过饱和区域交通管理与控制方法研究
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摘要
随着经济的飞速的发展,小汽车保有量的迅猛增长,城市交通问题不断加剧,特别是在大城市,过饱和交通拥堵已经成为常态。过饱和交通拥堵以及随之而来环境污染及能源短缺等问题已经成为影响城市发展和市民生活水平的重大问题。
     本文在分析各项过饱和管控措施的发展和研究现状的基础上,选择了过饱和区域边界主动控制和拥挤收费这两种对过饱和交通拥堵起到直接管控作用且互补性较强的措施作为过饱和区域交通管控的主要方法。针对这两种措施目前存在的问题,提出了具有创新性和实用性的方法和模型,形成了能够满足大多数过饱和区域交通拥堵情况的管控理论与方法体系。本文的主要工作和研究成果有:
     1、建立了基于车道组过饱和交叉口交通流宏观演化模型和支路宏观交通流模型。本文从过饱和区域边界主动控制的实际需求出发,对基于车道组的宏观交通流模型进行改进,建立了过饱和交叉口交通流宏观演化模型和支路宏观交通流模型,模型能够很好的模拟交叉口排队溢出时不同流向交通流的相互阻碍甚至死锁过程和交通流从支路出入的演化过程。改进后的模型在时间和精度上均能够满足过饱和区域边界主动控制的需求。
     2、提出了过饱和区域边界主动控制方法。本文设计了交通量清洗算法,排除过饱和时上游信号配时和拥堵的影响,获得真实交通需求,识别出引起区域交通拥堵的关键交叉口,设计了绿灯时间优化算法,主动控制进入过饱和区域的交通量,避免关键交叉口排队溢出和拥堵扩散,最大化区域路网通行能力,并采用遗传算法优化相序和相位差,最小化路网延误。本文分别研究了给定控制边界下的过饱和区域单层边界主动控制方法和动态确定边界下的过饱和多层边界主动控制方法,为过饱和交通信号控制提供了一个新的途径和思路。
     3、提出了过饱和干道动态协调控制方法。以干道主要交通流方向作为协调方向,利用过饱和区域边界主动控制方法对绿信比进行优化,并在确定绿信比的条件下,动态优化周期保证协调方向各交叉口之间的相位差满足理想相位差,避免绿灯损失和路段过饱和排队溢出,充分利用交叉口的通行能力和路段的存储能力,降低路网延误。
     4、提出了基于关键交叉口的过饱和交通控制子区划分方法。综合分析影响过饱和交通控制子区划分的因素,以过饱和干道动态协调控制方法为基础,给出过饱和区域边界至关键交叉口的交通量累积路径识别方法,将每条路径作为一个控制子区,具有同一关键交叉口的控制子区形成一个以关键交叉口为核心的子区组,突破了传统交通控制子区划分的理念和限制,为过饱和交通控制子区划分提供了一个新方法。
     5、提出了过饱和区域拥挤收费与停车换乘组合措施。考虑停车换乘(P&R)作为一种既不影响驾车便利性,又可以鼓励出行者使用公交的措施,将其与停车换乘措施相结合,充分发挥两种措施的优势,给出区域拥挤收费与停车换乘组合网络均衡条件,建立了组合网络均衡模型,设计了对角化算法进行求解,定义了基尼系数评估组合措施的公平程度。该措施在很大程度上降低社会和空间不公平性,提高组合措施的社会认可度和可操作性。
     6、提出一个双模式(小汽车和公交)多用户类的帕累托一致改进拥挤收费和税收返还策略。建立了双模式(小汽车和公交车)多用户类网络均衡模型,证明了帕累托一致改进拥挤收费及税收返还策略当且仅当拥挤收费策略降低路网一直驾驶小汽车的出行者和转而乘坐公交的出行者总的出行成本时存在,建立了双层规划模型并设计模拟退火算法进行求解。该策略能够在缓解交通拥挤的同时,不增加任何一个出行者的广义出行成本,使拥挤收费成为一个能够被公众接受的管控措施。但该理想策略并不一定总是存在,与区域的现状交通拥堵程度和公交服务水平相关。
     7、最后,本文对上述提出的多种过饱和区域管理与控制措施从适用范围、实施效益、实施成本和公平性四个方面进行了评价,为交通管理人员选择何种措施提供了参考。总的来说,本文为交通管理人员提供了一套的解决区域过饱和交通拥堵问题的理论与方法体系。
With the rapid development of economy, vehicle registrations are growing fast and traveltimes are generally high and increasing. Especially in large cities, oversaturated trafficcongestion has become the norm. Oversaturated traffic congestion and the attendant issuessuch as environmental pollution and energy shortage have become the major problems ofurban development and living standards.
