基于时刻表的地铁动态配流模型研究
|
摘要
随着城市化进程的加快，国内主要城市地铁建设快速发展，各大城市地铁运营网络逐步形成，地铁客流网络化特征日趋明显。与过去的单条或少数几条地铁线路的客流特征相比，网络化运营地铁乘客的路径选择行为以及在此基础上形成的网络客流时空分布特征均发生较大变化。按照目前北京地铁票制和票价政策，由于乘客换乘不需刷卡付费，导致线路路径流量和线路换乘流量的不确定性，给城市地铁运营调度管理和客流组织带来了挑战。因此，对地铁网络中乘客的路径选择规律以及客流分配方法进行深入研究，对提高城市地铁运营精细化管理水平具有重要意义。
本文的研究主要围绕城市地铁网络客流分配问题而进行。通过对城市地铁乘客出行特性的调查分析，得到影响乘客路径选择的主要因素以及相关规律，对乘客属性与路径选择行为之间的相关性进行了统计分析，基于调查数据确定了乘客分类模式，特别是提出了基于乘客属性的地铁配流模型及算法，并对算法进行了实证研究；同时，考虑了地铁需求的动态属性，给出了基于时刻表的地铁时空扩展网络的概念和构建方法，在此基础上，建立了基于时刻表的地铁客流动态分配模型及算法，并利用北京地铁网络运营客流数据对模型及算法的可行性和有效性进行了验证。具体而言，论文主要就以下方面进行了研究：
（1）为了充分掌握乘客的路径选择行为，同时，为了给后续研究提供可靠的数据支持和相关参数估计，针对北京市地铁运营网络，进行了乘客路径选择行为调查，并对调查数据进行了统计分析。结果表明：不同属性的乘客对路径选择存在明显差异，不同属性乘客对时间和换乘等影响因素的关注程度呈现明显差异。
（2）基于调查数据，采用卡方检验方法，对乘客属性和路径选择之间的相关性进行了分析，根据分析结果可知，在调查问卷所涉及到的乘客属性中，只有职业、出行目的和个人收入这三个属性和路径选择行为具有较强相关性。同时，对以上三个属性进行了合并分类，每个属性划分为两大类，并对不同类别属性与路径选择进行了相关性分析。最后，对这三个属性进行交叉分类，产生八个乘客类别，进而对样本数较少的类别进行了合并，最终，将全部乘客划分为五个类别。
（3）提出了考虑乘客类别的城市地铁网络流量分配方法，根据调查数据，对模型中的参数进行了估计和验证，并对O-D需求进行了类别划分，最后，通过实际网络数据对模型和算法进行了实证分析。得出如下结论：基于乘客分类的地铁配流方法相对于不考虑乘客分类的方法，其计算结果更接近实际；通过对模型中相关参数的灵敏度分析可知，表示乘客对网络熟悉度的参数i对计算结果影响相对较小，而有效路径判定条件中的扩展系数H以及换乘惩罚参数i和i对计算结果影响较大；通过对所有五类乘客所占百分比的变化对配流结果影响的分析可知，由于第二类和第三类乘客的路径选择偏好与其他类别相比有较大差异，因此这两类乘客所占乘客比例的变化对配流结果的影响较大。这些结论证明了根据乘客属性对乘客进行分类，并对不同类别的乘客重新进行模型参数估计并进行客流分配方法的合理性和必要性。
（4）总结了地铁网络的时变特征和O-D需求的时变特征，给出了基于物理站点和区间的地铁网络空间结构的定义和描述，结合列车运行时刻表信息，定义了基于时刻表的地铁时空扩展网络以及时空路径的概念，在此基础上，给出了基于时刻表信息构建地铁时空扩展网络的基本方法，并对该网络中的基本元素进行了定义和描述。
（5）综合考虑影响乘客出行选择的主要因素，分析和研究地铁乘客路径选择行为的时效性，基于地铁时空扩展网络，考虑了乘车时间、换乘因素以及车内拥挤因素，构建了基于地铁时空扩展网络的路径广义费用模型，在此基础上，提出了基于时刻表的地铁网络客流动态分配模型，并采用MSA算法进行求解，同时，还给出了针对地铁时空扩展网络的改进最短路搜索算法。最后，通过一个简单算例对模型及算法进行了验证和分析。
With the sustained construction of urban subway in China, the urban subway network will beenlarged gradually in metropolis.Compared to single or several subway lines, passengers’ behaviorsconsisting of line choice, route choice and transfer choice changed greatly. In accordance with the Beijingsubway tickets and fare policy, there is no dditional charge for transfer, the challenge to the operation andmanagement of such system is how to predict the nonlinear growth of travel demand and simulate thepassengers’ behaviors consisting of line choice, route choice and transfer choice. In such conditions, it is akey problem for its operation and management to predict scientifically passenger flow assignment throughurban railway transport network.
This thesis focused on the passenger flow assignment problem in the urban subway network. Throughthe analysis for the travel survey of Beijing subway passengers, this paper considered the main factorsaffecting passenger’s path-choice and analyzed the correlation between the passenger’s properties and thepath-choice behavior. Based on survey data, the classification of all passengers was determined. Then thesocio-economic attributes based choice probability models are given. Subsequently, the correspondingassignment process is proposed for urban subway network. Similarly, the Beijing subway network in2010is used as example to illustrate the applicaiotn of proposed model and algorithm. At the same time, thispaper considered the dynamic properties of the urban subway network and proposed both of concept and itsmodel of schedule-based subway space-time extended network. On the base of these, a schedule-baseddynamic assignment model and algorithm for subway network was presented with its solution algorithm inthis paper. Finally, the feasibility and effectiveness of the model and algorithm were tested by a simpleexample. The contents of this paper are summarized as follows:
(1) In practice, the flow assignment partern through urban rail transport network is resulted with theaggregation of all passengers’ cmbined choices. Therefore, understanding and mastering the passenger’schoice psychology is the the foundation of modeling the passenger’s route choice and flow assignmentthrough whole network. In order to fully grasp the characteristics of the passenger route choice behavior,meanwhile, in order to provide reliable data for future research support and related parameter estimation,this paper designed a questionnaire of passengers’ choice behavior and gives fully data statistical analysisof Beijing subway network.
(2) Based on the survey data, this paper analyzed the correlation between the passenger’s propertiesand path-choice behavior by using the chi-square test. According to the analysis results, only threeproperties including the occupation, the trip purpose and personal income have strong correlations with thepassenger’s route-choice behavior. Each attribute was divided into two major categories and eight types ofpassengers were found by cross-classification of these three attributes. Finally, the categories with therelatively small sample size were merged and resulted in five categories of all passengers.
