Arabian Journal for Science and Engineering

, Volume 44, Issue 3, pp 2837–2851 | Cite as

Robustness Analysis of Interdependent Urban Critical Infrastructure Networks Against Cascade Failures

  • Fang Zhou
  • Yongbo YuanEmail author
  • Mingyuan Zhang
Research Article - Systems Engineering


This paper presents the robustness analysis of the interdependencies between urban critical infrastructures (CI) against cascade failures. An analytical approach based on the dynamic percolation theory was introduced to investigate the multilayer interactional CI networks and to predict the urban calamity spreading as illustrate with example of China. The synergetic effect of the functional and geographical interdependencies between the networks on cascade failures of CI was studied by comparing four relevance patterns: no interdependency, the functional interdependency, the geographical interdependency, and the functional with geographical interdependency, where three different attack strategies were simultaneously considered. The results indicate that the geographical interdependency has a remarkable influence on the robustness of networks compared with functional interdependency. Moreover, excavating the scope and extent of the impact of these interdependencies, one can also find that the power network basically governs the cascade failures of global systems in contrast with water or gas network.


Critical infrastructures Cascade failures Interdependencies Robustness analysis Networks 


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This work was supported by General project of Department of Education of Liaoning Province (L2014034), Natural Science Foundation of Liaoning Province (2015020611) and Dalian Youth Technology Star Project Support Plan (2016RQ002).The authors also gratefully acknowledge the helpful comments and suggestions of the reviewers, which have improved the presentation.


