城市道路交通网络脆弱性辨识方法研究
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摘要
道路网络脆弱性描述了发生交通灾害时交通功能降低的敏感程度。道路网络脆弱性辨识是道路交通防灾减灾决策的前提，将为路段抢修资源分配和道路网络改造优先时序决策提供支持。为此，本文首先引入网络鲁棒性指数评价法，建立了考虑路段排队容量约束和断面通行能力约束的静态网络交通流模型，并利用Lagrange对偶算法将有约束问题转化为无约束问题进行求解。算例给出了关键路段的排序结果，并表明基于鲁棒性指数的辨识方法可以克服基于饱和度的辨识方法的片面性，从全局角度准确辨识路网中的瓶颈路段；此外，辨识模型中是否考虑路段排队容量和断面通行能力约束，也影响着道路网络脆弱性辨识结果的可靠性。其次，本文提出了动态网络脆弱性指数，根据动态用户最优（DUO）原则建立了基于路段的反应型动态模型，在等价的最优控制模型的基础上利用扩张的时空网络将动态模型转变为静态问题，并采用F-W算法和对角线法进行求解。通过模拟不同时段的路段失效，得到动态问题的脆弱路段排序以及路段上车辆数、流入量和流出量的变化规律和道路网络流量分布的变化情况。
Vulnerability in road transportation system describes the sensitivity for degradingserviceability of road network in disasters. Vulnerability identification on road networkis premise to prevent and mitigate disaster in road network, which will support thedecision such as resources allocation of road maintaining and timing priority oftransport network reconstruction. First, after introducing road network robustness index,static network traffic flow model with link queuing capacity constraint and capacityconstraint is proposed, which is solved by transforming constraint problem intounconstraint problem according to Lagrange dual algorithm. Numerical exampleprovides the rank of critical roads, and show that the identification methodology basedon network robustness index can accurately recognize the bottlenecks of the roadnetwork from a global perspective while overcoming the defect of methodology basedon saturation. In addition, the identification model whether considered road queuingcapacity constraint and capacity constraints concern the reliability of identificationresults of traffic network vulnerability Second, after putting forward the vulnerabilityindex of dynamic transportation network, it also sets up a link-based reactive dynamicmodel meeting the dynamic user optimal principle. In order to simplify the operationsprocess, it will transform the dynamic model to static one by using the expansion oftime-space network on the basis of equivalent optimal control model, then F-Walgorithm and diagonal algorithm can be used to solve the static problem. By simulatingthe breakdown of different links at different time intervals we can get the order ofvulnerable links, as well as the transformation of the vehicles’ number, inflow, outflowof the links and traffic distribution of the road network.
Vulnerability in road transportation system describes the sensitivity for degradingserviceability of road network in disasters. Vulnerability identification on road networkis premise to prevent and mitigate disaster in road network, which will support thedecision such as resources allocation of road maintaining and timing priority oftransport network reconstruction. First, after introducing road network robustness index,static network traffic flow model with link queuing capacity constraint and capacityconstraint is proposed, which is solved by transforming constraint problem intounconstraint problem according to Lagrange dual algorithm. Numerical exampleprovides the rank of critical roads, and show that the identification methodology basedon network robustness index can accurately recognize the bottlenecks of the roadnetwork from a global perspective while overcoming the defect of methodology basedon saturation. In addition, the identification model whether considered road queuingcapacity constraint and capacity constraints concern the reliability of identificationresults of traffic network vulnerability Second, after putting forward the vulnerabilityindex of dynamic transportation network, it also sets up a link-based reactive dynamicmodel meeting the dynamic user optimal principle. In order to simplify the operationsprocess, it will transform the dynamic model to static one by using the expansion oftime-space network on the basis of equivalent optimal control model, then F-Walgorithm and diagonal algorithm can be used to solve the static problem. By simulatingthe breakdown of different links at different time intervals we can get the order ofvulnerable links, as well as the transformation of the vehicles’ number, inflow, outflowof the links and traffic distribution of the road network.
引文
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[20] Sarewitz D., Pielke Jr., R., Keykhah M. Vulnerability and Risk: Some Thoughtsfrom a Political and Policy Perspective [J]. Risk Analysis,2003,23(4),805–810.
[21] Holmgren A.2004. Vulnerability analysis of electrical power delivery networks
[R]. Licentiate thesis TRITA-LWR LIC2020, Department of Land and WaterResources Engineering, KTH, Stockholm.
[22]黄海军.城市交通网络平衡分析——理论与实践[M].人民交通出版社,1994.
[23]韩渭敏，程晓良.变分不等式简介——基本理论、数值分析及应用[M].高等教育出版社,2007.
[24] Vandaele N., Van Woensel T., Verbruggen A. A Queuing Based Traffic FlowModel [J]. Transportation Research D,2000,5(2):121–135.
[25] Heidemann D.A Queuing Theory Approach to Speed-flow-density Relationships
[C]. J.-B. Lesort, ed. Transportation and Traffic Theory—Proceedings of the13thInternational Symposium on Transportation and Traffic Theory. Elsevier Science,Oxford/New York/Tokyo,1996:103–118.
[26] Jain R., Smith J. M. Modeling Vehicular Traffic Flow Using M/G/C/C StateDependent Queuing Models [J]. Transportation Science,1997,31(4):324–336.
[27] Little J. D. C. A Proof for the Queuing Formula: L=λW[J]. OperationsResearch,1961,9(3):383–387.
[28] Stidham S. Jr. A Last Word on L=λW[J]. Operations Research,1974,22(2):417–421.
[29]陆化普，黄海军.交通规划理论研究前沿[M].清华大学出版社,2007.
