摘要
随着我国城市轨道交通网络化进程的快速推进,轨道交通的运营管理方式逐步从单线相对独立运营向多线综合运营的方向转变,形成了城市轨道交通网络化运营的新局面。在网络条件下,城市轨道交通系统各线路间的相互关联和影响必不可免,对轨道交通运输组织的协调性要求更高。为此,从路网运营管理的角度进一步提高网络客流分析预测的准确性、线网运力资源配置的均衡性、网络列车运行的协调性,对提升网络化运营管理的水平,更好地发挥轨道交通网络系统的整体能力和综合效益,实现运营的高效、安全和可靠非常重要。
针对我国城市轨道交通网络化发展的现状,在充分借鉴国内外先进经验的基础上,本文以城市轨道交通网络化运输组织为研究对象,以网络化运输组织协调高效为根本目标,展开了一系列的相关研究。
(1)本文对城市轨道交通网络化运输组织及其呈现的新特点进行了研究,阐述了城市轨道交通网络化运输组织的协调标准及其内涵。对城市轨道交通网络化运输组织所涉及的协调优化问题进行了简单分析,初步建立了城市轨道交通网络化运输组织协调理论研究的基本体系,并界定了论文的研究范围和主要内容。
(2)对成网条件下轨道交通客流需求的网络化特性和动态性变化进行了分析研究,总结了客流随网络结构演变的变化规律。结合此后介绍的常规公交竞争与协作模式下的客流预测方法,可形成中长期客流预测技术。在轨道交通网络化客流分配方面,建立了一种考虑拥挤对路径广义费用影响的多路径出行选择随机用户平衡客流分配模型,并设计了相应的蚁群算法搜寻K短路与动态规划方法回溯验证相结合的K短路混合算法,且通过部分轨道交通路网客流数据验证了模型和算法的有效性。
(3)本文从超长线路列车运行交路设置、市郊轨道交通跨站停列车开行及覆盖区域重合线路的共线运营三个方面,探讨了网络条件下城市轨道交通行车组织可能出现的新问题。尤其针对跨站停列车的停站方案设计,根据线路的长、短途客流特点和通过能力利用状况,建立了以运营企业社会经济利益最大化和旅客总出行时间最小化为目标的多目标优化模型,并设计了蚁群算法对模型进行求解,最终得到了跨站停列车开行的停站方案、服务频率以及该方案下的社会经济效益和总旅行时间。
(4)借鉴交通流理论的基本思想和相关方法,发现了各线列车开行密度配置方案间存在的影响因素和约束关系,并定量描述了单条线路列车开行密度的传播规律。利用超网络流理论对网状线路列车开行密度配置问题进行了描述,进而将问题转化为部分与整体的关系进行分阶段求解。根据现有研究成果,总结了独立线路不同运营模式条件下的列车开行密度配置方案的求解方法。并且在单独线路列车开行密度配置已确定条件下,建立了网络化列车开行密度配置关系协调性评价指标,并通过DEA方法对任意两线路列车开行密度的配置进行协调性评价,最终得到了各列车开行密度配置协调与否的评价结果及导致不协调存在的原因。
(5)在各线路列车运行图已独立铺画完成的条件下,根据城市轨道交通网络客流特点,兼顾多线换乘衔接的便捷性和合理性,在保证运营费用不增加的条件下构造了一个以旅客换乘及等待时间最少为目标的多向列车换乘衔接模型。同时结合列车到发时刻在换乘节点内部的衔接与网络换乘节点间的外部协调,提出了分层协调的优化策略,最终通过平移线路列车运行图的方法实现了网络列车运行的综合协调优化。
In the process of rapid developing of China urban mass transit network, operation and management mode of urban mass transit has gradually changed from independent single-line operation to integrated multi-line operation, and a new phase of network operation of urban mass transit has been forming. On the network, there must exist some relations and impacts between different lines. So the coordination network operation and management is much more needed. Thus, improving the accuracy of network passenger flow analysis and forecast, the balance of network capacity resources arrangement and the coordination of train operation on network from the perspective of network operation, is very important to raise the level of rail network operation, play a better role on using the overall capacity, and achieve efficiency, security and reliability of operation.
