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2016 | OriginalPaper | Buchkapitel

4. Resilience of Spatial Networks

verfasst von : Daqing Li

Erschienen in: Complex Systems and Networks

Verlag: Springer Berlin Heidelberg

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Abstract

Critical infrastructures for transmitting materials, electricity and information between distant places, can be represented as spatial networks. The resilience of spatial networks usually shows unprecedented complexity, leading to the catastrophic cascading failures in the network under various local perturbations. From the viewpoint of physics, the cascading failure process of these networks can be considered as a phase transition, which is characterized by threshold and critical exponents. In this chapter, we first review our research on the definition and measurement of the dimension of these spatial networks, which is essential for determining the critical properties of the phase transition in the network failure process according to statistical physics. Secondly, we review our research on the dynamical organization of flow on these spatial networks, which can help to locate the relation between the flow and overload in the cascading failures. Thirdly, we review our research results on the failure propagation behaviors in the cascading failures, showing long-range decay of spatial correlation between component failures. Finally, we review our research on the modeling of self-healing against cascading failures and discuss the challenges in the reliability engineering for evaluating and improving the resilience of spatial networks.

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Literatur
2.
3.
Zurück zum Zitat Cardy, J.: Scaling and Renormalization in Statistical Physics. Cambridge University Press, Cambridge (1996) Cardy, J.: Scaling and Renormalization in Statistical Physics. Cambridge University Press, Cambridge (1996)
4.
Zurück zum Zitat Plischke, M., Bergersen, B.: Equilibrium Statistical Physics, World Scientific, Singapore (1994) Plischke, M., Bergersen, B.: Equilibrium Statistical Physics, World Scientific, Singapore (1994)
5.
Zurück zum Zitat Li, D., Kosmidis, K., Bunde, A., Havlin, S.: Dimension of spatially embedded networks. Nat. Phys. 7(6), 481–484 (2011)CrossRef Li, D., Kosmidis, K., Bunde, A., Havlin, S.: Dimension of spatially embedded networks. Nat. Phys. 7(6), 481–484 (2011)CrossRef
6.
Zurück zum Zitat Li, D., Li, G., Kosmidis, K., Stanley, H.E., Bunde, A., Havlin, S.: Percolation of spatially constraint networks. EPL (Europhysics Letters) 93(6), 68004 (2011)CrossRef Li, D., Li, G., Kosmidis, K., Stanley, H.E., Bunde, A., Havlin, S.: Percolation of spatially constraint networks. EPL (Europhysics Letters) 93(6), 68004 (2011)CrossRef
7.
Zurück zum Zitat Emmerich, T., Bunde, A., Havlin, S., Li, G., Li, D.: Complex networks embedded in space: dimension and scaling relations between mass, topological distance, and Euclidean distance. Phys. Rev. E 87(3), 032802 (2013)CrossRef Emmerich, T., Bunde, A., Havlin, S., Li, G., Li, D.: Complex networks embedded in space: dimension and scaling relations between mass, topological distance, and Euclidean distance. Phys. Rev. E 87(3), 032802 (2013)CrossRef
8.
Zurück zum Zitat Song, C., Havlin, S., Makse, H.: Self-similarity of complex networks. Nature 433, 392–395 (2005)CrossRef Song, C., Havlin, S., Makse, H.: Self-similarity of complex networks. Nature 433, 392–395 (2005)CrossRef
9.
Zurück zum Zitat Mandelbrot, B.B.: The Fractal Geometry of Nature. Macmillan (1983). ISBN 978-0-7167-1186-5. Retrieved 1 February 2012 Mandelbrot, B.B.: The Fractal Geometry of Nature. Macmillan (1983). ISBN 978-0-7167-1186-5. Retrieved 1 February 2012
10.
Zurück zum Zitat Vicsek, T.: Fractal Growth Phenomena, pp. 31; 139–146. World Scientific, Singapore/New Jersey (1992). ISBN 978-981-02-0668-0 Vicsek, T.: Fractal Growth Phenomena, pp. 31; 139–146. World Scientific, Singapore/New Jersey (1992). ISBN 978-981-02-0668-0
11.
Zurück zum Zitat Albert, R., Barabási, A.-L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74(47–97), (2002) Albert, R., Barabási, A.-L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74(47–97), (2002)
12.
Zurück zum Zitat Newman, M.E.: The structure and function of complex networks. SIAM Rev. 45(167–256), (2003) Newman, M.E.: The structure and function of complex networks. SIAM Rev. 45(167–256), (2003)
13.