[30] Larsson T, Patriksson M. An Augmented Lagrangean Dual Algorithm for LinkCapacity Side Constrained Traffic Assignment Problems [J]. TransportationResearch Part B,1995,29(6):433-455.
[31]李志纯，朱道立.能力约束下的停车行为模型及其求解算法[J].中国公路学报,2007,20(5):89-94
[2] D’Este, G.M., Taylor M. A. P. Network Vulnerability: An approach to reliabilityanalysis at the level of national strategic transport networks [C]. In The NetworkReliability of Transport. Edited by Y. Iida and M.G.H. Bell. Oxford: Elsevier,2003:23-44.
[3] Sohn J. Evaluating the significance of highway network links under the flooddamage: An accessibility approach [J]. Transportation Research A,2006,40(5):491-506.
[4] Sohn, J. et al. Retrofit priority of transportation network links under an earthquake[J]. Journal of Urban Planning and Development,2003,129(4):195–210.
[5] Jenelius E., Petersen T., Mattsson L. Importance and exposure in road networkvulnerability analysis [J]. Transportation Research Part A,2006,40:537–560.
[6] Scott D. M., et al. Network Robustness Index: A new method for identifyingcritical links and evaluating the performance of transportation networks [J].Journal of Transport Geography,2006,14(3):215-227.
[7] Sullivan J. L., Navak D. C., Aultman-Hall L., Scott D. M. Identifying CriticalRoad Segments and Measuring System-Wide Robustness in TransportationNetworks with Isolating Links: A Link-Based Capacity-Reduction Approach[J].Transportation Research A,2010,44(5):323-336.
[8]刘思峰,万寿庆,陆志鹏,方志耕,朱建军.复杂交通网络中救援点与事故点间的路段重要性评价模型研究[J].中国管理科学,2009,17:119-124
[9] Bell M. G. H., Anturska U. K, Schmocker J.D., Fonzone A. Attacker-DefenderModels and Road Network Vulnerability [J]. Philosophical Transactions of theRoyal Society A,2008,366(1872):1893-1906.
[10] Bell, M. G. H. The use of game theory to measure the vulnerability of stochasticnetworks. IEEE Transaction Reliability,2003,52:63–68.
[11] Pamela M. M., Mahmassani H. Methodology for determining vulnerable links in atransportation network [J]. Transportation Research Record,2004,1882:88–96.
[12] Lo., Szeto W.Y. A Cell-Based Variational Inequality Formulation of the DynamicUser Optimal Assignment Problem [J].Transportation Research Part B,2006,36:421-443.
[13] Daganzo C.F. The Cell Transmission Model: A Dynamic Representation ofHighway Traffic Consistent with the Hydrodynamic Theory [J].TransportationResearch Part B,1994,4:269-287.
[14] Daganzo C.F. The Cell Transmission Model, Part Ⅱ: Network Traffic[J].Transportation Research Part B,1995,2:79-93.
[15] Lo, Szeto W.Y.A Cell-Based Simultaneous Route and Departure Time ChoiceModel with Elastic Demand [J].Transportation Research Part B2004,38:593-612.
[16] Jang W., Ran B., Choi K. A Discrete Time Dynamic Flow Model and AFormulation and Solution Method for Dynamic Route Choice [J].TransportationResearch Part B,2005,39:593-620.
[17] Ran B., Boyce D.E. A Link-Based Variational Inequality Formulation of IdealDynamic User-Optimal Route Choice Problem [J].Transportation Research Part C,1996,4:1-12.
[18] Ran B., Boyce D.E. and LeBlanc L.J.A New Class of Instantaneous DynamicUser-Optimal Traffic Assignment Models [J]. Operations Research,1993,4:192-202.
[19] Berdica K. An Introduction to Road Vulnerability: What Has Been Done, is Doneand Be Done [J]. Transport Policy,2002,9(2):117-127.
[20] Sarewitz D., Pielke Jr., R., Keykhah M. Vulnerability and Risk: Some Thoughtsfrom a Political and Policy Perspective [J]. Risk Analysis,2003,23(4),805–810.
[21] Holmgren A.2004. Vulnerability analysis of electrical power delivery networks
[R]. Licentiate thesis TRITA-LWR LIC2020, Department of Land and WaterResources Engineering, KTH, Stockholm.
[22]黄海军.城市交通网络平衡分析——理论与实践[M].人民交通出版社,1994.
[23]韩渭敏，程晓良.变分不等式简介——基本理论、数值分析及应用[M].高等教育出版社,2007.
[24] Vandaele N., Van Woensel T., Verbruggen A. A Queuing Based Traffic FlowModel [J]. Transportation Research D,2000,5(2):121–135.
[25] Heidemann D.A Queuing Theory Approach to Speed-flow-density Relationships
[C]. J.-B. Lesort, ed. Transportation and Traffic Theory—Proceedings of the13thInternational Symposium on Transportation and Traffic Theory. Elsevier Science,Oxford/New York/Tokyo,1996:103–118.
[26] Jain R., Smith J. M. Modeling Vehicular Traffic Flow Using M/G/C/C StateDependent Queuing Models [J]. Transportation Science,1997,31(4):324–336.
[27] Little J. D. C. A Proof for the Queuing Formula: L=λW[J]. OperationsResearch,1961,9(3):383–387.
[28] Stidham S. Jr. A Last Word on L=λW[J]. Operations Research,1974,22(2):417–421.
[29]陆化普，黄海军.交通规划理论研究前沿[M].清华大学出版社,2007.
[30] Larsson T, Patriksson M. An Augmented Lagrangean Dual Algorithm for LinkCapacity Side Constrained Traffic Assignment Problems [J]. TransportationResearch Part B,1995,29(6):433-455.
[31]李志纯，朱道立.能力约束下的停车行为模型及其求解算法[J].中国公路学报,2007,20(5):89-94