Based on the development reality of urban mass transit network and the advanced experience at home and abroad, this paper take a series of related research on train operation theory of urban mass transit network taking the coordination as the goal.
(1) The new features of urban mass transit network operation have been studied, and the intension and basic features of the coordination of urban mass transit network operation has been clearly described. On this basis, this paper made a simple analysis about the problems which should be coordinated, set up a basic system of the coordination research of train operation on urban mass transit network, and then defined the scope and the main content of the study.
(2) The paper analysed network characteristics and the dynamic changing characteristics of passengers under the conditions of network, and summarized the evolution of passenger traffic with the network structure changes. After introduction of the combination of competition and collaboration bus passenger flow forecasting model, it could form long-term passenger flow prediction technology. Furthermore, considering the stochastic user equilibrium principle and impact of congestion, a mathematical model for optimizing passenger flow distribution of the urban mass transit network was presented. To solve the passenger flow distribution model, a combining K-short-circuit algorithm with an ant colony algorithm searching for K-short-circuits and a dynamic programming method verifing short-circuits has been designed. The model and algorithm is verified through part of passenger flow data on unban mass transit network.
(3) This paper explored some new problems of unban mass transit network operation, from three aspects of cross-road seting, skip-stop train scheduling and joint operation arrangement. In particular, according to passenger flow characteristics and capacity utilization, a multi-object optimization model for skip-stop train plans, with the aims of the maximal social economy profits and the minimal total travel time of passengers was proposed. The model can be solved using an ant-colony algorithm designed in this paper to generate a best compromise train service plan, including the optimal stop-schedule plan, service frequency, as well as the social economy profit and total passengers travel time.
(4) This paper studied the influencing factors and constraints exist in the relationship between the train operation density arrangements of various lines. Then it described the train operation density arrangements of urban mass transit network using the super-network flow theory, and proposed a solution method which can solve the single-line operation density arrangement under different conditions. Furthermore, the paper established a coordination evaluation index system of network train operation density arrangement, and through the DEA method evaluated the coordination of any two lines on the network. Ultimately, the evaluation results and the reasons leading to inconsistency could be got by this method, which could be used in improving harmonious train operation plan of urban mass transit network.
