. enhancing the basic capacity of every edge may weaken the network robustness, and fixing the basic capacity of every edge, simply improving the removal capacity of every edge sometimes makes the whole network more invulnerable. These findings show that investing more maintenance resources to alleviate flow congestion is not always better to avoid the cascading propagation, which is similar to Braess's paradox in traffic networks.