  1. 1.
    Gao, J.; Buldyrev, S.V.; Havlin, S.; Stanley, H.E.: Robustness of a network of networks. Phys. Rev. Lett. 107(19), 195701 (2011)Google Scholar
  2. 2.
    Havlin, S.; Kenett, D.Y.; Bashan, A.; Gao, J.; Stanley, H.E.: Vulnerability of network of networks. Eur. Phys. J. Spec. Top. 223(11), 2087–2106 (2014)Google Scholar
  3. 3.
    Liu, X.; Peng, H.; Gao, J.: Vulnerability and controllability of networks of networks. Chaos Solitons Fractals 80, 125–138 (2015)zbMATHGoogle Scholar
  4. 4.
    Gao, J.; Liu, X.; Li, D.; Havlin, S.: Recent progress on the resilience of complex networks. Energies 8(10), 12187–12210 (2015)Google Scholar
  5. 5.
    Shekhtman, L.M.; Danziger, M.M.; Havlin, S.: Recent advances on failure and recovery in networks of networks. Chaos Solitons Fractals 90, 28–36 (2016)zbMATHGoogle Scholar
  6. 6.
    Danziger, M.M.; Shekhtman, L.M.; Bashan, A.; Berezin, Y.; Havlin, S.: Vulnerability of Interdependent Networks and Networks of Networks, Interconnected Networks. Springer International Publishing, Berlin (2016)zbMATHGoogle Scholar
  7. 7.
    Shen, A.; Guo, J.; Wang, Z.: Research on methods for improving robustness of cascading failures of interdependent networks. Wirel. Pers. Commun. 1–16 (2017)Google Scholar
  8. 8.
    Wang, J.; Lao, S.; Ruan, Y.; Bai, L.; Hou, L.: Research on the robustness of interdependent networks under localized attack. Appl. Sci. 7(6), 597 (2017)Google Scholar
  9. 9.
    Qiu, J.; Wang, T.; Yin, S.; Gao, H.: Data-based optimal control for networked double-layer industrial processes. IEEE Trans. Ind. Electron. 64(5), 4179–4186 (2017)Google Scholar
  10. 10.
    Qiu, J.; Wei, Y.; Karimi, H.R.; Gao, H.: Reliable control of discrete-time piecewise-affine time-delay systems via output feedback. IEEE Trans. Reliab. 67(1), 1–13 (2018)Google Scholar
  11. 11.
    Buldyrev, S.V.; Parshani, R.; Paul, G.; Stanley, H.E.; Havlin, S.: Catastrophic cascade of failures in interdependent networks. Nature 464, 1025–1028 (2010)Google Scholar
  12. 12.
    Vespignani, A.: Complex networks: the fragility of interdependency. Nature 464(7291), 984–985 (2010)Google Scholar
  13. 13.
    Barsali, S.; Giglioli, R.; Poli, D.; Sforna, M.; Salvati, R.; Zaottini, R.: The restoration of an electric power system: International survey and discussion of possible innovative enhancements for the Italian system. Electr. Power Syst. Res. 78(2), 239–247 (2008)Google Scholar
  14. 14.
    Miaolei, S.; Jewell, W.: Analysis of protective relay performance in the August 2003 North American blackout. In: 2006 39th Annual Frontiers of Power Conference, Proceedings VII-A-1-VII/6 (2006)Google Scholar
  15. 15.
    Liu, L.; Liu, W.; Cartes, D.A.; Chung, I.Y.: Slow coherency and angle modulated particle swarm optimization based islanding of large-scale power systems. Adv. Eng. Inform. 23(1), 45–56 (2009)Google Scholar
  16. 16.
    Brown, S.W.: Leveraging mandatory and enforceable Electric Reliability Standards for non-registered rural electric utilities. Rural Electric Power Conference IEEE, pp. A1-1–A1-5 (2012)Google Scholar
  17. 17.
    Panasetsky, D.; Tomin, N.: Using of neural network technology and multi-agent systems to preventing large-scale emergencies in electric power systems. In: International Youth Conference on Energy IEEE, pp. 1–8 (2013)Google Scholar
  18. 18.
    McDaniels, T.; Chang, S.; Peterson, K.; Mikawoz, J.; Reed, D.: Empirical framework for characterizing infrastructure failure interdependencies. J. Infrastruct. Syst. 13(3), 175–184 (2007)Google Scholar
  19. 19.
    Ouyang, M.; Wang, Z.: Resilience assessment of interdependent infrastructure systems: with a focus on joint restoration modeling and analysis. Reliab. Eng. Syst. Saf. 141, 74–82 (2015)Google Scholar
  20. 20.
    Su, H.; Zio, E.; Zhang, J.; Li, X.: A systematic framework of vulnerability analysis of a natural gas pipeline network. Reliab. Eng. Syst. Saf. 175, 79–91 (2018)Google Scholar
  21. 21.
    Su, H.; Zhang, J.; Zio, E.; Yang, N.; Li, X.; Zhang, Z.: An integrated systemic method for supply reliability assessment of natural gas pipeline networks. Appl. Energy 209, 489–501 (2018)Google Scholar