(3) According to survey data, the passengers with different socio-economic attributes will havedifferent standards and preferences of traffic choices. This paper considers the different choice behaviors between different passengers fully and establishes the generalized travel cost functions for different typesof passengers. Then the socio-economic attributes based choice probability models are given. Subsequently,the corresponding assignment process is proposed for urban subway network. Similarly, the Beijing subwaynetwork in2010is used as example to illustrate the applicaiotn of proposed model and algorithm. Thefollowing conclusions were draw from this research: the calculation results from the socio-economicattributes based assignment method were closer to the actual case with respect to the method withoutpassenger classification; through sensitivity analysis, it is shown that the parameters that desribed thepassenger’s familiarity of the network had relatively small impact on the calculation results, while theexpansion coefficients for effective path as well as the transfer penalty parameters had more impacts on thecalculation results; due to the second class and the third class passengers had different path-choicepreferences compared to the other categories, the changes of these two types of passengers share wouldimpact the flow assignment results. These conclusions expained that the reasonableness and necessity ofthe socio-economic attributes based assignment method.
(4) This paper summed up the time-varying characteristics of both the subway network and O-Ddemand and proposed the definition of the spatial structure of the subway network based on the physicalsite and interval. Combined with the train schedule, this paper presented the space-time extended networkas well as the concept of space-time path. On this basis, this paper proposed a method to build thespace-time extended network for urban subway system based on the schedule information and gave thedefinition and description of the basic elements in such network.
(5) The major factors that influence passenger flow pattern in urban subway network are taken intoaccount. The timeliness of the impact on passenger travel choice was analyzed. Based on the space-timeextended network for urban subway system, the factors in term of travel time, transfer as well as thecongestion in vehicle were fully considered in order to build a generalized cost function for passenger’stravel path. On the base of this, this paper proposed a schedule-based dynamic assignment model for theurban subway network. The MSA algorithm was used to solve such model. Simultaneously, an improvedshortest path search algorithm was given for the space-time extended network. Finally, a simple numericalexample was used to illustrate validation and effection of the proposed model and algorithm.
本文的研究主要围绕城市地铁网络客流分配问题而进行。通过对城市地铁乘客出行特性的调查分析，得到影响乘客路径选择的主要因素以及相关规律，对乘客属性与路径选择行为之间的相关性进行了统计分析，基于调查数据确定了乘客分类模式，特别是提出了基于乘客属性的地铁配流模型及算法，并对算法进行了实证研究；同时，考虑了地铁需求的动态属性，给出了基于时刻表的地铁时空扩展网络的概念和构建方法，在此基础上，建立了基于时刻表的地铁客流动态分配模型及算法，并利用北京地铁网络运营客流数据对模型及算法的可行性和有效性进行了验证。具体而言，论文主要就以下方面进行了研究：
（1）为了充分掌握乘客的路径选择行为，同时，为了给后续研究提供可靠的数据支持和相关参数估计，针对北京市地铁运营网络，进行了乘客路径选择行为调查，并对调查数据进行了统计分析。结果表明：不同属性的乘客对路径选择存在明显差异，不同属性乘客对时间和换乘等影响因素的关注程度呈现明显差异。
（2）基于调查数据，采用卡方检验方法，对乘客属性和路径选择之间的相关性进行了分析，根据分析结果可知，在调查问卷所涉及到的乘客属性中，只有职业、出行目的和个人收入这三个属性和路径选择行为具有较强相关性。同时，对以上三个属性进行了合并分类，每个属性划分为两大类，并对不同类别属性与路径选择进行了相关性分析。最后，对这三个属性进行交叉分类，产生八个乘客类别，进而对样本数较少的类别进行了合并，最终，将全部乘客划分为五个类别。
（3）提出了考虑乘客类别的城市地铁网络流量分配方法，根据调查数据，对模型中的参数进行了估计和验证，并对O-D需求进行了类别划分，最后，通过实际网络数据对模型和算法进行了实证分析。得出如下结论：基于乘客分类的地铁配流方法相对于不考虑乘客分类的方法，其计算结果更接近实际；通过对模型中相关参数的灵敏度分析可知，表示乘客对网络熟悉度的参数i对计算结果影响相对较小，而有效路径判定条件中的扩展系数H以及换乘惩罚参数i和i对计算结果影响较大；通过对所有五类乘客所占百分比的变化对配流结果影响的分析可知，由于第二类和第三类乘客的路径选择偏好与其他类别相比有较大差异，因此这两类乘客所占乘客比例的变化对配流结果的影响较大。这些结论证明了根据乘客属性对乘客进行分类，并对不同类别的乘客重新进行模型参数估计并进行客流分配方法的合理性和必要性。
（4）总结了地铁网络的时变特征和O-D需求的时变特征，给出了基于物理站点和区间的地铁网络空间结构的定义和描述，结合列车运行时刻表信息，定义了基于时刻表的地铁时空扩展网络以及时空路径的概念，在此基础上，给出了基于时刻表信息构建地铁时空扩展网络的基本方法，并对该网络中的基本元素进行了定义和描述。
（5）综合考虑影响乘客出行选择的主要因素，分析和研究地铁乘客路径选择行为的时效性，基于地铁时空扩展网络，考虑了乘车时间、换乘因素以及车内拥挤因素，构建了基于地铁时空扩展网络的路径广义费用模型，在此基础上，提出了基于时刻表的地铁网络客流动态分配模型，并采用MSA算法进行求解，同时，还给出了针对地铁时空扩展网络的改进最短路搜索算法。最后，通过一个简单算例对模型及算法进行了验证和分析。
With the sustained construction of urban subway in China, the urban subway network will beenlarged gradually in metropolis.Compared to single or several subway lines, passengers’ behaviorsconsisting of line choice, route choice and transfer choice changed greatly. In accordance with the Beijingsubway tickets and fare policy, there is no dditional charge for transfer, the challenge to the operation andmanagement of such system is how to predict the nonlinear growth of travel demand and simulate thepassengers’ behaviors consisting of line choice, route choice and transfer choice. In such conditions, it is akey problem for its operation and management to predict scientifically passenger flow assignment throughurban railway transport network.