     On the basis of analysis of research and development status of the traffic demandmanagement measures, the perimeter active control and congestion pricing that directlymanage and control oversaturated traffic congestion are selected as the main study measures.In order to overcome the shortages of current methods, some creative and useful methods andalgoritms are proposed. Main research contents and results of this dissertation are asfollowing:
     (1) Based on requirements of oversaturated perimeter control method, the lane-groupbased macroscopic traffic flow formulations is improved, lane-group based oversaturatedintersection macroscopic traffic flow formulations and branch macroscopic traffic flowformulations are established. The formulations could model the dynamic interactions of trafficflows when queues spillback occurs and the entering and exiting traffic dynamic of brancheswell. The improved lane-based macroscopic traffic flow formulations could satisfy the needsof perimeter active control in time and accuracy.
     (2) Perimeter active control strategy of oversaturated area is proposed. Traffic volumcleaning algorithm is designed to gain real traffic demand and identify the key intersectionsthat cause regional traffic congestion. Then, the green splits are optimized, actively control thetraffic entering the oversaturated areas and hold a portion of traffic outside, avoid theoversaturated traffic congestion to occur. The single-layer perimeter active control strategyunder given perimeter and the multi-layer perimeter active control strategy under dynamicdetermined perimeters are put forward respectively, which provides a new way and thinkingfor oversaturated traffic control.
     (3) Based on static perimeter active control, the dynamic signal coordination model foroversaturated aterials is proposed. This model takes the main traffic flow direction of theatertial as the coordinate direction, optimizes the green splits by perimeter active controlstrategy and dynamic optimizes the cycles to make sure that offsets of all neighboringintersections satisfy the ideal offsets, avoids the queue spillback and the lose of green time,maximizes the intersections’ capacity and minimizes the network delays.
     (4) The key intersections based division method of oversaturated coorditnaed controlsubareas is proposed. By comprehensive analysis of the influences factors, the traffic volumeaccumulated paths from oversaturated area perimeter to the key intersections are indentified.Each path is considered as a control subarea and subareas having a common key intersectioncompose a subarea group. The divison method breaks through the traditional concept ofcoordinated control subareas division and proposes a new way for the division ofoversaturated coordinated control subareas.
     (5) As area-based congestion pricing could well restrict cars running into city center andpark and ride (P&R) could encourage public transport while doesn’t affect convenience ofdriving, two measures are combined to relieve traffic congestion problem in urban area.Combined area-based congestion pricing and P&R network equilibrium conditions isproposed and combined area-based congestion pricing and P&R network equilibrium modelis established. Further, a modified Gini coefficient is proposed to measure the social andspatial equity impact. The combined measure could increase the social and spacial equity andenhance the operability and social recognition.
     (6) Uniformly Pareto-improving congestion pricing and revenue refunding schemes inbimodal (automobile and bus) transportation networks is proposed. Bimodal multi-classnetwork equilibrium model is formulated, and the exsiting condition that uniformlyPareto-improving congestion pricing and revenue refunding scheme exist if and only if thetotal travel costs of people who have been driving cars before pricing is reduced is proposed.Further, a bi-level programming model and solution algorithm are proposed. The schemecould relieve traffic congestion while automobile-insistent users and shifting-automobile usersare equally better off regardless of their value of time (VOT) and origin-destination (OD)pairs and would be easily accepted by the public. However, related with the level of currentcongestion and transit service, the ideal scheme doesn’t always exist.
