Analysis and Optimization of Robustness in Multiplex Flow Networks Against Cascading Failures

Abstract

Networked systems are susceptible to cascading failures, where the failure of an initial set of nodes propagates through the network, often leading to system-wide failures. In this work, we propose a multiplex flow network model to study robustness against cascading failures triggered by random failures. The model is inspired by systems where nodes carry or support multiple types of flows, and failures result in the redistribution of flows within the same layer rather than between layers. To represent different types of interdependencies between the layers of the multiplex network, we define two cases of failure conditions: layer-independent overload and layer-influenced overload. We provide recursive equations and their solutions to calculate the steady-state fraction of surviving nodes, validate them through a set of simulation experiments, and discuss optimal load-capacity allocation strategies. Our results demonstrate that allocating the total excess capacity to each layer proportional to the mean effective load in the layer and distributing that excess capacity equally among the nodes within the layer ensures maximum robustness. The proposed framework for different failure conditions allows us to analyze the two overload conditions presented and can be extended to explore more complex interdependent relationships.

References in corpus (18)

• Catastrophic cascade of failures in interdependent networks
• Cascade-based attacks on complex networks
• A model for cascading failures in complex networks
• Interdependent networks: Reducing the coupling strength leads to a change from a first to second order percolation transition
• The Physics of Financial Networks
• Interdependent networks with correlated degrees of mutually dependent nodes
• Percolation in real interdependent networks
• Tri-critical behavior in rupture induced by disorder
• Robustness of supply chain networks against underload cascading failures
• Cascading failures in interdependent systems under a flow redistribution model
• The resilience of interdependent transportation networks under targeted attack
• Sandpiles on multiplex networks
• Optimizing the robustness of electrical power systems against cascading failures
• Robustness of power systems under a democratic fiber bundle-like model
• Cascades in interdependent flow networks
• Cascading failures in interdependent networks with finite functional components
• A Fiber Bundle Model of Traffic Jams
• Abrupt transition due to non-local cascade propagation in multiplex systems