Zurück zum Zitat Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwang, D.U.: Complex networks: structure and dynamics. Phys. Rep. 424, 175–308 (2006)MathSciNetCrossRef Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwang, D.U.: Complex networks: structure and dynamics. Phys. Rep. 424, 175–308 (2006)MathSciNetCrossRef
14.
Zurück zum Zitat Weiss, G.H.: Aspects and Applications of the Random Walk. North Holland (1994) Weiss, G.H.: Aspects and Applications of the Random Walk. North Holland (1994)
15.
Zurück zum Zitat 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)CrossRefMATH 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)CrossRefMATH
16.
Zurück zum Zitat Chowdhury, D., Santen, L., Schadschneider, A.: Statistical physics of vehicular traffic and some related systems. Phys. Rep. 329(4), 199–329 (2000)MathSciNetCrossRef Chowdhury, D., Santen, L., Schadschneider, A.: Statistical physics of vehicular traffic and some related systems. Phys. Rep. 329(4), 199–329 (2000)MathSciNetCrossRef
17.
Zurück zum Zitat Helbing, D.: Traffic and related self-driven many-particle systems. Rev. Mod. Phys. 73(4), 1067–1141 (2001)CrossRef Helbing, D.: Traffic and related self-driven many-particle systems. Rev. Mod. Phys. 73(4), 1067–1141 (2001)CrossRef
18.
19.
Zurück zum Zitat Lighthill, M., Whitham, G.: On kinematic waves. I. Flood movement in long rivers. Proc. R. Soc. Lond. A 229(1178), 281–316 (1955) Lighthill, M., Whitham, G.: On kinematic waves. I. Flood movement in long rivers. Proc. R. Soc. Lond. A 229(1178), 281–316 (1955)
20.
Zurück zum Zitat Prigogine, I., Herman, R.: Kinetic Theory of Vehicular Traffic. Elsevier, New York (1971)MATH Prigogine, I., Herman, R.: Kinetic Theory of Vehicular Traffic. Elsevier, New York (1971)MATH
21.
Zurück zum Zitat Newell, G.F.: A simplified theory of kinematic waves in highway traffic, part I: general theory. Transp. Res. Part B 27(4), 281–287 (1993)CrossRef Newell, G.F.: A simplified theory of kinematic waves in highway traffic, part I: general theory. Transp. Res. Part B 27(4), 281–287 (1993)CrossRef
22.
Zurück zum Zitat Bando, M., Hasebe, K., Nakayama, A., Shibata, A., Sugiyama, Y.: Dynamical model of traffic congestion and numerical simulation. Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 51(2), 1035–1042 (1995) Bando, M., Hasebe, K., Nakayama, A., Shibata, A., Sugiyama, Y.: Dynamical model of traffic congestion and numerical simulation. Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 51(2), 1035–1042 (1995)
23.
Zurück zum Zitat Treiber, M., Hennecke, A., Helbing, D.: Congested traffic states in empirical observations and microscopic simulations. Phys. Rev. E. Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 62(2 Pt A), 1805–1824 (2000) Treiber, M., Hennecke, A., Helbing, D.: Congested traffic states in empirical observations and microscopic simulations. Phys. Rev. E. Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 62(2 Pt A), 1805–1824 (2000)
24.
Zurück zum Zitat Nagel, K., Schreckenberg, M.: A cellular automaton model for freeway traffic. J. Phys. I 2(12), 2221–2229 (1992) Nagel, K., Schreckenberg, M.: A cellular automaton model for freeway traffic. J. Phys. I 2(12), 2221–2229 (1992)
25.
Zurück zum Zitat Kerner, B.S.: Experimental features of self-organization in traffic flow. Phys. Rev. Lett. 81, 3797–3800 (1998)CrossRefMATH Kerner, B.S.: Experimental features of self-organization in traffic flow. Phys. Rev. Lett. 81, 3797–3800 (1998)CrossRefMATH
26.
Zurück zum Zitat Helbing, D., Huberman, B.A.: Coherent moving states in highway traffic. Nature 396(6713), 738–740 (1998)CrossRef Helbing, D., Huberman, B.A.: Coherent moving states in highway traffic. Nature 396(6713), 738–740 (1998)CrossRef
27.
Zurück zum Zitat Bollobás, B.: Random Graphs. Academic, London (1985)MATH Bollobás, B.: Random Graphs. Academic, London (1985)MATH
28.
Zurück zum Zitat Toroczkai, Z., Bassler, K.E.: Network dynamics: Jamming is limited in scale-free systems. Nature 428, 716 (2004)CrossRef Toroczkai, Z., Bassler, K.E.: Network dynamics: Jamming is limited in scale-free systems. Nature 428, 716 (2004)CrossRef
29.