This thesis focused on the passenger flow assignment problem in the urban subway network. Throughthe analysis for the travel survey of Beijing subway passengers, this paper considered the main factorsaffecting passenger’s path-choice and analyzed the correlation between the passenger’s properties and thepath-choice behavior. Based on survey data, the classification of all passengers was determined. Then thesocio-economic attributes based choice probability models are given. Subsequently, the correspondingassignment process is proposed for urban subway network. Similarly, the Beijing subway network in2010is used as example to illustrate the applicaiotn of proposed model and algorithm. At the same time, thispaper considered the dynamic properties of the urban subway network and proposed both of concept and itsmodel of schedule-based subway space-time extended network. On the base of these, a schedule-baseddynamic assignment model and algorithm for subway network was presented with its solution algorithm inthis paper. Finally, the feasibility and effectiveness of the model and algorithm were tested by a simpleexample. The contents of this paper are summarized as follows:
(1) In practice, the flow assignment partern through urban rail transport network is resulted with theaggregation of all passengers’ cmbined choices. Therefore, understanding and mastering the passenger’schoice psychology is the the foundation of modeling the passenger’s route choice and flow assignmentthrough whole network. In order to fully grasp the characteristics of the passenger route choice behavior,meanwhile, in order to provide reliable data for future research support and related parameter estimation,this paper designed a questionnaire of passengers’ choice behavior and gives fully data statistical analysisof Beijing subway network.
(2) Based on the survey data, this paper analyzed the correlation between the passenger’s propertiesand path-choice behavior by using the chi-square test. According to the analysis results, only threeproperties including the occupation, the trip purpose and personal income have strong correlations with thepassenger’s route-choice behavior. Each attribute was divided into two major categories and eight types ofpassengers were found by cross-classification of these three attributes. Finally, the categories with therelatively small sample size were merged and resulted in five categories of all passengers.
(3) According to survey data, the passengers with different socio-economic attributes will havedifferent standards and preferences of traffic choices. This paper considers the different choice behaviors between different passengers fully and establishes the generalized travel cost functions for different typesof passengers. Then the socio-economic attributes based choice probability models are given. Subsequently,the corresponding assignment process is proposed for urban subway network. Similarly, the Beijing subwaynetwork in2010is used as example to illustrate the applicaiotn of proposed model and algorithm. Thefollowing conclusions were draw from this research: the calculation results from the socio-economicattributes based assignment method were closer to the actual case with respect to the method withoutpassenger classification; through sensitivity analysis, it is shown that the parameters that desribed thepassenger’s familiarity of the network had relatively small impact on the calculation results, while theexpansion coefficients for effective path as well as the transfer penalty parameters had more impacts on thecalculation results; due to the second class and the third class passengers had different path-choicepreferences compared to the other categories, the changes of these two types of passengers share wouldimpact the flow assignment results. These conclusions expained that the reasonableness and necessity ofthe socio-economic attributes based assignment method.
(4) This paper summed up the time-varying characteristics of both the subway network and O-Ddemand and proposed the definition of the spatial structure of the subway network based on the physicalsite and interval. Combined with the train schedule, this paper presented the space-time extended networkas well as the concept of space-time path. On this basis, this paper proposed a method to build thespace-time extended network for urban subway system based on the schedule information and gave thedefinition and description of the basic elements in such network.
(5) The major factors that influence passenger flow pattern in urban subway network are taken intoaccount. The timeliness of the impact on passenger travel choice was analyzed. Based on the space-timeextended network for urban subway system, the factors in term of travel time, transfer as well as thecongestion in vehicle were fully considered in order to build a generalized cost function for passenger’stravel path. On the base of this, this paper proposed a schedule-based dynamic assignment model for theurban subway network. The MSA algorithm was used to solve such model. Simultaneously, an improvedshortest path search algorithm was given for the space-time extended network. Finally, a simple numericalexample was used to illustrate validation and effection of the proposed model and algorithm.
引文
[1]国家发改委运输所.2012-2013年中国城市轨道交通年度报告[M].北京，2012.
[2]中国城市科学研究会.中国城市交通规划发展报告[M]．北京：中国城市出版社,2012．
[3] Wardrop J. G. Some theoretical aspects of road traffic research[C]. Proceedings of the Institution ofCiviI Engineers-part II,1952,36:325-378.
[4] Beckmann M. J., McGuire C. B., Winsten C. B. Studies in the economics of transportation [M]. NewHaven: Yale University Press,1956.
[5] LeBlance L. J., Morlok E. K., Pierskalla W. An efficient approach to solving the road networkequilibrium traffic assignment problem[J]. Transportation Research, l975,9(5):309-3l8.
[6] Dafermos S.C. Traffic equilibrium and variational inequalities[J]. Transportation Science,1980,14:42-54.
[7] Yang H., Yagar S. Traffic assignment and traffic control in general freeway-arterial corridorsystems[J]. Transportation Research-B,1994,28:463-486.
[8] Daganzo C. F., Sheffi Y. On Stochastic Models of Traffic Assignment [J]. Transportation Science,1977,11(3):253-274.
[9] Daganzo C. F. Multinomial probit：the theory and its application to demand forecasting [M]. NewYork: Academic Press,1979.
[10] Sheffi Y. Urban Transportation Networks: Equilibrium Analysis with Mathematical ProgrammingMethods[M]. Prentice-Hall, Englewood Cliffs, NJ,1985.
[11] Fisk C. Some Developments in Equilibrium Traffic Assignment[J]. Transportation Research,1980,14(3):243-255.
[12] Vuk, Goran, Hansen, Christian Overgaard. Validating the passenger traffic model for Copenhagen[J].Transportation,2006,
[13] Dial R.B. Transit pathfinder algorithms[J]. Highway Research Record,1967,205:67-85.
[14] LeClercq, F. A public transport assignment model[J]. Traffic Engineering and Control,1972,8(2):91-96.
[15] Chriqui C., Robillard P. Common bus lines[J]. Transportation Science,1975,9:115-121.
[16] Spiess H. Contribution à la théorie et aut outils de planificatin des réseaux de transport urbain, Ph.D.thesis, Département d'informatique et de recherche opérationnelle, Centre de recherche sur lestransports, Université de Montréal, Publication,1984.
[17] Spiess H., Florian M. Optimal strategies: a new assignment model for transit networks[J].Transportation Research-B,1989,23(2):83-102.
[18] Nguyen S., Pallotino S. Equilibrium traffic assignment in large scale transit networks[J]. EuropeanJournal of Operational Research,1988,37(2):176-186.
[19] Last A., Leak S. E. Transept: a bus model [J]. Traffic Engineering and Control,1976,17:91-96.
