Overview of precaution and recovery strategies for cascading failures in multilayer networks

Jiang Wen-Jun; Liu Run-Ran; Fan Tian-Long; Liu Shuang-Shuang; Lü Lin-Yuan

doi:10.7498/aps.69.20192000

Abstract

In real life, most of the infrastructure networks closely related to the national economy and people's livelihood do not exist independently, but are interconnected with or dependent on each other, so the multilayer network model is proposed to study the independent complex systems and infrastructures. When the nodes in the multilayer network suffer initial failure or attack, the cascade occurs due to the interaction between the “intra-layer” and “inter-layer”, and the failure can propagate in the network layer and across the layers iteratively, so that the scale of the failures is enlarged gradually. As a result, many multilayer networks are more fragile than single networks. The cascading failure of multilayer network usually brings very serious catastrophes to our society. So, conducting the research on preventing the multilayer network from cascading failure and recovering is of great significance. As far as the prevention of cascading failure is concerned, what are mainly included are the strategies such as the fault detection, the protection of important nodes, the optimization of the coupling method of networks, and the backup of nodes. As for the recovery of multi-layer network, included mainly are the strategies such as common boundary node recovery, the idle connected link recovery, the link addition, the priority recovery of important nodes, the topology perturbation, and the repairing of localized attack and adaptive link.

Keywords:

Authors and contacts

1.
Alibaba Research Center for Complexity Sciences, Hangzhou Normal University, Hangzhou 311121, China
2.
Institute of Fundamental and Frontier Science, University of Electronic Science and Technology of China, Chengdu 611731, China

Corresponding author: Liu Run-Ran, runranliu@163.com ; Lü Lin-Yuan, linyuan.lv@uestc.edu.cn

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References

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[47]	Chen D, Lü L, Shang M S, Zhang Y C, Zhou T 2012 Physica A 391 1777 Google Scholar
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[54]	Hu Y, Zhou D, Zhang R, Han Z, Rozenblat C, Havlin S 2013 Phys. Rev. E 88 052805 Google Scholar
[55]	Parshani R, Rozenblat C, Ietri D, Ducruet C, Havlin S 2011 EPL 92 68002
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[58]	Min B, Do Yi S, Lee K M, Goh K I 2014 Phys. Rev. E 89 042811 Google Scholar
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[62]	Quattrociocchi W, Caldarelli G, Scala A 2014 Plos one 9 e87986 Google Scholar
[63]	Nair D T, Malhotra M 2011 arXiv:1107.1956 v1 [cs.IR]
[64]	Mitchell J C, Teague V 2002 International Symposium on Software Security Nara, Japan, October 3–4, 2002 p58
[65]	Ishida Y, Mori T 2005 International Conference on Knowledge-Based and Intelligent Information and Engineering Systems Melbourne, VIC, Australia, September 14−16, 2005 p79
[66]	Schneider C M, Moreira A A, Andrade J S, Havlin S, Herrmann H J 2011 Proc. Natl. Acad. Sci. 108 3838 Google Scholar
[67]	La Rocca C E, Stanley H E, Braunstein L A 2018 Physica A 508 577 Google Scholar
[68]	Cui P, Zhu P, Wang K, Xun P, Xia Z 2018 Physica A 497 185 Google Scholar
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Cited By

图 1 电力基础设施依赖关系^[9]

Figure 1. Dependencies among power infrastructures^[9].

DownLoad: Full-Size Img PowerPoint

图 2 级联失效迭代过程的建模^[10]　(a) 网络在初始状态下遭到攻击; (b), (c)和(d) 网络在遭受攻击后网络级联失效的不同阶段, 并最终达到了稳态, 级联过程结束

Figure 2. Modeling of cascading failure iterative processes^[10]: (a) The network is attacked in the initial state; (b), (c), and (d) are the cascading failure processes of the network due to the dependencies between dependent networks after the attack, respectively. Eventually reached a steady state.

DownLoad: Full-Size Img PowerPoint

图 3 基于相依网络的保护节点模型^[17]

Figure 3. Nodes protection model based on interdependent networks^[17].