(5) In case of the single-line train operation diagram completed, based on the passengers flow characters of urban mass transit, both the convenience and rationality of connection between different lines were considered, and then an optimization model, with the aims of the minimal total waiting time of transfer passengers and inboard passengers, was set up. Combining the inner coordination of arriving and departure time sequence of trains in transfer nodes with the exterior coordination of transfer nodes on whole urban mass transit network, a multi-layers coordination policy was proposed, and the integrated optimization of the urban mass transit system was realized through taking some small time shifts of the proposed single-line timetables.
引文
[1]陈旭梅,童华磊.城市轨道交通线网规模影响因素分析[J].中国铁道科学,2001.22(6)59-62
[2]徐行方,忻铁朕,项宝余.城际列车的概念及其开行条件[J].同济大学学报：自然科学版,2003.31(4)：432-436
[3]谢美全,聂磊.周期性列车运行图编制模型研究[J].铁道学报,2009.31(4)：7-13
[4]许红,马建军,龙建成.客运专线列车运行图编制模型及计算方法的研究[J].铁道学报,2007.29(2)：1-7
[5]胡超凡,郭春安,蒋玉琨,蔡顺利.北京城市轨道交通线网合理规模的研究[J].铁道运输与经济,2006.28(10)：52-54
[6]朱海燕.城市轨道交通客运组织[M].北京：中国铁道出版社,2009
[7]刘丽波,叶霞飞,顾保南.东京私铁快慢车组合运营模式对上海市域轨道交通线的启示[J].城市轨道交通研究,2006.9(11)：38-41
[8]郭春安,胡超凡.北京城市轨道交通线网调整规划[J].北京规划建设,2002(4)：10-15
[9]李素莹,陈光华,车永兵.上海轨道交通1号线开行大小交路运行方案的实践[J].城市轨道交通研究,2007.10(1)：50-53
[10]郭锴.沪宁城际轨道交通列车开行方案研究[J].现代城市轨道交通,2005(2)：10-11、23
[11]毕艳祥,刘加华,江志彬.市域快速轨道交通线不同编组列车混合运行影响分析[J].城市轨道交通研究,2006.9(12)：54-57
[12]徐瑞华,马兴峰,宋键.上海轨道交通明珠线共线运营方案[J].同济大学学报,2003.31(6)：682-686
[13]徐瑞华,李侠,陈菁菁.市域快速轨道交通线路列车运行交路研究[J].城市轨道交通研究,2006.9(5)：36-39
[14]宋键,徐瑞华,缪和平.市域快速轨道交通线开行快慢车问题的研究[J].城市轨道交通研究.2006.9(12)：23-27
[15]徐瑞华,江志彬,朱效洁,吴强.城市轨道交通列车运行图计算机编制的关键问题研究[J].城市轨道交通研究,2005.8(5)：31-35
[16]洪玲,陈菁菁,徐瑞华.市域快速轨道交通线行车间隔优化问题研究[J].城市轨道交通研究,2006.9(3)：35-37、59
[17]徐行方,徐瑞华.高速客运专线列车运行组织相关问题的研究[J].同济大学学报,2003.31(5)：572-575
[18]徐瑞华,徐浩,宋键.城市交通列车共线运营的通过能力和延误[J].同济大学学报,2005.33(3)：301-305
[19]徐瑞华,陈菁菁,杜世敏.城轨交通多种列车交路模式下的通过能力和车体运用研究[J].铁道学报,2005.27(4)：6-10
[20]孙焰,施其洲,赵源,孔庆瑜.城市轨道交通列车开行方案的确定[J].同济大学学报,2004.32(8)：1005-1008、1014
[21]晏秋.轨道交通系统列车运营模式及其软件设计[D].成都：西南交通大学,2000.1
[22]林震,杨浩.城市轨道交通发车间距优化模型探讨[J].土木工程学报,2003.36(1)：1-5
[23]周建军,顾保南.国外市域轨道交通共线运营方式的发展和启示[J].城市轨道交通研究,2004.7(6)：75-77
[24]Khisty C J. Transportation engineering. New Jersey:prentice—Hall Inc.,1990:381
[25]Zak, Jacek. The methodology of multiple—criteria decision making in the optimization of an urban transportation system:case study of PoznanA city in Poland[J]. International transaction in operational research.1999:571-590
[26]陈鹏飞.关于某时段相邻地铁列车最佳时间间隔的研究[J].网络科技时代,2006(2)：20-23
[27]徐洪敏.城市轨道交通运用车设计计算方法[J].铁道标准设计,2003(9)：75-76
[28]袁博晖,王英涛.针对断面客流量差异的行车组织适应性探讨[J].城市轨道交通研究,2004.7(5)：32-33
[29]张国宝,于涛.关于城轨列车折返能力计算与加强的研究[J].都市快轨交通,2006.19(4)：55-58
[30]王印富,雷志厚.城市轨道交通行车组织方法的探讨——关于中心城与卫星城之间轨道交通按快慢行车运行的研究[J].科技交流,2001.31(4)：111-117
[31]罗丽云,吴汶麒.城市轨道交通移动闭塞列车安全间隔时间分析[J].中国铁道科学,2005.26(1)：119-123