[20] DeCea, J., Fernández, E. Transit assignment for congested public transport systems: an equilibriummodel [J]. Transportation Science,1993,27(2):133-147.
[21] Lam W. H. K., Gao Z.Y., Chan K.S., Yang H. A stochastic user equilibrium assignment model forcongested transit networks[J]. Transportation Research-B,1999,33:351-368.
[22]姜虹,高自友.用遗传算法求解拥挤条件下的公共交通随机用户平衡配流模型[J].公路交通科技,2000,17(2):37-41.
[23] Tong C. O., Wong S. C. A stochastic transit assignment model using a dynamic schedule-basednetwork[J]. Transportation Research,1999,33:107-121.
[24]吴祥云,刘灿齐.轨道交通客流量均衡分配模型与算法[J].同济大学学报(自然科学版),2004,32(9):1158-1162.
[25]赵烈秋,孔繁钰.基于GA的城市轨道交通客流分配问题[J].后勤工程学院学报,2008,24(02):106-110.
[26]四兵锋,毛保华,刘智丽．无缝换乘条件下城市轨道交通网络客流分配模型及算法[J].铁道学报,2007,29(6):12-18.
[27]孔繁钰,李献忠.弹性需求下的轨道交通客流分配模型和算法[J].西安工程大学学报,2008,22(1):104-108.
[28]牛新奇,潘荫荣.轨道交通系统中清分算法的研究[J].计算机时代,2005,(2):17-21.
[29] Guan J. F., Yang H., Wirasinghe S. C. Simultaneous optimization of transit line configuration andpassenger line assignment[J]. Transportation Research-B,2006,40:885-902.
[30]毛保华,四兵锋,刘智丽.城市轨道交通网络管理及收入分配理论与方法[M].北京:科学出版社,2007.
[31]叶晋,史有群,杨学斌,等.遗传算法在轨道交通换乘路径求解问题上的应用[J].电脑与信息技术,2009,17(4):24-27.
[32]刘剑锋,孙福亮,柏赟.城市轨道交通乘客路径选择模型及算法[J].交通运输系统工程与信息,2009,9(2):81-86.
[33] Poon M.H., Tong C.O., Wong S.C. Validation of a schedule-based capacity restraint transitassignment model for a large-scale network [J]. Journal of Advanced Transportation,2003,38(1):5-26.
[34] Nuzzolo A, Russo F and Crisalli U. A Doubly Dynamic Schedule-based Assignment Model forTransit Networks[J]. Transportation Science,2001,35(3):268-285.
[35] Moller-Pedersen, J. Assignment model for timetable-based systems[C]. Paper from The Associationfor European Transport Conference held in Cambridge on1January1999.
[36] Tong C.O., Wong S.C., Poon M.H. et al. A schedule-based dynamic transit network model-Recentadvances and prospective future research [J]. Journal of Advanced Transportation,2001,35(2):175-195.
[37] Nguyen S., Pallottino S., Malucelli F. A modeling framework for passenger assignment on atransport network with timetables[J]. Transportation Science,2001,35(3):238-249.
[38] Hamdoucha Y. and Lawphongpanich S. Schedule-based transit assignment model with travelstrategies and capacity constraints[J]. Transportation Research-B,2008,42(7):663–684.
[39] Hamdoucha Younes1, Ho H.W., Sumalee Agachai2et al. Schedule-based transit assignment modelwith vehicle capacity and seat availability[J]. Transportation Research-B,2011,45(10):1805-1830.
[40] Sumi T., Matsumoto Y. and Miyaki Y. Departure time and route choice of commuters on mass transitsystems [J]. Transportation Research-B,1990,24(4):247–262.
[41] Alfa A. S. and Chen M. Temporal distribution of public transport demand during the peak period [J].European Journal of Operational Research,1995,83(1):137–153.
[42] Tian Q. and Huang H. J. Commuting Equilibria on a Mass Transit System with CapacityConstraints[C]. Transportation and Traffic Theory2007, London,361-383.
[43] Nielsen, Otto Anker. A stochastic transit assignment model considering differences in passengersutility functions [J]. Transportation Research-B2000,34(5):377-402.
[44] Nielsen O. A. and Frederiksen R. D. Optimisation of timetable-based, stochastic transit assignmentmodels based on MSA[J]. Annals of Operations Research,2006,144(1):263-285.
[45] Friedrich M, Hofsaess I. and Wekeck S. Timetable-Based Transit Assignment Using Branch andBound Techniques[J]. Transportation Research Record: Journal of the Transportation ResearchBoard,2001,1752,100-107.
[46] Poon M. H., Wong, S.C., Tong, C.O. A dynamic schedule-based model for congested transitnetworks[J]. Transportation Research-B,2004,38:343-368.
[47] Schmockera J. D., Bell M.G.H. and Kurauchi F. A quasi-dynamic capacity constrainedfrequency-based transit assignment model[J]. Transportation Research-B,2008,42(10):925–945.
[48] Nuzzolo A. and Crisalli U. The schedule-based modeling of transportation systems: recentdevelopments[M]. In: Schedule-Based Modeling of Transportation Networks, OperationsResearch/Computer Science Interfaces Series,2009,46,1-26.
[49] Sumalee Agachai1,Uchida Kenetsu, Lam William H.K. Stochastic multi-modal transport networkunder demand uncertainties and adverse weather condition[J]. Transportation Research-C,2011,19(2):338-350.
[50] Gendreau M, Laporte G, Mesa J. Locating Rapid Transit Line[J].Journal of AdvancedTransportation,1995,29(2):145-162.
[51] Lee J.Y., Lam W.H.K. Pedestrian simulation-assignment model for a Hong Kong mass transitrailway station-Calibration and validation [C]. Annual Conference-Canadian Society for CivilEngineering, Canada, TR-173-1-TR-173-10.
[52] Lam W.H.K., Gao Z.Y., Chan K.S. Capacity restraint assignment model for congested publictransport systems[C]. A Proceedings of the Conference on Traffic and TransportationStudies(ICTTS), Beijing,1998,348-357.
[53]关宏志.非集计模型:交通行为分析的工具[M].北京:人民交通出版社,2004.
[54]邵春福.交通规划原理[M].北京:中国铁道出版社,2004.
[55]黄建玲.城市轨道交通客流后评估研究[D].北京.北京交通大学博士学位论文,2011.
[56]刘剑锋.基于换乘的城市轨道交通网络流量分配建模及其实证研究[D].北京:北京交通大学博士学位论文,2012.