  22. 22.
    Kang, F.; Han, S.; Salgado, R.; Li, J.: System probabilistic stability analysis of soil slopes using Gaussian process regression with Latin hypercube sampling. Comput. Geotech. 63, 13–25 (2015)Google Scholar
  23. 23.
    Levi, V.A.; Nahman, J.M.; Nedic, D.P.: Security modeling for power system reliability evaluation. IEEE Trans. Power Syst. 16(1), 29–37 (2001)Google Scholar
  24. 24.
    Pryor, R.J.; Basu, N.; Quint, T.: Development of Aspen: A microanalytic simulation model of the US economy. Energy Plan. Policy (1996)Google Scholar
  25. 25.
    Basu, N.; Pryor, R.; Quint, T.: ASPEN: a microsimulation model of the economy. Comput. Econ. 12(3), 223–41 (1998)zbMATHGoogle Scholar
  26. 26.
    Cardellini, V.; Casalicchio, E.; Galli, E.: Agent-based modeling of interdependencies in critical infrastructures through UML. In: Spring Simulation Multiconference Society for Computer Simulation, International, pp. 119–126 (2007)Google Scholar
  27. 27.
    Casalicchio, E.; Galli, E.; Tucci, S.: Federated agent-based modeling and simulation approach to study interdependencies in IT critical infrastructures. In: Distributed Simulation and Real-Time Applications, IEEE International Symposium, pp. 182–189. IEEE (2007)Google Scholar
  28. 28.
    Ravimaran, S.; Mohamed, M.A.M.: Integrated Obj\_FedRep: evaluation of surrogate object based mobile cloud system for federation, replica and data management. Arab. J. Sci. Eng. 39(6), 4577–4592 (2014)Google Scholar
  29. 29.
    Malik, F.H.; Lehtonen, M.: A review: agents in smart grids. Electr. Power Syst. Res. 131, 71–79 (2016)Google Scholar
  30. 30.
    Ouyang, M.: Review on modeling and simulation of interdependent critical infrastructure systems. Reliab. Eng. Syst. Saf. 121(1), 43–60 (2014)Google Scholar
  31. 31.
    Dauelsberg, L.; Outkin, A.: Modeling economic impacts to critical infrastructures in a system dynamics framework. In: Proceedings of the 23rd International Conference of the System Dynamics Society, Boston, July, pp. 17–21 (2005)Google Scholar
  32. 32.
    Fair, J.M.; LeClaire, R.J.; Wilson, M.L.; Turk, A.L.; DeLand, S.M.; Powell, D.R.; Klare, P.C.; Ewers, M.; Dauelsberg, L.; Izraelevitz, D.: An integrated simulation of pandemic influenza evolution, mitigation and infrastructure response. In: IEEE Conference on Technologies for Homeland Security IEEE, pp. 240–245 (2007)Google Scholar
  33. 33.
    Conrad, S.H.; LeClaire, R.J.; O’Reilly, G.P.; Uzunalioglu, H.: Critical national infrastructure reliability modeling and analysis. Bell Labs Tech. J. 11(3), 57–71 (2010)Google Scholar
  34. 34.
    Santos, J.R.: Inoperability input-output modeling of disruptions to interdependent economic systems. 9(1), 20–34 (2006)Google Scholar
  35. 35.
    Wei, H.; Dong, M.; Sun, S.: Inoperability input-output modeling (IIM) of disruptions to supply chain networks. Syst. Eng. 13(4), 324–339 (2010)Google Scholar
  36. 36.
    Kenett, D.Y.; Gao, J.; Huang, X.; Shao, S.; Vodenska, I.; Buldyrev, S.V.; Paul, G.; Stanley, H.E.; Havlin, S.: Network of Interdependent Networks: Overview of Theory and Applications, Networks of Networks: The Last Frontier of Complexity, Understanding Complex Systems, pp. 3–36. Springer International Publishing, Cham (2014)Google Scholar
  37. 37.
    Parshani, R.; Buldyrev, S.V.; Havlin, S.: Interdependent networks: reducing the coupling strength leads to a change from a first to second order percolation transition. Phys. Rev. Lett. 105(4), 048701 (2010)Google Scholar
  38. 38.
    Shao, J.; Buldyrev, S.V.; Braunstein, L.A.; Havlin, S.; Stanley, H.E.: Structure of shells in complex networks. Phys. Rev. E 80(2), 036105 (2009)Google Scholar
  39. 39.
    Gao, J.; Buldyrev, S.V.; Stanley, H.E.; Havlin, S.: Networks formed from interdependent networks. Nat. Phys. 8(1), 40–48 (2012)Google Scholar
  40. 40.
    Liu, X.; Stanley, H.E.; Gao, J.: Breakdown of interdependent directed networks. Proc. Natl. Acad. Sci. 113(5), 1138–1143 (2016)Google Scholar
  41. 41.
