Overload-Based Cascades in Multiplex Flow Networks with Partial Functionality
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.