[57] Liu Xinhua, Sun Zhuangzhi, Yao Guangzheng. Spectator Arrival&Departure Traffic Mode andInfluence Factors in Beijing Olympic Games Opening and Closing Ceremony [J]. Journal ofTransportation Systems Engineering and Information Technology,2011Bound Edition,52-56.
[58] Xinhua Liu, Zhuangzhi Sun,Chun-Fu Sha et al. Method and Practice about Sequencing the UrbanRail Transit Construction [C]. International Conference on Future Power and Energy Engineering,2010,54-59.
[59] Marcotte P., Wynter L. A New Look at the Multiclass Network Equilibrium Problem [J].Transportation Science,2004,38(3):282-292.
[60] Shimamoto Hiroshi1,Kurauchi Fumitaka,Schm cker Jan-Dirk3et al. Evaluating critical lines andstations considering the impact of the consequence using transit assignment model-case study ofLondon's underground network [J]. Journal of Advanced Transportation,2008,42(3):291-310.
[61]刘剑锋,四兵锋,刘新华.基于乘客类别的城市轨道交通流量分配模型研究[J].物流技术,2011,12(30):101-104.
[62]刘剑锋,孙福亮.基于IC卡数据的地铁客运量推算模型及求解算法.第五届中国智能交通年会优秀论文集（深圳）[C],2009,12:326-333.
[63]李丽群.城市轨道交通客流竞争理论与方法研究[D].镇江:江苏大学博士学位论文,2012.
[64]翟华伟.轨道交通客流动态分布形式建模及应用研究[D].大连:大连海事大学博士学位论文,2012.
[65]王玉萍.城市轨道交通客流预测与分析方法[D].西安:长安大学博士学位论文,2012.
[66]张天然.基于交通网络均衡理论的交通需求管理政策评价研究[D].上海:同济大学博士学位论文,2008.
[67]罗小强.城市轨道交通线网布局规划理论与方法研究[D].西安:长安大学博士学位论文,2010.
[68]四兵锋,张好智,高自友.求解logit随机网络配流问题的改进Dial算法[J].中国公路学报,2009,22(1):78-83.
[69]张天然.城市轨道交通客流最优策略分配模型的改进[J].城市轨道交通研究,2010,13(9):15-18.
[70]徐瑞华,罗钦,高鹏．基于多路径的城市轨道交通网络客流分布模型及算法研究[J].铁道学报,2009,31(2):110-114.
[71]范征.城市轨道交通系统经济效益分析[D].成都:西南交通大学博士学位论文,2012.
[72]马洪.轨道交通枢纽动态换乘效率及网络客流研究[D].北京:清华大学博士学位论文,2010.
[73]陈尚云.我国特大城市客运交通系统结构和发展战略研究[D].成都:西南交通大学大学博士学位论文,2004.
[74]赵莉.城市轨道交通枢纽交通设计理论与方法研究[D].北京:北京交通大学博士学位论文,2012.
[75]北京交通发展研究中心.《2011年北京交通发展年报》[R].北京:北京交通发展研究中心,2011.
[76]北京交通发展研究中心.《2011年北京交通运行报告》[R].北京:北京交通发展研究中心,2011.
[77]四兵锋,高自友.城市间公路客运的客票票价与其客流量之间的灵敏度分析[J].中国公路学报,2000(2),91-95.
[78]北京交通发展研究中心.《2012年北京交通发展年报》[R].北京:北京交通发展研究中心,2012.
[79]北京交通发展研究中心.《2012年北京交通运行报告》[R].北京:北京交通发展研究中心,2012.
[80]北京交通发展研究中心.《2010年北京交通发展年报》[R].北京:北京交通发展研究中心,2010.
[81]北京交通发展研究中心.《北京市轨道交通建设计划（2011-2015年）线网客流预测》[R].北京:北京交通发展研究中心,2011.
[82]黄海军.城市交通网络平衡分析理论与实践[M].北京:人民交通出版社,1994.
[83] N kel Klaus,Wekeck Steffen. Boarding and alighting in frequency-based transit assignment[J].Transportation Research Record,2009,2111:60-67.
[84] Gentile Guido,Nguyen Sang,Pallottino Stefano. Route choice on transit networks with onlineinformation at stops [J]. Transportation Science,2005,39(3):289-297.
[85] Cepeda M.,Cominetti R., Florian M. A frequency-based assignment model for congested transitnetworks with strict capacity constraints: Characterization and computation of equilibria [J].Transportation Research-B,2006,40(6):437-459.
[86] Szeto W.Y.,Solayappan, Muthu et al. Reliability-based transit assignment for congested stochastictransit networks [J]. Computer-Aided Civil and Infrastructure Engineering,2011,26(4):311-326.
[87]张莹.运筹学基础[M].北京:清华大学出版社,1995.
[88] Current J, Revelle C. The Median Shortest Path Problem: A Multiobjective Approach Analyze Costvs. Accessibility in the Design of Transportation Network[J]. Transportation Science,1987,12(3):188-197.
[89] Current J. Multiple Objectives in Transportation Network Design and Routing[J]. European Journalof Operational Research,1993,56(1):1-3.
[90] Rahbee Adam B. Farecard passenger flow model at chicago transit authority, Illinois[J].Transportation Research Record,2008,2072:3-9.
[91] Cominetti R.,Correa J. Common-lines and passenger assignment in congested transit networks[J].Transportation Science,2001,35(3):250-267.
[92]卢立能,刘建平.轨道交通无障碍换乘模式下的客流分配[J].计算机应用2011,31(11)3126-3128.
[93]刘志谦,宋瑞.基于时刻表的公交配流算法研究[J].重庆交通大学学报(自然科学版),2010,29(1):114-120.
[94] Cschm cke Jan-Dirk. Frequency-based transit assignment considering seat capacities [J].Transportation Research-B,2011,45(2):392-408.
[95] Yang H., Huang H.J. The multi-class, multi-criteria traffic network equilibrium and system optimumproblem [A]. Transpn Research-B [C],2004,38:1-15.
[96] Xinhua Liu, Zhuangzhi Sun. Architecture for Structural Optimization of Urban RoadNetworks—Case Study of Beijing City [C]. The Fifth Advanced Forum on Transportation of China2009, Beijing,176-180.
[97]牛学勤,王炜．基于最短路搜索的多路径公交客流分配模型研究[J].东南大学学报(自然科学版),2002,32(6):917-919.
[98]高圣国,吴忠.基于旅行时间分布的客流清分模型[J].交通运输系统工程与信息,2011,11(6):124-130.
