考虑节点过载的复杂网络级联失效模型
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摘要
针对现实网络中节点对负载的冗余能力,提出一种考虑节点过载状态的复杂网络级联失效模型。首先,根据过载系数、失效概率、剩余系数构建了级联失效模型;然后,基于节点的特性提出了过载节点负载分配策略;最后,运用BA无标度网络进行级联失效情况下的抗毁性仿真。结果表明:在过载节点负载分配策略中,混合分配策略整体上较优,能够显著控制级联失效的影响并且增加了网络的抗毁性;在一定范围内提高过载系数、分布系数有助于降低级联失效的影响,但提高到一定程度时效果并不理想;剩余系数存在某一值可增强网络的抗毁性。
In order to discuss redundant capacity of nodes against load,this paper proposes a cascading failure model of complex networks considering overloaded nodes.Firstly,the cascading failure model is constructed according to the overloaded coefficient,failure probability and residual coefficient.Then,based on the characteristics of nodes,the load distribution strategies of the overloaded nodes are proposed.Finally,under cascading failure,invulnerability is simulated in BA scale-free network.The results show that in the load distribution strategies of the overloaded nodes,the mixed distribution strategy is better on the whole,which can significantly control cascading failure and increase the invulnerability;to a certain extent,raising the overloaded coefficient and distribution coefficient is helpful to reduce the impact of cascading failure,while this is not effective when both are large;and the invulnerability gets enhanced,when the residual coefficient is a certain value.
In order to discuss redundant capacity of nodes against load,this paper proposes a cascading failure model of complex networks considering overloaded nodes.Firstly,the cascading failure model is constructed according to the overloaded coefficient,failure probability and residual coefficient.Then,based on the characteristics of nodes,the load distribution strategies of the overloaded nodes are proposed.Finally,under cascading failure,invulnerability is simulated in BA scale-free network.The results show that in the load distribution strategies of the overloaded nodes,the mixed distribution strategy is better on the whole,which can significantly control cascading failure and increase the invulnerability;to a certain extent,raising the overloaded coefficient and distribution coefficient is helpful to reduce the impact of cascading failure,while this is not effective when both are large;and the invulnerability gets enhanced,when the residual coefficient is a certain value.
引文
[1]WU J J,SUN H J,GAO Z Y.Cascading failures on weighted urban traffic equilibrium networks[J].Physica A Statistical Mechanics&Its Applications,2007,386(1):407-413.
[2]种鹏云,帅斌.连环恐怖袭击下危险品运输网络级联失效建模[J].系统工程理论与实践,2014,34(4):1059-1065.CHONG P Y,SHUAI B.Model of cascading failure in hazardous materials transportation network under series of terrorist attacks[J].Systems Engineering-Theory&Practice,2014,34(4):1059-1065.
[3]KINNEY R,ALBERT R.Modeling cascading failures in the north American power grid[J].The European Physical Journal B-Condensed Matter and Complex Systems,2005,46(1):101-107.
[4]WEI D Q,LUO X S,ZHANG B.Analysis of cascading failure in complex power networks under the load local preferential redistribution rule[J].Physica A Statistical Mechanics&Its Applications,2012,391(8):2771-2777.
[5]ROHDEN M,JUNG D,TAMRAKAR S,et al.Cascading failures in ac electricity grids[J].Physical Review E,2016,94(3/1):032209.
[6]张超,张凤鸣,王瑛,等.基于复杂网络视角的航空通信网络鲁棒性分析[J].系统工程与电子技术,2015,37(1):180-184.ZHANG C,ZHANG F M,WANG Y,et al.Method to analyses the robustness of aviation communication network based on com-plex networks[J].Systems Engineering and Electronics,2015,37(1):180-184.
[7]崔琼,李建华,王鹏,等.指挥信息系统双层耦合网络模型级联失效研究[J].哈尔滨工业大学学报,2017,49(5):100-108.CUI Q,LI J H,WANG P,et al.Cascading failure of command information system bi-layer coupled network model[J].Journal of Harbin Institute of Technology,2017,49(5):100-108.
[8]韩海艳,杨任农,李浩亮,等.双层相依指挥控制网络级联失效研究[J].中南大学学报(自然科学版),2015,46(12):4542-4547.HAN H Y,YANG R N,LI H L,et al.Cascading failure of two-layered interdependent command and control network[J].Journal of Central South University(Science and Technology),2015,46(12):4542-4547.
[9]SHUANG Q,LIU Y,TANG Y,et al.System reliability evaluation in water distribution networks with the impact of valves experiencing cascading failures[J].Water,2017,9(6):413-429.
[10]SHUANG Q,ZHANG M,YUAN Y.Node vulnerability of water distribution networks under cascading failures[J].Reliability Engineering&System Safety,2014,124:132-141.
[11]MOTTER A E,LAI Y C.Cascade-based attacks on complex networks[J].Physical Review E Statistical Nonlinear&Soft Matter Physics,2002,66(2):065102.
[12]DOU B L,WANG X G,ZHANG S Y.Robustness of networks against cascading failures[J].Physica A Statistical Mechanics&Its Applications,2010,389(11):2310-2317.
