Abstract
Robustness and cascading failures in interdependent systems has been an active research field in the past decade. However, most existing works use percolation-based models where only the largest component of each network remains functional throughout the cascade. Although suitable for communication networks, this assumption fails to capture the dependencies in systems carrying a flow (e.g., power systems, road transportation networks), where cascading failures are often triggered by redistribution of flows leading to overloading of lines. Here, we consider a model consisting of systems and with initial line loads and capacities given by and , respectively. When a line fails in system , fraction of its load is redistributed to alive lines in , while remaining fraction is redistributed equally among all functional lines in ; a line failure in is treated similarly with giving the fraction to be redistributed to . We give a thorough analysis of cascading failures of this model initiated by a random attack targeting fraction of lines in and fraction in . We show that (i) the model captures the real-world phenomenon of unexpected large scale cascades and exhibits interesting transition behavior: the final collapse is always first order, but it can be preceded by a sequence of first- and second-order transitions; (ii) network robustness tightly depends on the coupling coefficients and , and robustness is maximized at non-trivial values in general; (iii) unlike most existing models, interdependence has a multifaceted impact on system robustness in that interdependency can lead to an improved robustness for each individual network.
4 More- Received 5 September 2017
- Revised 31 January 2018
DOI:https://doi.org/10.1103/PhysRevE.97.022307
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