Scale-free resilience of real traffic jams

Limiao Zhang, Guanwen Zeng, Daqing Li, Hai Jun Huang, H. Eugene Stanley, Shlomo Havlin

Research output: Contribution to journalArticlepeer-review

93 Scopus citations


The concept of resilience can be realized in natural and engineering systems, representing the ability of a system to adapt and recover from various disturbances. Although resilience is a critical property needed for understanding and managing the risks and collapses of transportation systems, an accepted and useful definition of resilience for urban traffic as well as its statistical property under perturbations are still missing. Here, we define city traffic resilience based on the spatiotemporal clusters of congestion in real traffic and find that the resilience follows a scale-free distribution in 2D city road networks and 1D highways with different exponents but similar exponents on different days and in different cities. The traffic resilience is also revealed to have a scaling relation between the cluster size of the spatiotemporal jam and its recovery duration independent of microscopic details. Our findings of universal traffic resilience can provide an indication toward better understanding and designing of these complex engineering systems under internal and external disturbances.

Original languageEnglish
Pages (from-to)8673-8678
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number18
StatePublished - 30 Apr 2019

Bibliographical note

Funding Information:
ACKNOWLEDGMENTS. H.-J.H. and D.L. acknowledge support from the National Natural Science Foundation of China (Grants 71890971/71890970 and 71890973/71890970). D.L. also acknowledges support from National Natural Science Foundation of China Grants 71822101 and 71771009. S.H. thanks the Israel Ministry of Science and Technology with the Italian Ministry of Foreign Affairs, the Israel Ministry of Foreign Affairs with the Japan Science Foundation, the Israel Science Foundation, the Office of Naval Research Global, Defense Threat Reduction Agency Grant HDTRA-1-10-1-0014, the Army Research Office, the Binational Science Foundation with the National Science Foundation, and the Bar-Ilan University Center for Cybersecurity and Applied Cryptography for financial support. The Boston University Center for Polymer Studies is supported by National Science Foundation Grant PHY-1505000 and by Defense Threat Reduction Agency Grant HDTRA1-14-1-0017.

Publisher Copyright:
© 2019 National Academy of Sciences. All rights reserved.


  • Complex systems
  • Resilience
  • Scaling laws
  • Spatiotemporal
  • Traffic congestion

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