     (7) At last, the oversaturated areas traffic management and control measures proposedare evaluated from the scope of application, implementation effectiveness, implementationcosts and equity, providing the gudie for traffic managers to select the suitable measure.Overall, this dissertation provides a set of oversaturated traffic managent and controlmeasures for traffic managers.
引文
[1] Daganzo C.F., Geroliminis N.. An analytical approximation for the macroscopicfundamental diagram of urban traffic[J]. Transportation Research Part B,2008,42(9):771-781.
    [2] Daganzo C.F.. Urban gridlock: macroscopic modeling and mitigation approaches[J].Transportation Research Part B,2007,41(1):49-62.
    [3] Geroliminis N., Daganzo C.F.. Existence of urban-scale macroscopic fundamentaldiagrams: Some experimental findings[J]. Transportation Research Part B,2008,42(9):758-770.
    [4] Gazis, D.C.. Optimum control of a system of oversaturated intersections[J]. OperationsResearch,1964,12(6):815-831.
    [5] Transportation Research Board (TRB). Highway Capacity Manual[R]. Washington, D.C:Transportation Research Board, National Research Council,2000.
    [6] Pignataro, L.J., McShane, W.R., Crowley, K.W., Lee, B., Casey, T.W. Traffic control inoversaturated conditions[R]. Washington D.C.: Transportation Research Board,1978.
    [7] Longley D. A control strategy for a congested computer controlled traffic network[J].Transportation Research,1968,2(4):391-408.
    [8] Chaudary, N.A., Balke, K.N.. Real-time coordinated actuated traffic control duringcongested conditions[D]. Texas: Texas transportation Institute,1997.
    [9] Gartner, N.H., Little, J.D.C., Gabbay, H.. Optimization of traffic signal settings by mixedinteger linear programming. Part I: the network coordination problem[J]. TransportationScience1975,9(4):321-343.
    [10] Gartner, N.H., Little, J.D.C., Gabbay, H.. Optimization of traffic signal settings by mixedinteger linear programming. Part II: the network synchronization problem[J]. TransportationScience1975,9(4):344-363.
    [11] Little, J.D.C., Kelson, M.D., Gartner, N.H.. MAXBAND: a program for setting signalson arterials and triangular networks[J]. Transportation Research Record,1981,795:40-46.
    [12] Cohen, S.L., Liu, C.C.. The bandwidth-constrained TRANSYT signal optimizationprogram[J]. Transportation Research Record,1986,1057:1-7.
    [13] Gartner, N.H., Assmann, S.F., Lasaga, F.L., Hou, D.L.. A multi-band approach to arterialtraffic signal optimization[J]. Transportation Research Part B,1991,25(1):55-74.
    [14] Chaudhary, N.A., Messer, C.J.. PASSER-IV: a program for optimizing signal timing ingrid networks[C]. Washington, DC:72nd Annual Meeting of the Transportation ResearchBoard,1993.
    [15] Wong, S.C.. A lane-based optimization method for minimizing delay at isolatedsignal-controlled junctions[J]. Journal of Mathematical Modeling and Algorithms,2003,2:379-406.
    [16] Wallace, C.E., Courage, K.G., Reaves, D.P., Shoene, G.W., Euler, G.W., Wilbur, A..TRANSYT-7F User’s Manual: Technical Report[R]. Gainesville, FL: University of Florida,1988.
    [17] Wong, S.C.. Group-based optimisation of signal timings using the TRANSYT trafficmodel[J]. Transportation Research Part B,1996,30(3):217-244.
    [18] Robertson, D.I., Bretherton, R.D.. Optimizing networks of traffic signals in real-time: theSCOOT method[J]. IEEE Transactions on Vehicular Technology,1991,40:11-15.
