中国物理B ›› 2009, Vol. 18 ›› Issue (11): 4754-4759.doi: 10.1088/1674-1056/18/11/025

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Cascading failures in congested complex networks with feedback

郑建风1, 高自友1, 傅白白2, 李峰2   

  1. (1)Institute of System Science, School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China; (2)State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China
  • 收稿日期:2008-11-14 修回日期:2009-03-07 出版日期:2009-11-20 发布日期:2009-11-20
  • 基金资助:
    Project partly supported by National Basic Research Program of China (Grant No 2006CB705500), National Natural Science Foundation of China (Grant Nos 70631001, 70671008 and 70801005) and the Innovation Foundation of Science and Technology for Excellent Doctorial Candidate of Beijing Jiaotong University (Grant No 48033).

Cascading failures in congested complex networks with feedback

Zheng Jian-Feng(郑建风)a)†, Gao Zi-You(高自友)a) ‡, Fu Bai-Bai(傅白白) b), and Li Feng(李峰)b)   

  1. a Institute of System Science, School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China; b State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China
  • Received:2008-11-14 Revised:2009-03-07 Online:2009-11-20 Published:2009-11-20
  • Supported by:
    Project partly supported by National Basic Research Program of China (Grant No 2006CB705500), National Natural Science Foundation of China (Grant Nos 70631001, 70671008 and 70801005) and the Innovation Foundation of Science and Technology for Excellent Doctorial Candidate of Beijing Jiaotong University (Grant No 48033).

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摘要： In this article, we investigate cascading failures in complex networks by introducing a feedback. To characterize the effect of the feedback, we define a procedure that involves a self-organization of trip distribution during the process of cascading failures. For this purpose, user equilibrium with variable demand is used as an alternative way to determine the traffic flow pattern throughout the network. Under the attack, cost function dynamics are introduced to discuss edge overload in complex networks, where each edge is assigned a finite capacity (controlled by parameter α). We find that scale-free networks without considering the effect of the feedback are expected to be very sensitive to α as compared with random networks, while this situation is largely improved after introducing the feedback.

Abstract: In this article, we investigate cascading failures in complex networks by introducing a feedback. To characterize the effect of the feedback, we define a procedure that involves a self-organization of trip distribution during the process of cascading failures. For this purpose, user equilibrium with variable demand is used as an alternative way to determine the traffic flow pattern throughout the network. Under the attack, cost function dynamics are introduced to discuss edge overload in complex networks, where each edge is assigned a finite capacity (controlled by parameter $\alpha$). We find that scale-free networks without considering the effect of the feedback are expected to be very sensitive to α as compared with random networks, while this situation is largely improved after introducing the feedback.

Key words: complex networks, cascading failures, feedback

中图分类号:  (Self-organized systems)

  • 05.65.+b
89.75.Hc (Networks and genealogical trees)