[99]孟祥定.绿色交通视角下城市轨道交通网络规划决策方法及应用[D].长沙:湖南大学博士学位论文,2007.
[100] de Cea,Joaquin1,Fernandez, Enrique. Transit assignment for congested public transport systems: Anequilibrium model [J]. Transportation Science,1993,27(2):133-147.
[101]周刚,王炜.地铁线路客流分配方法与算法研究[J].广东公路交通,2001,(4):32-35.第四章
[102]赵峰,张星臣,刘智丽.城市轨道交通系统运费清分方法研究[J].交通运输系统工程与信息,2007,7(6):85-90.
[103]李中华.垂直交通客流分析与电梯群控制优化研究[D].广州:华南理工大学博士学位论文,2005.
[104]李仁涵.我国大都市交通圈发展模式的研究[D].上海:同济大学博士学位论文,2007.
[105]四兵锋,孙壮志,赵小梅.基于随机用户平衡的混合交通网络流量分离模型[J].中国公路学报,2006,19(11):93-98.
[106]闫会娟,林国顺.地铁客流分流模型[J].中国科技信息,2005,(18):39-41.
[107]徐兵.多用户准则随机交通均衡理论与应研究——基于变分不等式方法[D].上海:复旦大学博士学位论文,2006.
[108]刘晓佳,李友好,施其洲.运输通道结构配置中的客流量分配模型及算法[J].同济大学学报(自然科学版),2007,35(7):924-928.
[109]孙壮志,唐孝飞,胡思继.基于混合模式客流分配的城市轨道交通线路设计模型[J].北方交通大学学报,2002,26(5):67-70.
[110]刘剑锋.基于IC卡数据的城市轨道交通网络配流模型研究[J].物流技术,2010,29(8):64-67.
[111]董春娇,邵春福,胡超凡,刘新华.城市道路基础设施建设时序规划方法及实践[J].交通信息与安全,2011,29(4):10-14.
[2]中国城市科学研究会.中国城市交通规划发展报告[M]．北京：中国城市出版社,2012．
[3] Wardrop J. G. Some theoretical aspects of road traffic research[C]. Proceedings of the Institution ofCiviI Engineers-part II,1952,36:325-378.
[4] Beckmann M. J., McGuire C. B., Winsten C. B. Studies in the economics of transportation [M]. NewHaven: Yale University Press,1956.
[5] LeBlance L. J., Morlok E. K., Pierskalla W. An efficient approach to solving the road networkequilibrium traffic assignment problem[J]. Transportation Research, l975,9(5):309-3l8.
[6] Dafermos S.C. Traffic equilibrium and variational inequalities[J]. Transportation Science,1980,14:42-54.
[7] Yang H., Yagar S. Traffic assignment and traffic control in general freeway-arterial corridorsystems[J]. Transportation Research-B,1994,28:463-486.
[8] Daganzo C. F., Sheffi Y. On Stochastic Models of Traffic Assignment [J]. Transportation Science,1977,11(3):253-274.
[9] Daganzo C. F. Multinomial probit：the theory and its application to demand forecasting [M]. NewYork: Academic Press,1979.
[10] Sheffi Y. Urban Transportation Networks: Equilibrium Analysis with Mathematical ProgrammingMethods[M]. Prentice-Hall, Englewood Cliffs, NJ,1985.
[11] Fisk C. Some Developments in Equilibrium Traffic Assignment[J]. Transportation Research,1980,14(3):243-255.
[12] Vuk, Goran, Hansen, Christian Overgaard. Validating the passenger traffic model for Copenhagen[J].Transportation,2006,
[13] Dial R.B. Transit pathfinder algorithms[J]. Highway Research Record,1967,205:67-85.
[14] LeClercq, F. A public transport assignment model[J]. Traffic Engineering and Control,1972,8(2):91-96.
[15] Chriqui C., Robillard P. Common bus lines[J]. Transportation Science,1975,9:115-121.
[16] Spiess H. Contribution à la théorie et aut outils de planificatin des réseaux de transport urbain, Ph.D.thesis, Département d'informatique et de recherche opérationnelle, Centre de recherche sur lestransports, Université de Montréal, Publication,1984.
[17] Spiess H., Florian M. Optimal strategies: a new assignment model for transit networks[J].Transportation Research-B,1989,23(2):83-102.
[18] Nguyen S., Pallotino S. Equilibrium traffic assignment in large scale transit networks[J]. EuropeanJournal of Operational Research,1988,37(2):176-186.
[19] Last A., Leak S. E. Transept: a bus model [J]. Traffic Engineering and Control,1976,17:91-96.
[20] DeCea, J., Fernández, E. Transit assignment for congested public transport systems: an equilibriummodel [J]. Transportation Science,1993,27(2):133-147.
[21] Lam W. H. K., Gao Z.Y., Chan K.S., Yang H. A stochastic user equilibrium assignment model forcongested transit networks[J]. Transportation Research-B,1999,33:351-368.
[22]姜虹,高自友.用遗传算法求解拥挤条件下的公共交通随机用户平衡配流模型[J].公路交通科技,2000,17(2):37-41.
[23] Tong C. O., Wong S. C. A stochastic transit assignment model using a dynamic schedule-basednetwork[J]. Transportation Research,1999,33:107-121.
[24]吴祥云,刘灿齐.轨道交通客流量均衡分配模型与算法[J].同济大学学报(自然科学版),2004,32(9):1158-1162.
[25]赵烈秋,孔繁钰.基于GA的城市轨道交通客流分配问题[J].后勤工程学院学报,2008,24(02):106-110.
[26]四兵锋,毛保华,刘智丽．无缝换乘条件下城市轨道交通网络客流分配模型及算法[J].铁道学报,2007,29(6):12-18.
[27]孔繁钰,李献忠.弹性需求下的轨道交通客流分配模型和算法[J].西安工程大学学报,2008,22(1):104-108.
[28]牛新奇,潘荫荣.轨道交通系统中清分算法的研究[J].计算机时代,2005,(2):17-21.
[29] Guan J. F., Yang H., Wirasinghe S. C. Simultaneous optimization of transit line configuration andpassenger line assignment[J]. Transportation Research-B,2006,40:885-902.
[30]毛保华,四兵锋,刘智丽.城市轨道交通网络管理及收入分配理论与方法[M].北京:科学出版社,2007.
[31]叶晋,史有群,杨学斌,等.遗传算法在轨道交通换乘路径求解问题上的应用[J].电脑与信息技术,2009,17(4):24-27.
