The effect of different couplings on mitigating failure cascades in interdependent networks

Many real-world (cyber-)physical infrastructure systems are multi-layered, consisting of multiple inter-dependent networks/layers. Due to this interdependency, the failure cascade can be catastrophic in a inter-dependent, multi-layered system, and even lead to the break-down of the entire system. The 2003 blackout of the Italian power grid is reportedly the result of a cascading failure due to the inter-dependency of the power grid and the communication network that it relies on. In this paper, we propose a theoretical framework for studying cascading failures in an inter-dependent, multi-layer system, where we consider the effects of cascading failures both within and across different layers. The goal of the study is to investigate how different couplings (i.e., inter-dependencies) between network elements across layers affect the cascading failure dynamics. Through experiments using the proposed framework, we show that under the one-to-one coupling, how nodes from two inter-dependent networks are coupled together play a crucial role in the final size of the resulting failure cascades: coupling corresponding nodes from two networks with equal importance (i.e., 'highto-high' coupling) result in smaller failure cascades than other forms of inter-dependence coupling such as 'random' or 'lowto-high' coupling. Our results shed lights on potential strategies for mitigating cascading failures in inter-dependent networks.