Zurück zum Zitat Baldick, R., et al.: Initial review of methods for cascading failure analysis in electric power transmission systems IEEE PES CAMS task force on understanding, prediction, mitigation and restoration of cascading failures. In: IEEE Power and Energy Society General Meeting-Conversion and Delivery of Electrical Energy in the 21st Century, pp. 1–8. IEEE (2008) Baldick, R., et al.: Initial review of methods for cascading failure analysis in electric power transmission systems IEEE PES CAMS task force on understanding, prediction, mitigation and restoration of cascading failures. In: IEEE Power and Energy Society General Meeting-Conversion and Delivery of Electrical Energy in the 21st Century, pp. 1–8. IEEE (2008)
30.
Zurück zum Zitat Caldarelli, G., Chessa, A., Pammolli, F., Gabrielli, A., Puliga, M.: Reconstructing a credit network. Nat. Phys. 9, 125–126 (2013)CrossRef Caldarelli, G., Chessa, A., Pammolli, F., Gabrielli, A., Puliga, M.: Reconstructing a credit network. Nat. Phys. 9, 125–126 (2013)CrossRef
31.
Zurück zum Zitat Helbing, D.: Globally networked risks and how to respond. Nature 497, 51–59 (2013)CrossRef Helbing, D.: Globally networked risks and how to respond. Nature 497, 51–59 (2013)CrossRef
32.
Zurück zum Zitat Buldyrev, S.V., Parshani, R., Paul, G., Stanley, H.E., Havlin, S.: Catastrophic cascade of failures in interdependent networks. Nature 464, 1025–1028 (2010)CrossRef Buldyrev, S.V., Parshani, R., Paul, G., Stanley, H.E., Havlin, S.: Catastrophic cascade of failures in interdependent networks. Nature 464, 1025–1028 (2010)CrossRef
33.
Zurück zum Zitat Zhao, J.H., Zhou, H.J., Liu, Y.Y.: Inducing effect on the percolation transition in complex networks. Nat. Commun. 4, 2412 (2013) Zhao, J.H., Zhou, H.J., Liu, Y.Y.: Inducing effect on the percolation transition in complex networks. Nat. Commun. 4, 2412 (2013)
34.
Zurück zum Zitat Radicchi, F., Arenas, A.: Abrupt transition in the structural formation of interconnected networks. Nat. Phys. 9, 717–720 (2013)CrossRef Radicchi, F., Arenas, A.: Abrupt transition in the structural formation of interconnected networks. Nat. Phys. 9, 717–720 (2013)CrossRef
35.
Zurück zum Zitat Hines, P., Apt, J., Talukdar, S.: Trends in the history of large blackouts in the United States. In: 2008 IEEE Power and Energy Society General Meeting-Conversion and Delivery of Electrical Energy in the 21st Century, pp. 1–8. IEEE (2008) Hines, P., Apt, J., Talukdar, S.: Trends in the history of large blackouts in the United States. In: 2008 IEEE Power and Energy Society General Meeting-Conversion and Delivery of Electrical Energy in the 21st Century, pp. 1–8. IEEE (2008)
36.
Zurück zum Zitat Bak, P., Tang, C., Wiesenfeld, K.: Self-organized criticality—an explanation of 1/f noise. Phys. Rev. Lett. 59, 381–384 (1987)MathSciNetCrossRef Bak, P., Tang, C., Wiesenfeld, K.: Self-organized criticality—an explanation of 1/f noise. Phys. Rev. Lett. 59, 381–384 (1987)MathSciNetCrossRef
38.
Zurück zum Zitat Gao, J., Buldyrev, S.V., Stanley, H.E., Havlin, S.: Networks formed from interdependent networks. Nat. Phys. 8, 40–48 (2012)CrossRef Gao, J., Buldyrev, S.V., Stanley, H.E., Havlin, S.: Networks formed from interdependent networks. Nat. Phys. 8, 40–48 (2012)CrossRef
39.
Zurück zum Zitat Lorenz, J., Battiston, S., Schweitzer, F.: Systemic risk in a unifying framework for cascading processes on networks. Eur. Phys. J. B 71, 441–460 (2009)MathSciNetCrossRefMATH Lorenz, J., Battiston, S., Schweitzer, F.: Systemic risk in a unifying framework for cascading processes on networks. Eur. Phys. J. B 71, 441–460 (2009)MathSciNetCrossRefMATH
40.