    [19] Lowrie, P.. The Sydney coordinated adaptive control system-principles, methodology,algorithms[C]. IEEE Conference Publication,1982:207.
    [20] Gartner, N.. OPAC: a demand-responsive strategy for traffic signal control[J].Transportation Research Record,1983,906:75-81.
    [21] Mirchandani, P., Head, L.. A real-time traffic signal control system: architecture,algorithms, and analysis[J]. Transportation Research Part C,2001,9(6):415-432.
    [22] D’Ans, G.C., Gazis, D.C.. Optimal control of oversaturated store-and forwardtransportation networks[J]. Transportation Science,1976,10(1):1-19.
    [23] Papageorgiou, M.. An integrated control approach for traffic corridors[J]. TransportationResearch Part C,1995,3:19-30.
    [24] Kashani, H.R., Saridis, G.N.. Intelligent control for urban traffic systems[J]. Automatica,1983,19(2):191-197.
    [25] Wu, J., Chang, G.L.. An integrated optimal control and algorithm for commutingcorridors[J]. International Transactions on Operations Research,1999,6(1):39-55.
    [26] Van den Berg, A., Hegyi, B., De Schutter, Hellendoorn, J.. A macroscopic traffic flowmodel for integrated control of freeway and urban traffic networks[C]. Hawaii:42nd IEEEInternational Conference on Decision and Control,2003:2774-2779.
    [27] Yu, X.H., Recker, W.W.. Stochastic adaptive control model for traffic signal systems[J].Transportation Research Part C,2006,14(4):263-282.
    [28] Lo, H., Chang, E., Chan, Y.. Dynamic network traffic control[J]. Transportation ResearchPart A,2001,35(8):721-744.
    [29] Michalopoulos, P.G., Stephanopolos, G.. Oversaturated signal system with queue lengthconstraints-I[J]. Transportation Research,1977,11(6):413-421.
    [30] Michalopoulos, P.G., Stephanopolos, G.. Optimal control of oversaturated intersections:theoretical and practical considerations[J]. Traffic Engineering and Control,1978,19(5):216-221.
    [31] Chang, T.-H., Lin, J.-T.. Optimal signal timing for an oversaturated intersection[J].Transportation Research Part B,2000,34(6):471-491.
    [32] Chang, T.-H., Sun, G.-Y.. Modeling and optimization of an oversaturated signalizednetwork[J]. Transportation Research Part B,2004,38(8):687-707.
    [33] Abu-Lebdeh, G., Benekohal, R.F.. Development of a traffic and queue managementprocedure for oversaturated arterials[J]. Transportation Research Record,1997,1603:119-127.
    [34] Abu-Lebdeh, G., Benekohal, R.F.. Design and evaluation of dynamic traffic managementstrategies for congested conditions[J]. Transportation Research Part A,2003,37(2):109-127.
    [35] Girianna, M., Benekohal, R.F.. Using genetic algorithms to design signal coordination foroversaturated networks[J]. Journal of Intelligent Transportation Systems,2004,8(2):117-129.
    [36] Li, M.-T., Gan, A.C.. Signal timing optimization for oversaturated networks usingTRANSYT-7F[J]. Transportation Research Record,1999,1683:118-126.
    [37] Binning, J.C., Burtenshaw, G., Crabtree, M.,2008. TRANSYT13User Guide[R]. UK:Transport Research Laboratory.
    [38] Park, B., Messer, C.J., Urbanik, T.. Traffic signal optimization program for oversaturatedconditions: genetic algorithm approach[J]. Transportation Research Record,1999,1683:133-142.
    [39] Yun, I., Park, B.. Application of stochastic optimization method for an urban corridor[C].Proceedings of the Winter Simulation Conference,2006:1493-1499.
    [40] Stevanovic, A., Martin, P.T., Stevanovic, J.. VisSim-based genetic algorithm optimizationof signal timings[J]. Transportation Research Record,2007,2035:59-68.
