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Dynamic Effects Increasing Network Vulnerability to Cascading Failures
Ingve Simonsen, Lubos Buzna, Karsten Peters, Stefan Bornholdt, Dirk Helbing
TL;DR
The paper asks whether static overload models adequately estimate cascading-failure robustness when transient load redistribution is neglected. It uses a generic flow-conserving dynamical model and finds that transient overshoots can reduce robustness, with χ = τ/τ0 governing the interplay between topology and dynamics.
Problem
Existing cascading-failure studies treat load redistribution as static, switching directly to perturbed-network stationary loads while neglecting transient adjustment.
Method
The paper compares static and dynamical robustness estimates using a minimal flow model incorporating network topology, flow conservation, and load redistribution.
Results
Static and instantaneous dynamic models provide upper and lower robustness estimates, respectively, differing by up to 80% and by more than 95% for more homogeneous link weights.
Takeaways & Limitations
Accurate robustness estimates require considering both network topology and flow dynamics, particularly the timescale ratio χ = τ/τ0.
Takeaways & Limitations
The model is generic rather than a realistic representation of a specific system, so particular system details and features are neglected.
Abstract
from arXiv · showhide
We study cascading failures in networks using a dynamical flow model based on simple conservation and distribution laws to investigate the impact of transient dynamics caused by the rebalancing of loads after an initial network failure (triggering event). It is found that considering the flow dynamics may imply reduced network robustness compared to previous static overload failure models. This is due to the transient oscillations or overshooting in the loads, when the flow dynamics adjusts to the new (remaining) network structure. We obtain {\em upper} and {\em lower} limits to network robustness, and it is shown that {\it two} time scales $τ$ and $τ_0$, defined by the network dynamics, are important to consider prior to accurately addressing network robustness or vulnerability. The robustness of networks showing cascading failures is generally determined by a complex interplay between the network topology and flow dynamics, where the ratio $χ=τ/τ_0$ determines the relative role of the two of them.