基于Markov更新过程的城市交通网络级联失效评价模型
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摘要
根据路段单元状态与其功能之间的关系,给出了路段单元状态的‘失效—非失效'二态表示方法,进一步根据网络中路段单元之间的连接关系,提出了道路交通网络‘级联失效'态的定义及识别方法;利用更新理论及Markov链相关理论,分析了道路交通网络级联失效态—非级联失效态持续时间随机变化的概率分布规律,给出了对假想分布的未知参数进行估计及对假想分布进行假设检验的方法,并提出了以失效次数及转移概率为主要评价参数的交通网络级联失效评价模型。以一个实际路网为例,对模型进行了标定,将标定好的模型评价结果与实际观察结果进行了比对,结果显示模型具有较好的实用性。
According to the relationship between the state of the link and its function,a " failure-non failure" state representation for the link is given.Furthermore,the definition and recognition method of cascading failure state of road traffic network is proposed according to the connection between the links in the network.Using the renewal and Markov chain theory,the probability distribution of the ‘cascading failure-non cascading failure 'state duration time is analyzed.The method for estimating the unknown parameters and testing the hypothetical distribution is given,and the cascading failure evaluation model of traffic network based on the number of failures and the transfer probability is also proposed.Taking an actual road network as an example,the model is calibrated,the calibrated model evaluation results are compared with the actual observation results,and the two results are very close,which indicates that the model is of high accuracy.
According to the relationship between the state of the link and its function,a " failure-non failure" state representation for the link is given.Furthermore,the definition and recognition method of cascading failure state of road traffic network is proposed according to the connection between the links in the network.Using the renewal and Markov chain theory,the probability distribution of the ‘cascading failure-non cascading failure 'state duration time is analyzed.The method for estimating the unknown parameters and testing the hypothetical distribution is given,and the cascading failure evaluation model of traffic network based on the number of failures and the transfer probability is also proposed.Taking an actual road network as an example,the model is calibrated,the calibrated model evaluation results are compared with the actual observation results,and the two results are very close,which indicates that the model is of high accuracy.
引文
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[26]王正武,周振宇,胡静.基于节点修复效果的故障路网修复策略[J].长沙理工大学学报(自然科学版),2014,11(4):25-31.
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[28]王芳.基于级联失效的均衡路网脆弱性研究[D].西南交通大学,成都,2013.
[29]陈小兰.城市交通复杂网络级联失效影响源辨识[D].长沙理工大学,长沙,2013.
[30]尹洪英,权小锋.交通运输网络级联失效影响规律及影响范围[J].系统管理学报,2013,22(6):869-875.
[31]Trivedi K S.Probability and statistics with reliability,queuing,and computer science applications[M].Wiley,2002:47-57.
[32]Ross S M.Introduction to probability models[J].Technometrics,2006,82(1):625-627.
[33]Kerner,Boris S,Rehborn,et al.Recognition and tracking of spatial–temporal congested traffic patterns on freeways[J].Transportation Research Part C,2004,12(5):369-400.
[34]关伟,何蜀燕.基于统计特性的城市快速路交通流状态划分[J].交通运输系统工程与信息,2007(05):42-50.
[35]蔡燕飞.基于交通相特征的交通系统状态识别[D].华南理工大学,广州,2011.
[36]袁鹏程,隽志才.区域交通网络行程时间估计的半Markov链模型[J].系统管理学报,2014,23(5):690-697.
[2]Albert R,Jeong H.Barabasi A L:Error and attack tolerance of complex networks[J].Nature,2000,406(6794):378-382.
[3]Jeong H,Mason S P,Barabási A L,Oltvai Z N.Lethality and centrality in protein networks[J].Nature,2001,411(6833):41-42.
[4]Dunne J A,Williams R J,Martinez N D.Network structure and biodiversity loss in food webs:robustness increases with connectance[J].Ecology Letters,2002,5(4):558–567.
[5]Samant K,Bhattacharyya S.Topology,Search,and Fault Tolerance in Unstructured P2P Networks[C].Hawaii International Conference on System Sciences,2004,DOI:10.1109/HICSS.2004.1:265-682.
[6]Magoni D.Tearing down the Internet[J].IEEE Journal on Selected Areas in Communications,2003,21(6):949-960.
[7]曾小舟,唐笑笑,江可申.基于复杂网络理论的中国航空网络抗毁性测度分析[J].系统仿真技术,2012,08(2):111-116.
[8]刘杰.基于复杂网络理论的城市轨道交通网络抗毁性研究[D].西南交通大学,成都,2012.
