π€ AI Summary
This study addresses the limitation of traditional cascade failure models, which assume binary node states and thus fail to capture the partial functionality commonly observed in real-world multilayer systems. To overcome this, the authors propose a multilayer flow network model incorporating partial node functionality and introduce an interlayer influence factor to characterize cross-layer resource competition. Leveraging mean-field theory, they derive recursive equations that predict the fraction of surviving nodes in each layer after cascade termination. This work presents the first systematic modeling of cascade dynamics under partial functionality, uncovering novel phenomena such as non-monotonic robustness curves and equivalent single-layer survival phases. Furthermore, the authors develop a capacity allocation strategy that integrates interlayer influence with local topological information, demonstrating significantly improved system robustness over baseline methods under a fixed total capacity budget.
π Abstract
Cascading failures driven by load or flow redistribution arise in networked systems such as power grids, supply chains, and cloud computing centers. Most flow-network models assume that a node either functions or fails as a whole. In many real systems, however, a node supports several distinct flows that share node-level resources, and failure in one of them does not necessarily imply failure in the others. We study this setting through multiplex flow networks with partial functionality, where a node can remain operational in some functionalities while failing in others. A heavy load on one functionality reduces the capacity available to the others, as quantified by cross-layer influence factors. When a node fails in one layer, its load is redistributed among surviving nodes in that layer, while the node may continue to operate in the others. Using mean-field analysis, we derive recursive equations for the final system sizes, namely the fraction of surviving nodes in each layer after the cascade stops. We validate the analysis through simulations for several load-capacity distributions. We then examine key features of the cascade dynamics, including non-monotone robustness curves, different cascade-outcome regimes, and their relation with cross-layer influence. We map the outcomes to distinct steady-state regimes, including single-layer survival phases absent in joint-functionality models, and show that partial functionality can increase robustness relative to the joint-functionality case. Finally, we study robustness maximization under a fixed total capacity budget by comparing several capacity allocation strategies. We propose a strategy that combines cross-layer influence with local neighborhood information on load and degree, and show that it gives the strongest robustness performance across the configurations considered.