Zurück zum Zitat Araújo, N.A., Andrade, J.S., Ziff, R.M., Herrmann, H.J.: Tricritical point in explosive percolation. Phys. Rev. Lett. 106, 095703 (2011) Araújo, N.A., Andrade, J.S., Ziff, R.M., Herrmann, H.J.: Tricritical point in explosive percolation. Phys. Rev. Lett. 106, 095703 (2011)
41.
Zurück zum Zitat Li, D., Jiang, Y., Kang, R., Havlin, S.: Spatial correlation analysis of cascading failures: congestions and blackouts. Sci. Rep. 4 (2014) Li, D., Jiang, Y., Kang, R., Havlin, S.: Spatial correlation analysis of cascading failures: congestions and blackouts. Sci. Rep. 4 (2014)
42.
Zurück zum Zitat Motter, A.E., Lai, Y.C.: Cascade-based attacks on complex networks. Phys. Rev. Lett. 66, 065102 (2002) Motter, A.E., Lai, Y.C.: Cascade-based attacks on complex networks. Phys. Rev. Lett. 66, 065102 (2002)
43.
Zurück zum Zitat Cohen, R., et al.: Resilience of the internet to random breakdowns. Phys. Rev. Lett. 85, 4626–4628 (2000)CrossRef Cohen, R., et al.: Resilience of the internet to random breakdowns. Phys. Rev. Lett. 85, 4626–4628 (2000)CrossRef
44.
Zurück zum Zitat Cohen, R., Erez, K., Ben-Avraham, D., Havlin, S.: Breakdown of the Internet under intentional attack. Phys. Rev. Lett. 86(16), 3682 (2001)CrossRef Cohen, R., Erez, K., Ben-Avraham, D., Havlin, S.: Breakdown of the Internet under intentional attack. Phys. Rev. Lett. 86(16), 3682 (2001)CrossRef
45.
46.
Zurück zum Zitat Berezin, Y., Bashan, A., Danziger, M.M., Li, D., Havlin, S.: Localized attacks on spatially embedded networks with dependencies. Sci. Rep. 5 (2015) Berezin, Y., Bashan, A., Danziger, M.M., Li, D., Havlin, S.: Localized attacks on spatially embedded networks with dependencies. Sci. Rep. 5 (2015)
47.
48.
Zurück zum Zitat Bashan, A., Parshani, R., Havlin, S.: Percolation in networks composed of connectivity and dependency links. Phys. Rev. E 83, 051127 (2011)CrossRef Bashan, A., Parshani, R., Havlin, S.: Percolation in networks composed of connectivity and dependency links. Phys. Rev. E 83, 051127 (2011)CrossRef
49.
Zurück zum Zitat 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, 048701 (2010)CrossRef 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, 048701 (2010)CrossRef
50.
Zurück zum Zitat Cohen, R., Havlin, S.: Complex Networks: Structure, Robustness and Function. Cambridge University Press, Cambridge (2010)CrossRef Cohen, R., Havlin, S.: Complex Networks: Structure, Robustness and Function. Cambridge University Press, Cambridge (2010)CrossRef
51.
Zurück zum Zitat Carreras, B.A., Newman, D.E., Dobson, I., Poole, A.B.: Evidence for self-organized criticality in a time series of electric power system blackouts. IEEE Trans. Circuits Syst. I: Regul. Pap. 51(9), 1733–1740 (2004)CrossRef Carreras, B.A., Newman, D.E., Dobson, I., Poole, A.B.: Evidence for self-organized criticality in a time series of electric power system blackouts. IEEE Trans. Circuits Syst. I: Regul. Pap. 51(9), 1733–1740 (2004)CrossRef
52.
Zurück zum Zitat Liu, C., Li, D., Fu, B., Yang, S., Wang, Y., Lu, G.: Modeling of self-healing against cascading overload failures in complex networks. EPL (Europhysics Letters) 107(6), 68003 (2014)CrossRef Liu, C., Li, D., Fu, B., Yang, S., Wang, Y., Lu, G.: Modeling of self-healing against cascading overload failures in complex networks. EPL (Europhysics Letters) 107(6), 68003 (2014)CrossRef
53.
Zurück zum Zitat Mingjun, W.: Self healing grid and distributed energy resource. Power Syst. Technol. Beijing 31(6), 1 (2007) Mingjun, W.: Self healing grid and distributed energy resource. Power Syst. Technol. Beijing 31(6), 1 (2007)
54.