    Hu, Y.; Havlin, S.; Makse, H.A.: Conditions for viral influence spreading through multiplex correlated social networks. Phys. Rev. X 4(2), 021031 (2014)Google Scholar
  42. 42.
    Tayan, O.; Binali, A.M.A.; Kabir, M.N.: Analytical and computer modelling of transportation systems for traffic bottleneck resolution: a Hajj case study. Arab. J. Sci. Eng. 39(10), 7013–7037 (2014)Google Scholar
  43. 43.
    Radicchi, F.: Percolation in real interdependent networks. Nat. Phys. 11(7), 597–602 (2015)Google Scholar
  44. 44.
    Li, D.; Fu, B.; Wang, Y.; Lu, G.; Berezin, Y.; Stanley, H.E.; Havlin, S.: Percolation transition in dynamical traffic network with evolving critical bottlenecks. Proc. Natl. Acad. Sci. 112(3), 669–672 (2015)Google Scholar
  45. 45.
    Deng, Y.; Song, L.; Zhou, J.; Wang, J.: Evaluation and reduction of vulnerability of subway equipment: an integrated framework. Saf. Sci. 103, 172–182 (2018)Google Scholar
  46. 46.
    Rinaldi, S.M.; Peerenboom, J.P.; Kelly, T.K.: Identifying, understanding, and analyzing critical infrastructure interdependencies. IEEE Control Syst. 21(6), 11–25 (2001)Google Scholar
  47. 47.
    Dueñas-Osorio, L.; Craig, J.I.; Goodno, B.J.; Bostrom, A.: Interdependent response of networked systems. J. Infrastruct. Syst. 13(3), 185–194 (2007)Google Scholar
  48. 48.
    Patterson, S.A.; Apostolakis, G.E.: Identification of critical locations across multiple infrastructures for terrorist actions. Reliab. Eng. Syst. Saf. 92(9), 1183–1203 (2007)Google Scholar
  49. 49.
    Robert, B.; Morabito, L.: An approach to identifying geographic interdependencies among critical infrastructures. Int. J. Crit. Infrastruct. 6(1), 17–30 (2010)Google Scholar
  50. 50.
    Johansson, J.; Hassel, H.: An approach for modelling interdependent infrastructures in the context of vulnerability analysis. Reliab. Eng. Syst. Saf. 95(12), 1335–1344 (2010)Google Scholar
  51. 51.
    González, A.D.; Dueñas-Osorio, L.; Sánchez-Silva, M.; Medaglia, A.L.: The interdependent network design problem for optimal infrastructure system restoration. Comput. Aided Civ. Infrastruct. Eng. 31(5), 334–350 (2016)Google Scholar
  52. 52.
    González, A.D.; Sanchez-Silva, M.; Dueñas-Osorio, L.; Medaglia, A.L.: Mitigation strategies for lifeline systems based on the interdependent network design problem. In: International Conference on Vulnerability and Risk Analysis and Management, pp. 762–771 (2014)Google Scholar
  53. 53.
    Dorogovtsev, S.N.; Mendes, J.F.F.; Samukhin, A.N.: Giant strongly connected component of directed networks. Phys. Rev. E 64(2 Pt 2), 025101 (2001)Google Scholar
  54. 54.
    Newman, M.; Strogatz, S.H.; Watts, D.J.: Random graphs with arbitrary degree distributions and their applications. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 64(2), 026118 (2001)Google Scholar
  55. 55.
    Selcuk, A.S.; Yücemen, M.S.: Reliability of lifeline networks under seismic hazard. Reliab. Eng. Syst. Saf. 65(3), 213–227 (1999)Google Scholar
  56. 56.
    Zimmerman, R.: Social implications of infrastructure network interactions. J. Urban Technol. 8(3), 97–119 (2001)Google Scholar
  57. 57.
    Zhang, P.; Peeta, S.: A generalized modeling framework to analyze interdependencies among infrastructure systems. Transp. Res. Part B Methodol. 45(3), 553–579 (2011)Google Scholar
  58. 58.
    Martinez-Anido, C.B.; Bolado, R.; Vries, L.D.; Fulli, G.; Vandenbergh, M.; Masera, M.: European power grid reliability indicators, what do they really tell? Electr. Power Syst. Res. 90(90), 79–84 (2012)Google Scholar
  59. 59.
    Ouyang, M.; Dueñas-Osorio, L.: An approach to design interface topologies across interdependent urban infrastructure systems. Reliab. Eng. Syst. Saf. 96(11), 1462–1473 (2011)Google Scholar
  60. 60.
    Ouyang, M.; Dueñas-Osorio, L.: Efficient approach to compute generalized interdependent effects between infrastructure systems. J. Comput. Civ. Eng. 25(5), 394–406 (2011)Google Scholar

Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  1. 1.Department of Construction ManagementDalian University of TechnologyDalianChina

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