[9]Watts D J.A Simple Model of Global Cascades on Random Networks[J].Proceedings of the National Academy of Sciences of the United States of America,2002,99(9):5766-5771.
[10]Moreno Y,Pastor-Satorras R,Vázquez A,Vespignani A.Critical load and congestion instabilities in scalefree networks[J].Eur ophysics Letters,2002,62(2):292-298.
[11]Holme P,Kim B J.Vertex overload breakdown in evolving networks[J].Physical Review E Statistical Nonlinear&Soft Matter Physics,2002,65(2):036-119.
[12]Crucitti P,Latora V,Marchiori M.Model for cascading failures in complex networks[J].Physical Review E Statistical Nonlinear&Soft Matter Physics,2004,69(4):045-104.
[13]Lise S,Paczuski M.A Nonconservative Earthquake Model of Self-Organized Criticality on a Random Graph[J].Physical Review Letters,2002,88(22):228-301.
[14]Dobson I,Chen J,Thorp J S,et al.Examining criticality of blackouts in power system models with cascading events[C].Hawaii International Conference on System Sciences,2002,DOI:10.1109/HICSS.2002.993-975.
[15]Yi G,Wang Z,Luo S,Wang Y.A cascading failure model for interdomain routing system[J].International Journal of Communication Systems,2012,25(8):1068-1076.
[16]Parrilo P A,Lall S,Paganini F,et al.Model reduction for analysis of cascading failures in power systems[C].American Control Conference,1999.Proceedings of the1999,1999(6):4208-4212.
[17]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.
[18]Zheng J F,Gao Z Y,Zhao X M.Modeling cascading failures in congested complex networks[J].Physica A Statistical Mechanics&Its Applications,2007,385(2):700-706.
[19]Qian Y,Wang B,Xue Y,et al.A simulation of the cascading failure of a complex network model by considering the characteristics of road traffic conditions[J].Nonlinear Dynamics,2015,80(1-2):413-420.
[20]Zhan X,Ukkusuri S V,Rao P S C.Dynamics of functional failures and recovery in complex road networks[J].PHYSICAL REVIEW E,2017,96(5).052-301.
[21]Li K,Ma X,Shao F.An improved network model for railway traffic[J].International Journal of Modern Physics C,2017,28(3):1750037.
[22]Chen S.Invulnerability Optimization of Chinese Railway Traffic Network for Suppressing Cascading Failure[J].Journal of Information&Computational Science,2014,11(5):1501-1509.
[23]Zhang L,Fu B B,Li Y X.Cascading Failure of Urban Weighted Public Transit Network under Single Station Happening Emergency[J].Procedia Engineering,2016,137:259-266.
[24]Minglei S,Xiaoxiong W,Shushen Y,et al.Research on the Importance of the Nodes of the Cascading Failure Public Transportation Network Based on Complex Network Theory[J].Journal of Computational and Theoretical Nanoscience,2016,13(8):5294-5304.
[25]王正武,况爱武,王贺杰.考虑级联失效的交通网络节点重要度测算[J].公路交通科技,2012,29(5):96-101.
[26]王正武,周振宇,胡静.基于节点修复效果的故障路网修复策略[J].长沙理工大学学报(自然科学版),2014,11(4):25-31.
[27]王正武,彭烁,黄中祥等.城市道路交通网络级联失效的灾害蔓延动力学模型[J].安全与环境学报,2014,14(3).
[28]王芳.基于级联失效的均衡路网脆弱性研究[D].西南交通大学,成都,2013.
[29]陈小兰.城市交通复杂网络级联失效影响源辨识[D].长沙理工大学,长沙,2013.
[30]尹洪英,权小锋.交通运输网络级联失效影响规律及影响范围[J].系统管理学报,2013,22(6):869-875.
[31]Trivedi K S.Probability and statistics with reliability,queuing,and computer science applications[M].Wiley,2002:47-57.
[32]Ross S M.Introduction to probability models[J].Technometrics,2006,82(1):625-627.
[33]Kerner,Boris S,Rehborn,et al.Recognition and tracking of spatial–temporal congested traffic patterns on freeways[J].Transportation Research Part C,2004,12(5):369-400.
[34]关伟,何蜀燕.基于统计特性的城市快速路交通流状态划分[J].交通运输系统工程与信息,2007(05):42-50.
[35]蔡燕飞.基于交通相特征的交通系统状态识别[D].华南理工大学,广州,2011.
[36]袁鹏程,隽志才.区域交通网络行程时间估计的半Markov链模型[J].系统管理学报,2014,23(5):690-697.