[32]刘剑锋,孙福亮,柏赟.城市轨道交通乘客路径选择模型及算法[J].交通运输系统工程与信息,2009,9(2):81-86.
[33] Poon M.H., Tong C.O., Wong S.C. Validation of a schedule-based capacity restraint transitassignment model for a large-scale network [J]. Journal of Advanced Transportation,2003,38(1):5-26.
[34] Nuzzolo A, Russo F and Crisalli U. A Doubly Dynamic Schedule-based Assignment Model forTransit Networks[J]. Transportation Science,2001,35(3):268-285.
[35] Moller-Pedersen, J. Assignment model for timetable-based systems[C]. Paper from The Associationfor European Transport Conference held in Cambridge on1January1999.
[36] Tong C.O., Wong S.C., Poon M.H. et al. A schedule-based dynamic transit network model-Recentadvances and prospective future research [J]. Journal of Advanced Transportation,2001,35(2):175-195.
[37] Nguyen S., Pallottino S., Malucelli F. A modeling framework for passenger assignment on atransport network with timetables[J]. Transportation Science,2001,35(3):238-249.
[38] Hamdoucha Y. and Lawphongpanich S. Schedule-based transit assignment model with travelstrategies and capacity constraints[J]. Transportation Research-B,2008,42(7):663–684.
[39] Hamdoucha Younes1, Ho H.W., Sumalee Agachai2et al. Schedule-based transit assignment modelwith vehicle capacity and seat availability[J]. Transportation Research-B,2011,45(10):1805-1830.
[40] Sumi T., Matsumoto Y. and Miyaki Y. Departure time and route choice of commuters on mass transitsystems [J]. Transportation Research-B,1990,24(4):247–262.
[41] Alfa A. S. and Chen M. Temporal distribution of public transport demand during the peak period [J].European Journal of Operational Research,1995,83(1):137–153.
[42] Tian Q. and Huang H. J. Commuting Equilibria on a Mass Transit System with CapacityConstraints[C]. Transportation and Traffic Theory2007, London,361-383.
[43] Nielsen, Otto Anker. A stochastic transit assignment model considering differences in passengersutility functions [J]. Transportation Research-B2000,34(5):377-402.
[44] Nielsen O. A. and Frederiksen R. D. Optimisation of timetable-based, stochastic transit assignmentmodels based on MSA[J]. Annals of Operations Research,2006,144(1):263-285.
[45] Friedrich M, Hofsaess I. and Wekeck S. Timetable-Based Transit Assignment Using Branch andBound Techniques[J]. Transportation Research Record: Journal of the Transportation ResearchBoard,2001,1752,100-107.
[46] Poon M. H., Wong, S.C., Tong, C.O. A dynamic schedule-based model for congested transitnetworks[J]. Transportation Research-B,2004,38:343-368.
[47] Schmockera J. D., Bell M.G.H. and Kurauchi F. A quasi-dynamic capacity constrainedfrequency-based transit assignment model[J]. Transportation Research-B,2008,42(10):925–945.
[48] Nuzzolo A. and Crisalli U. The schedule-based modeling of transportation systems: recentdevelopments[M]. In: Schedule-Based Modeling of Transportation Networks, OperationsResearch/Computer Science Interfaces Series,2009,46,1-26.
[49] Sumalee Agachai1,Uchida Kenetsu, Lam William H.K. Stochastic multi-modal transport networkunder demand uncertainties and adverse weather condition[J]. Transportation Research-C,2011,19(2):338-350.
[50] Gendreau M, Laporte G, Mesa J. Locating Rapid Transit Line[J].Journal of AdvancedTransportation,1995,29(2):145-162.
[51] Lee J.Y., Lam W.H.K. Pedestrian simulation-assignment model for a Hong Kong mass transitrailway station-Calibration and validation [C]. Annual Conference-Canadian Society for CivilEngineering, Canada, TR-173-1-TR-173-10.
[52] Lam W.H.K., Gao Z.Y., Chan K.S. Capacity restraint assignment model for congested publictransport systems[C]. A Proceedings of the Conference on Traffic and TransportationStudies(ICTTS), Beijing,1998,348-357.
[53]关宏志.非集计模型:交通行为分析的工具[M].北京:人民交通出版社,2004.
[54]邵春福.交通规划原理[M].北京:中国铁道出版社,2004.
[55]黄建玲.城市轨道交通客流后评估研究[D].北京.北京交通大学博士学位论文,2011.
[56]刘剑锋.基于换乘的城市轨道交通网络流量分配建模及其实证研究[D].北京:北京交通大学博士学位论文,2012.
[57] Liu Xinhua, Sun Zhuangzhi, Yao Guangzheng. Spectator Arrival&Departure Traffic Mode andInfluence Factors in Beijing Olympic Games Opening and Closing Ceremony [J]. Journal ofTransportation Systems Engineering and Information Technology,2011Bound Edition,52-56.
[58] Xinhua Liu, Zhuangzhi Sun,Chun-Fu Sha et al. Method and Practice about Sequencing the UrbanRail Transit Construction [C]. International Conference on Future Power and Energy Engineering,2010,54-59.
[59] Marcotte P., Wynter L. A New Look at the Multiclass Network Equilibrium Problem [J].Transportation Science,2004,38(3):282-292.
[60] Shimamoto Hiroshi1,Kurauchi Fumitaka,Schm cker Jan-Dirk3et al. Evaluating critical lines andstations considering the impact of the consequence using transit assignment model-case study ofLondon's underground network [J]. Journal of Advanced Transportation,2008,42(3):291-310.
[61]刘剑锋,四兵锋,刘新华.基于乘客类别的城市轨道交通流量分配模型研究[J].物流技术,2011,12(30):101-104.
[62]刘剑锋,孙福亮.基于IC卡数据的地铁客运量推算模型及求解算法.第五届中国智能交通年会优秀论文集（深圳）[C],2009,12:326-333.
[63]李丽群.城市轨道交通客流竞争理论与方法研究[D].镇江:江苏大学博士学位论文,2012.
[64]翟华伟.轨道交通客流动态分布形式建模及应用研究[D].大连:大连海事大学博士学位论文,2012.
[65]王玉萍.城市轨道交通客流预测与分析方法[D].西安:长安大学博士学位论文,2012.
[66]张天然.基于交通网络均衡理论的交通需求管理政策评价研究[D].上海:同济大学博士学位论文,2008.
[67]罗小强.城市轨道交通线网布局规划理论与方法研究[D].西安:长安大学博士学位论文,2010.