[13]BAO Z J,CAO Y J,DING L J,et al.Comparison of cascading failures in small-world and scale-free networks subject to vertex and edge attacks[J].Physica A Statistical Mechanics&Its Applications,2009,388(20):4491-4498.
[14]WANG W X,CHEN G.Universal robustness characteristic of weighted networks against cascading failure[J].Physical Review E Statistical Nonlinear&Soft Matter Physics,2008,77(2):026101.
[15]丁琳,张嗣瀛.面向级联失效的复杂网络加权策略[J].控制与决策,2013,28(9):1399-1402.DING L,ZHANG S Y.Cascading failures-oriented weighting strategies on complex networks[J].Control and Decision,2013,28(9):1399-1402.
[16]崔文岩,孟相如,康巧燕,等.基于复合边权重的加权复杂网络级联抗毁性优化[J].系统工程与电子技术,2017,39(2):355-361.CUI W Y,MENG X R,KANG Q Y,et al.Optimization of cascading invulnerability on weighted complex networks based on composite edge weight model[J].Systems Engineering and Electronics,2017,39(2):355-361.
[17]WANG J W,ZHANG C,HUANG Y,et al.Attack robustness of cascading model with node weight[J].Nonlinear Dynamics,2014,78(1):37-48.
[18]WANG J W,RONG L L,ZHANG L,et al.Attack vulnerability of scale-free networks due to cascading failures[J].Physica A Statistical Mechanics&Its Applications,2008,387(26):6671-6678.
[19]段东立,吴俊,邓宏钟,等.基于可调负载重分配的复杂网络级联失效模型[J].系统工程理论与实践,2013,33(1):203-208.DUAN D L,WU J,DENG H Z,et al.Cascading failure model of complex networks based on tunable load redistribution[J].Systems Engineering-Theory&Practice,2013,33(1):203-208.
[20]DUAN D L,LING X D,WU X Y,et al.Critical thresholds for scale-free networks against cascading failures[J].Physica A Statistical Mechanics&Its Applications,2014,416:252-258.
[21]李勇,吕欣,谭跃进.基于级联失效的战域保障网络节点容量优化[J].复杂系统与复杂性科学,2009,6(1):69-76.LI Y,LU X,TAN Y J.Optimizing node capacity of campaign logistics networks based on cascading failure[J].Complex Systems and Complexity Science,2009,6(1):69-76.
[22]陈世明,庞少鹏,邹小群,等.面向级联失效的加权网络负载容量非线性模型鲁棒性优化[J].控制与决策,2013,28(7):1041-1045.CHEN S M,PANG S P,ZOU X Q,et al.Robustness optimization of load-capacity nonlinear model in weighted network for cascading failure[J].Control and Decision,2013,28(7):1041-1045.
[23]ASH J,NEWTH D.Optimizing complex networks for resilience against cascading failure[J].Physica A Statistical Mechanics&Its Applications,2007,380:673-683.
[24]TIAN M,WANG X,DONG Z,et al.Cascading failures of interdependent modular scale-free networks with different coupling preferences[J].Europhysics Letters,2015,111:18007.
[25]ZHU G,WANG X,TIAN M,et al.Cascading failures of interdependent modular small-world networks[J].Modern Physics Letters B,2016,30(18):1650174.
[26]HONG C,ZHANG J,DU W B,et al.Cascading failures with local load redistribution in interdependent Watts-Strogatz networks[J].International Journal of Modern Physics C,2016,27(11):1650131.
[27]ZHANG X J,GU B,GUAN X M,et al.Cascading failure in scale-free networks with tunable clustering[J].International Journal of Modern Physics C,2016,27(8):1650093.
[2]种鹏云,帅斌.连环恐怖袭击下危险品运输网络级联失效建模[J].系统工程理论与实践,2014,34(4):1059-1065.CHONG P Y,SHUAI B.Model of cascading failure in hazardous materials transportation network under series of terrorist attacks[J].Systems Engineering-Theory&Practice,2014,34(4):1059-1065.
[3]KINNEY R,ALBERT R.Modeling cascading failures in the north American power grid[J].The European Physical Journal B-Condensed Matter and Complex Systems,2005,46(1):101-107.
[4]WEI D Q,LUO X S,ZHANG B.Analysis of cascading failure in complex power networks under the load local preferential redistribution rule[J].Physica A Statistical Mechanics&Its Applications,2012,391(8):2771-2777.
[5]ROHDEN M,JUNG D,TAMRAKAR S,et al.Cascading failures in ac electricity grids[J].Physical Review E,2016,94(3/1):032209.
[6]张超,张凤鸣,王瑛,等.基于复杂网络视角的航空通信网络鲁棒性分析[J].系统工程与电子技术,2015,37(1):180-184.ZHANG C,ZHANG F M,WANG Y,et al.Method to analyses the robustness of aviation communication network based on com-plex networks[J].Systems Engineering and Electronics,2015,37(1):180-184.