    [41] Liu, Y., Chang, G. L.. An arterial signal optimization model for intersections experiencingqueue spillback and lane blockage[J]. Transportation Research Part C,2011,19(1):130-144.
    [42] Gazis, D.C., Potts, R.B.. The oversaturated intersection[C]. Paris: Proceedings of the2nd International Symposium on the Theory of Road Traffic Flow. Organization for EconomicCooperation and Development,1965:221-237.
    [43] Green, D.H.. Control of oversaturated intersections[J]. Operational Research Quarterly,1968,18(2):161-173.
    [44] Burhardt, K.K.. Urban traffic system optimization[D]. Minneapolis, MN: University ofMinnesota,1971.
    [45] Kaltenbach, M., Koivo, H.N.. Modeling and control of urban traffic flow[C]. Houston,TX: Proceedings of the Joint Automatic Control Conference,1974:147-154.
    [46] Michalopoulos, P.G., Stephanopolos, G.. Oversaturated signal system with queue lengthconstraints-I[J]. Transportation Research,1977,11(6):413-421.
    [47] Michalopoulos, P.G., Stephanopolos, G.. Optimal control of oversaturated intersectionstheoretical and practical considerations[J]. Traffic Engineering&Control,1978,19(5):216-221.
    [48] Choi, B.-K.. Adaptive signal control for oversaturated arterials[D]. PolytechnicUniversity,1997.
    [49] Ahn, G.H., Machemehl, R.B.. Methodology for traffic signal timing in oversaturatedarterial networks[R]. University of Texas at Austin,1997.
    [50] Hadi, M.A., Wallace, C.E.. Optimization of signal phasing and timing using cauchysimulated annealing[J]. Transportation Research Record,1994,1456:64-71.
    [51] Yagar S. and Dion F., Distributed Approach to Real Time Control of ComplexSignalized Networks[J]. Transportation Research Record,1996,1554:1-8.
    [52] Lieberman, E.B., Chang, J., Prassas, E.S.. Formulation of real-time control policy foroversaturated arterials[J]. Transportation Research Record,2000,1727:77-78.
    [53] Abu-Lebdeh, G., Benekohal, R.F.. Genetic algorithms for traffic signal control and queuemanagement of oversaturated two-way arterials[J]. Transportation Research Record,2000,1727:61-67.
    [54] Girianna, M., Benekohal, R.F.. Dynamic signal coordination for networks withoversaturated intersections[J].Transportation Research Record,2002,1811:122-130.
    [55]
    [56] Aboudolas K., Papageorgiou, Kouvelas A., Kosmatopoulos E.. A rolling-horizionquadratic-programming approach to the signal control problem in large-scale congested urbanroad network[J]. Transportation Research Part C,2010,18(5):680-694.
    [57] Markos Papageorgiou, Christina Diakaki. Review of road traffic control strategies[C].Proceedings of the IEEE.2003,91(12):2043-2067.
    [58] Pigou, A.C. Wealth and Welfare[M]. London: Macmillan,1920.
    [59] Knight, F.H.. Some fallacies in the interpretation of social cost[J]. Quarterly Journal ofEconomics,1924,38:582-606.
    [60] Walters, A.A.. The theory and measurement of private and social cost of highwaycongestion[J]. Econometrica,1961,29:676-699.
    [61] Hau, T.D.. Economic fundamentals of road pricing: a diagrammatic analysis, part I–fundamentals[J]. Transportmetrica,2005,1:81–117.
    [62] Yang, H., Zhang, X.N.. Multiclass network toll design problem with social and spatialequity constraints[J]. Journal of Transportation Engineering.,2002,128:420–428.
    [63] Lawphongpanich, S., Hearn, D.W.. An MPEC approach to second-best toll pricing[J]. MathematicalProgramming,2004,101:33–55.
    [64] Song, Z., Yin, Y., Lawphongpanich, S.. Nonnegative Pareto-improving tolls withmulticlass network equilibria[J]. Transportation Research Record,2009,2091:70–78.