[68]四兵锋,张好智,高自友.求解logit随机网络配流问题的改进Dial算法[J].中国公路学报,2009,22(1):78-83.
[69]张天然.城市轨道交通客流最优策略分配模型的改进[J].城市轨道交通研究,2010,13(9):15-18.
[70]徐瑞华,罗钦,高鹏．基于多路径的城市轨道交通网络客流分布模型及算法研究[J].铁道学报,2009,31(2):110-114.
[71]范征.城市轨道交通系统经济效益分析[D].成都:西南交通大学博士学位论文,2012.
[72]马洪.轨道交通枢纽动态换乘效率及网络客流研究[D].北京:清华大学博士学位论文,2010.
[73]陈尚云.我国特大城市客运交通系统结构和发展战略研究[D].成都:西南交通大学大学博士学位论文,2004.
[74]赵莉.城市轨道交通枢纽交通设计理论与方法研究[D].北京:北京交通大学博士学位论文,2012.
[75]北京交通发展研究中心.《2011年北京交通发展年报》[R].北京:北京交通发展研究中心,2011.
[76]北京交通发展研究中心.《2011年北京交通运行报告》[R].北京:北京交通发展研究中心,2011.
[77]四兵锋,高自友.城市间公路客运的客票票价与其客流量之间的灵敏度分析[J].中国公路学报,2000(2),91-95.
[78]北京交通发展研究中心.《2012年北京交通发展年报》[R].北京:北京交通发展研究中心,2012.
[79]北京交通发展研究中心.《2012年北京交通运行报告》[R].北京:北京交通发展研究中心,2012.
[80]北京交通发展研究中心.《2010年北京交通发展年报》[R].北京:北京交通发展研究中心,2010.
[81]北京交通发展研究中心.《北京市轨道交通建设计划（2011-2015年）线网客流预测》[R].北京:北京交通发展研究中心,2011.
[82]黄海军.城市交通网络平衡分析理论与实践[M].北京:人民交通出版社,1994.
[83] N kel Klaus,Wekeck Steffen. Boarding and alighting in frequency-based transit assignment[J].Transportation Research Record,2009,2111:60-67.
[84] Gentile Guido,Nguyen Sang,Pallottino Stefano. Route choice on transit networks with onlineinformation at stops [J]. Transportation Science,2005,39(3):289-297.
[85] Cepeda M.,Cominetti R., Florian M. A frequency-based assignment model for congested transitnetworks with strict capacity constraints: Characterization and computation of equilibria [J].Transportation Research-B,2006,40(6):437-459.
[86] Szeto W.Y.,Solayappan, Muthu et al. Reliability-based transit assignment for congested stochastictransit networks [J]. Computer-Aided Civil and Infrastructure Engineering,2011,26(4):311-326.
[87]张莹.运筹学基础[M].北京:清华大学出版社,1995.
[88] Current J, Revelle C. The Median Shortest Path Problem: A Multiobjective Approach Analyze Costvs. Accessibility in the Design of Transportation Network[J]. Transportation Science,1987,12(3):188-197.
[89] Current J. Multiple Objectives in Transportation Network Design and Routing[J]. European Journalof Operational Research,1993,56(1):1-3.
[90] Rahbee Adam B. Farecard passenger flow model at chicago transit authority, Illinois[J].Transportation Research Record,2008,2072:3-9.
[91] Cominetti R.,Correa J. Common-lines and passenger assignment in congested transit networks[J].Transportation Science,2001,35(3):250-267.
[92]卢立能,刘建平.轨道交通无障碍换乘模式下的客流分配[J].计算机应用2011,31(11)3126-3128.
[93]刘志谦,宋瑞.基于时刻表的公交配流算法研究[J].重庆交通大学学报(自然科学版),2010,29(1):114-120.
[94] Cschm cke Jan-Dirk. Frequency-based transit assignment considering seat capacities [J].Transportation Research-B,2011,45(2):392-408.
[95] Yang H., Huang H.J. The multi-class, multi-criteria traffic network equilibrium and system optimumproblem [A]. Transpn Research-B [C],2004,38:1-15.
[96] Xinhua Liu, Zhuangzhi Sun. Architecture for Structural Optimization of Urban RoadNetworks—Case Study of Beijing City [C]. The Fifth Advanced Forum on Transportation of China2009, Beijing,176-180.
[97]牛学勤,王炜．基于最短路搜索的多路径公交客流分配模型研究[J].东南大学学报(自然科学版),2002,32(6):917-919.
[98]高圣国,吴忠.基于旅行时间分布的客流清分模型[J].交通运输系统工程与信息,2011,11(6):124-130.
[99]孟祥定.绿色交通视角下城市轨道交通网络规划决策方法及应用[D].长沙:湖南大学博士学位论文,2007.
[100] de Cea,Joaquin1,Fernandez, Enrique. Transit assignment for congested public transport systems: Anequilibrium model [J]. Transportation Science,1993,27(2):133-147.
[101]周刚,王炜.地铁线路客流分配方法与算法研究[J].广东公路交通,2001,(4):32-35.第四章
[102]赵峰,张星臣,刘智丽.城市轨道交通系统运费清分方法研究[J].交通运输系统工程与信息,2007,7(6):85-90.
[103]李中华.垂直交通客流分析与电梯群控制优化研究[D].广州:华南理工大学博士学位论文,2005.
[104]李仁涵.我国大都市交通圈发展模式的研究[D].上海:同济大学博士学位论文,2007.
[105]四兵锋,孙壮志,赵小梅.基于随机用户平衡的混合交通网络流量分离模型[J].中国公路学报,2006,19(11):93-98.
[106]闫会娟,林国顺.地铁客流分流模型[J].中国科技信息,2005,(18):39-41.
[107]徐兵.多用户准则随机交通均衡理论与应研究——基于变分不等式方法[D].上海:复旦大学博士学位论文,2006.
[108]刘晓佳,李友好,施其洲.运输通道结构配置中的客流量分配模型及算法[J].同济大学学报(自然科学版),2007,35(7):924-928.
[109]孙壮志,唐孝飞,胡思继.基于混合模式客流分配的城市轨道交通线路设计模型[J].北方交通大学学报,2002,26(5):67-70.
[110]刘剑锋.基于IC卡数据的城市轨道交通网络配流模型研究[J].物流技术,2010,29(8):64-67.
[111]董春娇,邵春福,胡超凡,刘新华.城市道路基础设施建设时序规划方法及实践[J].交通信息与安全,2011,29(4):10-14.