DownLoad: Full-Size Img PowerPoint

图 4 故障恢复策略图解^[14] 网络A和网络B的巨分支如图所示. 情况1: 两个通过相依边连接的失效节点(节点1和节点2)分别距离其巨分支的距离l = 1, 然后以恢复概率γ进行修复; 情况2: 如果两个相互依赖的故障节点(节点3和节点5)中至少有一个与其巨分支的距离大于1, 则不符合恢复的条件, 所以放弃恢复这一对节点

Figure 4. Illustration of failure recovery strategy^[14]. The giant components of network A and network B are shown in the figure. Case 1: Two failed nodes (nodes 1 and 2) connected by dependent edges are respectively at a distance of l = 1 from their maximal cluster, and then repaired with recovery probability γ. Case 2: If at least one of the two interdependentdent failed nodes (nodes 3 and 5) is more than 1 away from its maximal cluster, the recovery condition is not met, so the pair of nodes is abandoned to be restored.

DownLoad: Full-Size Img PowerPoint

图 5 网络B中恢复策略的实现示意图^[67]　(a) GC表示网络巨分支, 虚线表示空闲连边, 带有空闲连边的簇表示可修复的簇, 没有空闲连边的簇表示无法进行恢复的簇; (b)网络B完成重连后的巨分支

Figure 5. Schematic diagram of the implementation of recovery strategy in network B^[67]: (a) GC represents the giant component of the network, the dashed lines indicate idle connected edges, clusters with free connected edges repre-sent repairable clusters, and clusters without free connected edges represent clusters that cannot be recovered; (b) the giant component of network B after reconnection.

DownLoad: Full-Size Img PowerPoint

图 6 恢复模型

Figure 6. Schematic diagram of recovery model.

DownLoad: Full-Size Img PowerPoint

表 1 重大停电事故数据^[11]

Table 1. Data on major power outages^[11].

地点	日期	受灾人数/百万
巴西	1999/3/11	97
印度	2001/1/2	230
美国, 加拿大	2003/8/14-15	55
意大利, 瑞士	2003/9/28	55
印度尼西亚	2005/8/18	100
巴西, 巴拉圭	2009/11/10-11	87
土耳其	2015/3/31	70
印度	2012/7/30-31	620
孟加拉	2014/11/1/	150
肯尼亚	2016/6/7	44