    [65] Lawphongpanich, S., Yin, Y.. Solving the Pareto-improving toll problem via manifoldsuboptimization[J]. Transportation Research Part B,2010,18:234-246.
    [66] Hagstrom, J.N., Abrams, R.A.. Characterizing Braess’s paradox for traffic networks[C].Oakland, California: Proc. of IEEE2001Conference on Intelligent Transportation Systems,2001:837–842.
    [67] Guo, X., Yang, H.. Pareto-improving congestion pricing and revenue refunding withmultiple user classes[J]. Transportation Research Part B,2010,(44):972–982.
    [68] Arnott, R., Small, K.. The economists of traffic congestion[J]. American Science,1994,82:446–455.
    [69] Larsson, T., Patriksson, M.. An augmented Lagrangean dual algorithm for link capacityside constrainted traffic assignment problems[J]. Transportation Research Part B,1995,26:443–455.
    [70] Liu, L.N., McDonald, J.F.. Economic efficiency of second-best congestion pricingschemes in urban highway systems[J]. Transportation Research Part B,1999,33:157–188.
    [71] Liu, Y., Guo, X., Yang, H.. Pareto-improving and revenue-neutral congestion pricingschemes in two-mode traffic networks[J]. Netnomics,2009,10:123–140.
    [72] PTV Corporation. VISSIM5.0User Guide[R]. PTV Corporation,2007.
    [73]陈军华,张星臣,赵凛,黄玲.基于元胞自动机的交叉口仿真平台研究[J].交通运输系统工程与信息,2009,1:68-73.
    [74]王炜,过秀成.交通工程学[M].南京:东南大学出版社,2001.
    [75] Gal-Tzur, A., Mahalel. D., and Prashker, N.. Signal design for congested networks basedon metering[J]. Transportation Research Record,1993,1398:111-118.
    [76]张勇,白玉,杨晓光.城市道路交通网络死锁控制策略[J].中国公路学报,2010,23(6):96-102.
    [77] Hale D.K.. TRANSYT-7F User’s Guide[R]. Florida: University of Florida,2006.
    [78]杨晓光,黄玮,马万经.过饱和状态下交通控制小区动态划分方法[J].同济大学学报(自然科学版),2010,38(10):1450-1457.
    [79]雷磊,吴洋,刘昱岗.过饱和交叉口群系统建模及优化模型[J].计算机工程及应用,2010,46(4):26-28.
    [80] Morgan J. T., Little J. D. C.. Synchronizing Traffic Signals for Maximal Bandwidth[J].Operations Research,1964,12(6):896-912.
    [81] Little J. D. C.. The Synchronization of Traffic Signals by Mixed-Integer LinearProgramming[J]. Operations Research,1966,14(4):568-594.
    [82] Little J. D. C., Kelson M. D., Gartner N. H.. MAXBAND: A Versatile Program forSetting Signals on Arteries and Triangular Networks[J]. Transportation Research Record,1981,795:40-46.
    [83]常云涛,彭国雄.基于遗传算法的城市干道协调控制[J].交通运输工程学报,2003,3(2):106-112.
    [84]卢凯,徐建闽.干道协调控制相位差模型及其优化方法[J].中国公路学报,2008,21(1):83-88.
    [85]万绪军,陆化普.线控系统中相位差优化模型的研究[J].中国公路学报,2001,14(2):99-102.
    [86]刘智勇,吴今培,李秀平.城市交通大系统递阶模糊神经网络控制[J].信息与控制,1997,26(6):441-448.
    [87]沈国江,孙优贤.城市交通干线递阶模糊控制及其神经网络实现[J].系统工程理论与实践,2004,24(4):99-105.
    [88] Yagar,S., Dion,F.. Distributed Approach to Real Time Control of Complex SignalizedNetworks[J]. Transportation Research Record,1996,1554:1-8.
    [89] Wolshon,B.,&Taylor,W.C.. Analysis of intersection delay under real-time adaptivesignal control[J]. Transportation Research Part C,1999,7:53-72.