[32]韩立春,吴汶麒.数字轨道电路列车最小安全间隔时间计算[J].城市轨道交通研究,2001.4(2)：36-40
[33]严波.城市轨道交通行车间隔时间优化模型研究[J].城市轨道交通研究,2008.11(6)：53-57、62
[34]边晓春,汪履直.重庆轨道交通2号线远景年列车交路方案初议[J].现代城市轨道交通,2007(1)：54-56
[35]秦应兵杜文.城市轨道交通对城市结构的影响因素分析[J].西南交通大学学报,2000.35(3)：284-287
[36]郭丽丽.成都地铁一号线列车开行方案研究[J].上海铁道科技,2006(4)：43-45
[37]项宝余.德国铁路行车组织简介[J].上海铁道科技,1996(2)：40-42
[38]田福生,吕红霞,李致宏.基于车底配置最优的地铁列车交路设计[J].铁道运输与经济,2006.28(1)：26-28
[39]施泉,吴中.城市轨道交通客流预测内容与方法探讨[J].现代城市轨道交通,2006(6)：63-65
[40]王海丹,李映红.高峰期城市轨道交通线路通过能力的研究[J].上海铁道科技,2005(3)：39-40
[41]谢敏.轨道交通项目行车组织设计要点[C].天津市土木工程学会第七届年会优秀论文集,2005
[42]李军.城市轨道交通运营管理模式的探讨[J].城市公共交通,2001(6)：22-23
[43]叶海行.城市轨道交通客流预测及运营组织优化[D].北京：北京交通大学,2004.3
[44]赵跃.北京市城市铁路列车运营组织模拟研究[D].北京：北京交通大学,2001.2
[45]徐国平,宗蓓华.交通运输中网络效应问题探讨[J].综合运输,2007(9)：12-15
[46]鲁放,韩宝明,李德伟.网络化城市轨道交通在城市客运中的骨干作用[J].综合运输,2008(2)：67-72
[47]张铭,徐瑞华.轨道交通网络列车衔接组织的递阶协调优化[J].系统工程,2007.25(9)： 33-37
[48]张铭,徐瑞华,杨珂.城市轨道交通网络运营组织协调性研究[J].城市轨道交通研究,2007.10(11)：44-48
[49]孙琦,周磊山,乐逸祥,吴晓东.编组站到解系统匹配与协调关系动态仿真分析『J].系统仿真学报,2007.19(15)：3595-3598、3608
[50]Alberto Caprara,Michele Monaci,Paolo Toth,Pier Luigi Guida. A Lagrangian heuristic algorithm for a real-world train timetabling problem, Discrete Applied Mathematics 154 (2006) 738-753
[51]Fei LU, Mumin SONG. Subway Train Motion Modeling and the Event-based Optimal Control. ICIEA,2006
[52]Christian Liebchen. the First Mathematically Optimized Service Concept for Railways in Practice. Transportation Science, Transportation Science archive.Volume 42, Issue 4 (November 2008),420-435
[53]Eiichi Taniguchi, Hiroshi Shimamoto. Intelligent transportation system based dynamic vehicle routing and scheduling with variable travel times, Transportation Research Part C 12 (2004) 235-250
[54]M. Schroder, I. Solchenbach. Optimization of Transfer Quality in Regional Public Transit, Berichte des Fraunhofer-Instituts fur Techno-und Wirtschaftsmathematik (ITWM Report),December 8,2005
[55]徐瑞华,张铭,江志彬.基于线网运营协调的城市轨道交通首末班列车发车时间域研究[J].铁道学报,2008.30(2)：7-11
[56]陈玲玲,王慈光.基于旅客列车合理接续条件的发车时刻确定方法[J].西南交通大学学报,2007.42(2)：234-237
[57]肖鹏.城市轨道交通列车自动调整模型算法研究[D].成都：西南交通大学,2006.4
[58]许红,马建军,龙建成,杨浩,龙昭.城市轨道交通列车运行图编制的数学模型及方法[J].北京交通大学学报,2006.30(3)：10-14
[59]缪道平.城市轨道交通车体运用计划自动编制及优化研究[D].北京：北京交通大学,2009.7
[60]徐立国.上海市城市轨道交通停车线设置探讨[J].城市轨道交通研究,2006.9(2)：10-12
[61]徐瑞华、邹晓磊.客运专线列车开行方案的优化方法的研究[J].同济大学学报：自然科学版,2005.33(12)：1068-1611
[62]高明,刘红艳.城际铁路与城市轨道共线运营的探讨[J].都市快轨交通,2009.22(2)：72-75
[63]杨崇明.市区内城际客运专线与城市轨道共轨的可能性[J].都市快轨交通,2007.20(5)18-20
[64]王江.地铁运营评估[M].北京：中国铁道出版社,2008
[65]杨浩,何世伟.铁路运输组织学[M].北京：中国铁道出版社,2001
[66]郑时德.铁路行车组织[M].北京：中国铁道出版社,1995
[67]马建军,刘东.京沪高速铁路列车运行图编制基本理论的研究[J].北方交通大学学报,2002,26(2)：47-50、59
[68]马建军,胡思继.网状线路列车运行图实验平台基础理论的研究[J].北方交通大学学报,2002,26(5)：23-27
[69]马建军,周磊山,胡思继.计算机编制网状线路列车运行图系统研究[J].铁道学报,2000.22(1)：7-11
[70]Chien, S. and Chowdhury, M. Scheduling of Coordinated Transfers for Public Transit Services. The office of Sponsored Program, New Jersey Institute of Technology, Acc.# 421580, Final Report. 1997