Zurück zum Zitat Wu, D.Y., Meure, S., Solomon, D.: Self-healing polymeric materials: a review of recent developments. Prog. Polym. Sci. 33(5), 479–522 (2008)CrossRef Wu, D.Y., Meure, S., Solomon, D.: Self-healing polymeric materials: a review of recent developments. Prog. Polym. Sci. 33(5), 479–522 (2008)CrossRef
55.
Zurück zum Zitat Sylvester, D., Blaauw, D., Karl, E.: Elastic: An adaptive self-healing architecture for unpredictable silicon. IEEE Des. Test Comput. 23(6), 484–490 (2006)CrossRef Sylvester, D., Blaauw, D., Karl, E.: Elastic: An adaptive self-healing architecture for unpredictable silicon. IEEE Des. Test Comput. 23(6), 484–490 (2006)CrossRef
56.
Zurück zum Zitat Li, H., Rosenwald, G.W., Jung, J., Liu, C.C.: Strategic power infrastructure defense. Proc. IEEE 93(5), 918–933 (2005)CrossRef Li, H., Rosenwald, G.W., Jung, J., Liu, C.C.: Strategic power infrastructure defense. Proc. IEEE 93(5), 918–933 (2005)CrossRef
57.
Zurück zum Zitat Ming, L., Guangyu, H., Chen, S.: Brief introduction to the IECSA project. Autom. Electr. Power Syst. 30(13), 99–104 (2006) (in Chinese) Ming, L., Guangyu, H., Chen, S.: Brief introduction to the IECSA project. Autom. Electr. Power Syst. 30(13), 99–104 (2006) (in Chinese)
58.
Zurück zum Zitat Liu, C., Li, D., Zio, E., Kang, R.: A modeling framework for system restoration from cascading failures. PLoS ONE 9(12), e112363 (2014)CrossRef Liu, C., Li, D., Zio, E., Kang, R.: A modeling framework for system restoration from cascading failures. PLoS ONE 9(12), e112363 (2014)CrossRef
59.
Zurück zum Zitat Zio, E., Sansavini, G.: Modeling failure cascades in networks systems due to distributed random disturbances and targeted intentional attacks. In: Proceeding of the European Safety and Reliability Conference (2008) Zio, E., Sansavini, G.: Modeling failure cascades in networks systems due to distributed random disturbances and targeted intentional attacks. In: Proceeding of the European Safety and Reliability Conference (2008)
60.
Zurück zum Zitat Watts, D.J., Strogatz, S.H.: Collective dynamics of small-world networks. Nature 393, 440–442 (1998)CrossRef Watts, D.J., Strogatz, S.H.: Collective dynamics of small-world networks. Nature 393, 440–442 (1998)CrossRef
61.
Zurück zum Zitat Elsayed, E.A.: Reliability Engineering, vol. 88. Wiley (2012) Elsayed, E.A.: Reliability Engineering, vol. 88. Wiley (2012)
62.
Zurück zum Zitat Wilkov, R.: Analysis and design of reliable computer networks. IEEE Trans. Commun. 20(3), 660–678 (1972)CrossRef Wilkov, R.: Analysis and design of reliable computer networks. IEEE Trans. Commun. 20(3), 660–678 (1972)CrossRef
63.
Zurück zum Zitat Wilson, J.M.: An improved minimizing algorithm for sum of disjoint products [reliability theory]. IEEE Trans. Reliab. 39(1), 42–45 (1990)CrossRefMATH Wilson, J.M.: An improved minimizing algorithm for sum of disjoint products [reliability theory]. IEEE Trans. Reliab. 39(1), 42–45 (1990)CrossRefMATH
64.
Zurück zum Zitat Wood, R.K.: Factoring algorithms for computing K-terminal network reliability. IEEE Trans. Reliab. 35(3), 269–278 (1986)CrossRefMATH Wood, R.K.: Factoring algorithms for computing K-terminal network reliability. IEEE Trans. Reliab. 35(3), 269–278 (1986)CrossRefMATH
65.
Zurück zum Zitat Lin, Y., Li, D., Liu, C., Kang, R.: Framework design for reliability engineering of complex systems. In: IEEE 4th Annual International Conference on Cyber Technology in Automation, Control, and Intelligent Systems (CYBER), June 2014, pp. 19–24. IEEE (2014) Lin, Y., Li, D., Liu, C., Kang, R.: Framework design for reliability engineering of complex systems. In: IEEE 4th Annual International Conference on Cyber Technology in Automation, Control, and Intelligent Systems (CYBER), June 2014, pp. 19–24. IEEE (2014)
Metadaten
Titel
Resilience of Spatial Networks
verfasst von
Daqing Li
Copyright-Jahr
2016
Verlag
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-662-47824-0_4

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