    [85]徐建闽.交通管理与控制[M].广州:华南理工大学出版社,2007.
    [86] Walinchus R J. Real-time network decomposition and sub-network interfacing[J].Highway Research Record,1971:20-28.
    [87] Stockfisch, C R. Guidelines for computer signal system selection in urban areas[J].Traffic Engineering,1972,43(3):30-63.
    [88] Pinell, C.. Areawide Traffic Control Systems[J]. Traffic Engineering&Control,1975,45(4):16-21.
    [89] Kell, J. H., Fullerton, I. J.. Manual of Traffic Signal Design Control[R]. Institute ofTransportation Engineers,1991.
    [90] Yagoda, N H. Subdivision of Signal Systems into Control Areas[J]. Traffic Engineering,1973,43(12):42-45.
    [91] Chang Edmond Chin-Ping. Evaluation of Interconnected Arterial Traffic Signals[J].Transportation Planning Journal,1986,15(1):137-156.
    [92]莫汉康,彭国雄,云美萍.诱导条件下的交通控制子区自动划分[J].交通运输工程学报,2002(2):67-72.
    [93]卢凯,徐建闽,李轶舜.基于关联度分析的协调控制子区划分方法[J].华南理工大学学报(自然科学版),2009,37(7):6-9.
    [94] West, D B. Introduction to graph theory[M]. Prentice Hall,2001.
    [95] Callaway, D.S., Newman E.J., Strogatez S.H.. Network robustness and fragility:percolation on random graphs[J]. Physical Review Letters,2000,85(25):5468-5471.
    [96] Freeman L.C.. A set o f measures of centrality based upon betweenness[J]. Sociometry,1977,40(1):35-41.
    [97]陈勇,胡爱群,胡俊等.通信网络中最重要节点确定方法[J].高技术通讯,2004(1):573-575.
    [98]陈静,孙林夫.复杂网络中节点重要度评估[J].西南交通大学学报,2009(3):426-429.
    [99]高洁.交通运输网络节点重要度评价体系研究[J].聊城大学学报(自然科学版),2010,3:92-95.
    [100]周涛,柏文洁,汪秉宏.复杂网络研究概述[J].物理,2005,34(1):31-36.
    [101]方锦清,汪小帆,郑志刚.一门崭新的交叉科学-网络科学:上[J].物理学进展,2007,27(3):239-343.
    [102]谭跃进,吴俊,邓宏钟.复杂网络中节点重要度评估的节点收缩方法[J].系统工程理论与实践,2006,26(11):79-83.
    [103]陆化普,黄海军.交通规划理论研究前沿[M].北京:清华大学出版社,2007:155-161.
    [104] Sheffi, Y. Urban transportation networks: equilibrium analysis with mathematicalprogramming methods [M]. New York: Prentice-Hall,1985:238-242.
    [105] Fernadez E, De CeaJ, Florian M, Cabrera E. Network equilibrium models withcombined modes[J]. Transportation Science,28(3):182-192.
    [106] Spiess, H., Florian, M.. Optimal strategies: A new assignment model for transitnetworks[J]. Transportation Research Part B,1989,23:83–102.
    [107] Wu, J., Florian, M., Marcotte, P.. Transit equilibrium assignment: A model and solutionalgorithms[J]. Transportation Science,1994,3:193–203.
    [108] Cepeda, M., Cominetti, R., Florian, M,. A frequency-based assignment model forcongested transit networks with strict capacity constraints: Characterization and computationof equilibira[J]. Transportation Research Part B,2006,40:437-459.
    [109] Yang H. and Bell M.G.H., Transport bilevel programming problems recentmethodological advances [J]. Transportation Research Part B,2001,35:1-4.
    [110] Bazaraa, M.S., Sherali, H.D., Shetty, C.M.. Nonlinear Programming: Theory andAlgorithms. New York: John Wiley and Sons, Inc.,1993.

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