Self-organization of dragon king failures

Yuansheng Lin, Keith Burghardt, Martin Rohden, Pierre-André Noël, and Raissa M. D'Souza
Phys. Rev. E 98, 022127 – Published 27 August 2018

Abstract

The mechanisms underlying cascading failures are often modeled via the paradigm of self-organized criticality. Here we introduce a simple network model where nodes self-organize to be either weakly or strongly protected against failure in a manner that captures the trade-off between degradation and reinforcement of nodes inherent in many network systems. If strong nodes cannot fail, any failure is contained to a single, isolated cluster of weak nodes and the model produces power-law distributions of failure sizes. We classify the large, rare events that involve the failure of only a single cluster as “black swans.” In contrast, if strong nodes fail once a sufficient fraction of their neighbors fail, then failure can cascade across multiple clusters of weak nodes. If over 99.9% of the nodes fail due to this cluster hopping mechanism, we classify this as a “dragon king,” which are massive failures caused by mechanisms distinct from smaller failures. The dragon kings observed are self-organized, existing over a wide range of reinforcement rates and system sizes. We find that once an initial cluster of failing weak nodes is above a critical size, the dragon king mechanism kicks in, leading to piggybacking system-wide failures. We demonstrate that the size of the initial failed weak cluster predicts the likelihood of a dragon king event with high accuracy and we develop a simple control strategy that can dramatically reduce dragon kings and other large failures.

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  • Received 13 July 2017
  • Revised 4 June 2018

DOI:https://doi.org/10.1103/PhysRevE.98.022127

©2018 American Physical Society

Physics Subject Headings (PhySH)

NetworksStatistical Physics & ThermodynamicsNonlinear DynamicsInterdisciplinary Physics

Authors & Affiliations

Yuansheng Lin1,2,3,*, Keith Burghardt4, Martin Rohden3, Pierre-André Noël3, and Raissa M. D'Souza3,5,6

  • 1School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China
  • 2Beijing Jingdong Century Trade Co., Ltd., Beijing 101111, China
  • 3Department of Computer Science, University of California, Davis, California 95616, USA
  • 4Information Sciences Institute, University of Southern California, Marina del Rey, California 90292, USA
  • 5Department of Mechanical and Aerospace Engineering, University of California, Davis, California 95616, USA
  • 6Santa Fe Institute, Santa Fe, New Mexico 87501, USA

  • *bhlys1106@gmail.com

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Issue

Vol. 98, Iss. 2 — August 2018

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