Cascading Failures in Interdependent Lattice Networks: The Critical Role of the Length of Dependency Links

TL;DR

This study investigates how the length of dependency links affects cascading failures in interdependent lattice networks, revealing a transition from second to first order and identifying the most vulnerable dependency range.

Contribution

It introduces a model analyzing the impact of dependency link length on failure cascades, combining analytical and simulation approaches to identify critical thresholds and transition types.

Findings

Percolation transition changes from second to first order at r_max≈8

Critical threshold peaks at 0.738 for r=r_max

Vulnerability is maximized at intermediate dependency distances

Abstract

We study the cascading failures in a system composed of two interdependent square lattice networks A and B placed on the same Cartesian plane, where each node in network A depends on a node in network B randomly chosen within a certain distance $r$ from the corresponding node in network A and vice versa. Our results suggest that percolation for small $r$ below $r_{\rm max}\approx 8$ (lattice units) is a second-order transition, and for larger $r$ is a first-order transition. For $r<r_{\rm max}$, the critical threshold increases linearly with $r$ from 0.593 at $r=0$ and reaches a maximum, 0.738 for $r=r_{\rm max}$ and then gradually decreases to 0.683 for $r=\infty$. Our analytical considerations are in good agreement with simulations. Our study suggests that interdependent infrastructures embedded in Euclidean space become most vulnerable when the distance between interdependent nodes is in the intermediate range, which is much smaller than the size of the system.