[7]崔琼,李建华,王鹏,等.指挥信息系统双层耦合网络模型级联失效研究[J].哈尔滨工业大学学报,2017,49(5):100-108.CUI Q,LI J H,WANG P,et al.Cascading failure of command information system bi-layer coupled network model[J].Journal of Harbin Institute of Technology,2017,49(5):100-108.
[8]韩海艳,杨任农,李浩亮,等.双层相依指挥控制网络级联失效研究[J].中南大学学报(自然科学版),2015,46(12):4542-4547.HAN H Y,YANG R N,LI H L,et al.Cascading failure of two-layered interdependent command and control network[J].Journal of Central South University(Science and Technology),2015,46(12):4542-4547.
[9]SHUANG Q,LIU Y,TANG Y,et al.System reliability evaluation in water distribution networks with the impact of valves experiencing cascading failures[J].Water,2017,9(6):413-429.
[10]SHUANG Q,ZHANG M,YUAN Y.Node vulnerability of water distribution networks under cascading failures[J].Reliability Engineering&System Safety,2014,124:132-141.
[11]MOTTER A E,LAI Y C.Cascade-based attacks on complex networks[J].Physical Review E Statistical Nonlinear&Soft Matter Physics,2002,66(2):065102.
[12]DOU B L,WANG X G,ZHANG S Y.Robustness of networks against cascading failures[J].Physica A Statistical Mechanics&Its Applications,2010,389(11):2310-2317.
[13]BAO Z J,CAO Y J,DING L J,et al.Comparison of cascading failures in small-world and scale-free networks subject to vertex and edge attacks[J].Physica A Statistical Mechanics&Its Applications,2009,388(20):4491-4498.
[14]WANG W X,CHEN G.Universal robustness characteristic of weighted networks against cascading failure[J].Physical Review E Statistical Nonlinear&Soft Matter Physics,2008,77(2):026101.
[15]丁琳,张嗣瀛.面向级联失效的复杂网络加权策略[J].控制与决策,2013,28(9):1399-1402.DING L,ZHANG S Y.Cascading failures-oriented weighting strategies on complex networks[J].Control and Decision,2013,28(9):1399-1402.
[16]崔文岩,孟相如,康巧燕,等.基于复合边权重的加权复杂网络级联抗毁性优化[J].系统工程与电子技术,2017,39(2):355-361.CUI W Y,MENG X R,KANG Q Y,et al.Optimization of cascading invulnerability on weighted complex networks based on composite edge weight model[J].Systems Engineering and Electronics,2017,39(2):355-361.
[17]WANG J W,ZHANG C,HUANG Y,et al.Attack robustness of cascading model with node weight[J].Nonlinear Dynamics,2014,78(1):37-48.
[18]WANG J W,RONG L L,ZHANG L,et al.Attack vulnerability of scale-free networks due to cascading failures[J].Physica A Statistical Mechanics&Its Applications,2008,387(26):6671-6678.
[19]段东立,吴俊,邓宏钟,等.基于可调负载重分配的复杂网络级联失效模型[J].系统工程理论与实践,2013,33(1):203-208.DUAN D L,WU J,DENG H Z,et al.Cascading failure model of complex networks based on tunable load redistribution[J].Systems Engineering-Theory&Practice,2013,33(1):203-208.
[20]DUAN D L,LING X D,WU X Y,et al.Critical thresholds for scale-free networks against cascading failures[J].Physica A Statistical Mechanics&Its Applications,2014,416:252-258.
[21]李勇,吕欣,谭跃进.基于级联失效的战域保障网络节点容量优化[J].复杂系统与复杂性科学,2009,6(1):69-76.LI Y,LU X,TAN Y J.Optimizing node capacity of campaign logistics networks based on cascading failure[J].Complex Systems and Complexity Science,2009,6(1):69-76.
[22]陈世明,庞少鹏,邹小群,等.面向级联失效的加权网络负载容量非线性模型鲁棒性优化[J].控制与决策,2013,28(7):1041-1045.CHEN S M,PANG S P,ZOU X Q,et al.Robustness optimization of load-capacity nonlinear model in weighted network for cascading failure[J].Control and Decision,2013,28(7):1041-1045.
[23]ASH J,NEWTH D.Optimizing complex networks for resilience against cascading failure[J].Physica A Statistical Mechanics&Its Applications,2007,380:673-683.
[24]TIAN M,WANG X,DONG Z,et al.Cascading failures of interdependent modular scale-free networks with different coupling preferences[J].Europhysics Letters,2015,111:18007.
[25]ZHU G,WANG X,TIAN M,et al.Cascading failures of interdependent modular small-world networks[J].Modern Physics Letters B,2016,30(18):1650174.
[26]HONG C,ZHANG J,DU W B,et al.Cascading failures with local load redistribution in interdependent Watts-Strogatz networks[J].International Journal of Modern Physics C,2016,27(11):1650131.
[27]ZHANG X J,GU B,GUAN X M,et al.Cascading failure in scale-free networks with tunable clustering[J].International Journal of Modern Physics C,2016,27(8):1650093.