DownLoad: CSV

[1]	Eubank S, Guclu H, Kumar V A, Marathe M V, Srinivasan A, Toroczkai Z, Wang N J N 2004 Nature 429 180 Google Scholar
[2]	Keeling M J, Eames K T 2005 J. R. Soc. Interface 2 295 Google Scholar
[3]	Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821 Google Scholar
[4]	Yu W, Chen G, Lü J J A 2009 Automatica 45 429 Google Scholar
[5]	Qi X, Yang G, Liu L 2020 Physica A 539 122870 Google Scholar
[6]	Liu Y Y, Slotine J J, Barabási A L 2011 Nature 473 167 Google Scholar
[7]	Wang X F, Chen G 2002 Physica A 310 521 Google Scholar
[8]	Rueda D F, Calle E 2017 Int. J. Crit. Infrastruct. Prot. 16 3 Google Scholar
[9]	Rinaldi S M, Peerenboom J P, Kelly T K 2001 IEEE Control Syst. Mag. 21 11 Google Scholar
[10]	Buldyrev S V, Parshani R, Paul G, Stanley H E, Havlin S 2010 Nature 464 1025 Google Scholar
[11]	Tootaghaj D Z, Bartolini N, Khamfroush H, La Porta T 2007 IEEE 36th Symposium on Reliable Distributed Systems (SRDS) pp54−63
[12]	崔聪聪 http://mini.eastday.com/a/180419160201052.html [2018-04-19] Cui C C http://mini.eastday.com/a/180419160201052.html [2018-04-19] (in chinese)
[13]	中国日报网 http://www.xinhuanet.com/world/2015-07/24/c_128056543.htm [2015-07-24] China Daily http://www.xinhuanet.com/world/2015-07/24/ c_128056543.htm [2015-07-24] (in Chinese)
[14]	Di Muro M A, La Rocca C E, Stanley H, Havlin S, Braunstein L A 2016 Sci. Rep. 6 22834 Google Scholar
[15]	Gao J, Buldyrev S V, Stanley H E, Havlin S 2012 Nat. Phys. 8 40 Google Scholar
[16]	Gao J, Li D, Havlin S 2014 Natl. Sci. Rev. 1 346 Google Scholar
[17]	Gong M, Wang Y, Wang S, Liu W 2017 Sci. Rep. 7 12753 Google Scholar
[18]	Baxter G, Dorogovtsev S, Goltsev A, Mendes J 2012 Phys. Rev. Lett. 109 248701 Google Scholar
[19]	Faqeeh A, Melnik S, Colomer-de-Simón P, Gleeson J P 2016 Phys. Rev. E 93 062308
[20]	Murakami M, Ishikura S, Kominami D 2017 Appl. Netw. Sci. 2 6 Google Scholar
[21]	Malgorzata T, Keith B, Martin R, Ananthram S, Raissa M D 2019 Phys. Rev. E 99 032308 Google Scholar
[22]	Shekhtman L M, Berezin Y, Danziger M M, Havlin S 2014 Phys. Rev. E 90 012809 Google Scholar
[23]	Zhao J, Li D, Sanhedrai H, Cohen R, Havlin S 2016 Nat. Commun. 7 10094 Google Scholar
[24]	Dorogovtsev S N, Mendes J F F, Samukhin A N 2001 Phys. Rev. E 64 025101 Google Scholar
[25]	Liu X, Stanley H E, Gao J 2016 Proc. Natl. Acad. Sci. 113 1138 Google Scholar
[26]	Azimi Tafreshi N, Dorogovtsev S N, Mendes J F 2014 Phys. Rev. E 90 052809 Google Scholar
[27]	van der Hoorn P, Litvak N 2015 Phys. Rev. E 92 022803 Google Scholar
[28]	Klimek P, Thurner S, Hanel R 2009 J. Theor. Biol. 256 142 Google Scholar
[29]	Baxter G J, Dorogovtsev S N, Goltsev A V, Mendes J F 2010 Phys. Rev. E 82 011103 Google Scholar
[30]	Parisi G, Sellitto M 2015 EPL 109 36001 Google Scholar
[31]	Liu R R, Eisenberg D A, Seager T P, Lai Y C 2018 Sci. Rep. 8 2111 Google Scholar
[32]	Albert R, Jeong H, Barabási A L 2000 Nature 406 378 Google Scholar
[33]	Lü L, Chen D, Ren X L, Zhang Q M, Zhang Y C, Zhou T 2016 Phys. Rep. 650 1 Google Scholar
[34]	Fan T, Lü L, Shi D, Zhou T 2020 arXiv: 2001.08541 [physics.soc-ph]
[35]	Parshani R, Buldyrev S V, Havlin S 2010 Phys. Rev. Lett. 105 048701 Google Scholar
[36]	范天龙, 朱燕燕, 吴蕾蕾, 任晓龙, 吕琳媛 2017 电子科技大学学报 46 766 Google Scholar Fan T L, Zhu Y Y, Wu L L, Ren X L, Lü L Y 2017 JEST 46 766 Google Scholar
[37]	Schneider C M, Yazdani N, Araújo N A, Havlin S, Herrmann H J 2013 Sci. Rep. 3 1969 Google Scholar
[38]	Huang X, Gao J, Buldyrev S V, Havlin S, Stanley H E 2011 Phys. Rev. E 83 065101 Google Scholar
[39]	Barabási A L, Albert R 1999 Science 286 509
[40]	Du R, Dong G, Tian L, Liu R 2016 Physica A 450 687 Google Scholar
[41]	Osat S, Faqeeh A, Radicchi F 2017 Nat.Commun. 8 1540 Google Scholar
[42]	De Domenico M, Solé-Ribalta A, Omodei E, Gómez S, Arenas A 2015 Nat. Commun. 6 6868 Google Scholar
[43]	Bonacich P 1972 J. Math. Sociol. 2 113 Google Scholar
[44]	Freeman L C 1978 Soc. Networks 1 215 Google Scholar
[45]	Freeman L C 1977 Soc. Networks 40 35
[46]	Kitsak M, Gallos L K, Havlin S, Liljeros F, Muchnik L, Stanley H E, Makse H A 2010 Nat. Phys. 6 888 Google Scholar
[47]	Chen D, Lü L, Shang M S, Zhang Y C, Zhou T 2012 Physica A 391 1777 Google Scholar
[48]	Brin S, Page L 1998 Comput. Networks 30 107
[49]	Lü L, Zhang Y C, Yeung C H, Zhou T 2011 PloS one 6 e21202 Google Scholar
[50]	Blondel V D, Guillaume J L, Lambiotte R, Lefebvre E 2008 J. Stat. Mech.:Theory Exp. 2008 P10008 Google Scholar
[51]	Dugué N, Perez A 2015 HAL Id: hal-01231784
[52]	Reis S D, Hu Y, Babino A, Andrade Jr J S, Canals S, Sigman M, Makse H A 2014 Nat. Phys. 10 762 Google Scholar
[53]	Liu R R, Jia C X, Lai Y C 2019 Phys. Rev. E 100 052306
[54]	Hu Y, Zhou D, Zhang R, Han Z, Rozenblat C, Havlin S 2013 Phys. Rev. E 88 052805 Google Scholar
[55]	Parshani R, Rozenblat C, Ietri D, Ducruet C, Havlin S 2011 EPL 92 68002
[56]	Zhou D, Stanley H E, D’Agostino G, Scala A 2012 Phys. Rev. E 86 066103 Google Scholar
[57]	Radicchi F, Bianconi G 2017 Phys. Rev. X 7 011013
[58]	Min B, Do Yi S, Lee K M, Goh K I 2014 Phys. Rev. E 89 042811 Google Scholar
[59]	Yuan X, Hu Y, Stanley H E, Havlin S 2017 Proc. Natl. Acad. Sci. 114 3311 Google Scholar
[60]	Ishida Y 2005 International Conference on Knowledge-Based and Intelligent Information and Engineering Systems Melbourne, VIC, Australia, September 14−16, 2005 p86
[61]	Valdez L D, Macri P A, Braunstein L 2014 J. Phys. A: Math. Theor. 47 055002 Google Scholar
[62]	Quattrociocchi W, Caldarelli G, Scala A 2014 Plos one 9 e87986 Google Scholar
[63]	Nair D T, Malhotra M 2011 arXiv:1107.1956 v1 [cs.IR]
[64]	Mitchell J C, Teague V 2002 International Symposium on Software Security Nara, Japan, October 3–4, 2002 p58
[65]	Ishida Y, Mori T 2005 International Conference on Knowledge-Based and Intelligent Information and Engineering Systems Melbourne, VIC, Australia, September 14−16, 2005 p79
[66]	Schneider C M, Moreira A A, Andrade J S, Havlin S, Herrmann H J 2011 Proc. Natl. Acad. Sci. 108 3838 Google Scholar
[67]	La Rocca C E, Stanley H E, Braunstein L A 2018 Physica A 508 577 Google Scholar
[68]	Cui P, Zhu P, Wang K, Xun P, Xia Z 2018 Physica A 497 185 Google Scholar
[69]	吴佳键, 龚凯, 王聪, 王磊 2018 物理学报 67 88901 Wu J J, Gong K, Wang C, Wang L 2018 Acta Phys. Sin. 67 88901
[70]	Berezin Y, Bashan A, Danziger M M, Li D, Havlin S 2015 Sci. Rep. 5 8934 Google Scholar
[71]	Gong K, Wu J J, Liu Y, Li Q, Liu R R, Tang M 2019 Complexity 2019 10
[72]	Stippinger M, Kertész J J 2014 Physica A 416 481 Google Scholar
[73]	Gong M, Ma L, Cai Q, Jiao L 2015 Sci. Rep. 5 8439 Google Scholar
[74]	Erdős P, Rényi A 1959 Publ. Math. Debrecen 4 3286
[75]	Shao S, Huang X, Stanley H E, Havlin S 2015 New J. Phys. 17 023049 Google Scholar
[76]	Li W, Bashan A, Buldyrev S V, Stanley H E, Havlin S 2012 Phys. Rev. Lett. 108 228702 Google Scholar
[77]	Liu R R, Jia C X, Lai Y C 2019 New J. Phys. 21 045002 Google Scholar

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Vol. 69, Issue 8 - 2020-04-20

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