[71]Md. Shoaib Chowdhury, and Steven I-Jy Chien. Optimization of Transfer Coordination For Intermodal Transit Networks. Transportation Research Board 80th Annual Meeting, January 7-11, 2001
[72]Giuseppe Bruno, Gennaro Improta, Antonino Sgalambro. Optimization of the Departure Schedule at a Public Transit Terminal with Multiple Destinations. MISTA 2007,104-111
[73]Eiichi Taniguchi, Hiroshi Shimamoto. "Intelligent transportation system based dynamic vehicle routing and scheduling with variable travel times", Transportation Research Part C 12.2004, 235-250
[74]Ching-Jung Ting and Paul Schonfeld, F.ASCE. Schedule Coordination in a Multiple Hub Transit Network. JOURNAL OF URBAN PLANNING AND DEVELOPMENT, June 2005, 112-124
[75]沈丽萍,陈茜,李洪.城市轨道变通超长线路规划问题研究[J].城市轨道交通研究,2008.11(11)：37-39
[76]胡毓达.实用多目标最优化[M].上海：上海科学技术出版社,1990
[77]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
[78]郭峰.城市综合交通枢纽的衔接换乘研究——火车站前综合交通枢纽的衔接换乘[D].武汉：华中科技大学,2004
[79]刘有军,晏克非.城市交通枢纽规划方案的模糊多目标决策研究[J].华中科技大学学报,2006.23(2)：63-66
[80]田福生.城市轨道交通行车组织的相关问题研究[D].成都：西南交通大学,2006
[81]周妍.网络化城市轨道交通行车组织相关问题研究[D].北京：北京交通大学,2008
[82]汪波,杨浩,张志华.基于周期运行图的京津城际铁路列车开行方案研究[J].铁道学报,2007.29(2)：8-13
[83]史峰,邓连波,霍亮.旅客列车开行方案的双层规划模型和算法[J].中国铁道科学,2007.28(3)：110-116
[84]张国宝,傅嘉,刘明姝.城轨列车非站站停车及派生的越行问题研究[J].都市快轨交通,2005.18(5)：18-22
[86]Yu-Hern Chang, Chung-Hsing Yeh, Ching-Cheng Shen. A multiobjective model for passenger train services planning:application to Taiwan's high-speed rail line. Transportation Research Part B 34.2000,91-106;
[86]Huizhong Yang, Xiangli Li, Cuimei Bo, Xinguang Shao. A Graphic Clustering Algorithm Based on MMAS.2006 IEEE Congress on Evolutionary Computation, July 16-21,2006
[87]Chandrasekharan Rajendran, Hans Ziegler. Ant-colony algorithms for permutation flowshop scheduling to minimize makespan/total flowtime of jobs. European Journal of Operational Research 155.2004,426-438.
[88]Sekine,S, Imaski,N, Endo,T. Application of fuzzy neural network control to automatic train operation and tuning of its control rules. International Joint Conference of the Fourth IEEE International Conference on Fuzzy Systems and Proceedings of 1995 IEEE International Conference on The Second International Fuzzy Engineering Symposiu.,vol.4,20-24, pp.1741-1746, March 1995.
[89]Ning, Xi.Event-based motion planning and control for robotic system[D]. Washington University,St Louis, MO,1993.
[90]N. Xi,T.J.Tarn,A.K.Bejczy. Intelligent planning and control for multi-robot coordination:An Event-based approach[J]. IEEE Transactions on robotics and automation,vol.12,1996,439-452.
[91]W.Kang, N.Xi and Andy Sparks. Theory and Application of Formation Control in a Perceptive Referenced Frame. Proc.of 39th IEEE Conference on Decision and control,2000,352-357.
[92]Kanayama,M., Seki,Y., Fujiwara,Y, Sobu,K. Development of train control simulator. International Conference on Developments in Mass Transit Systems,20-23, April 1998,196-201.
[93]Geir Dahl, Disjoint congruence classes and a timetabling application, Discrete Applied Mathematics, v.157 n.8, April,2009,1702-1710,
[94]Christian Liebchen, Michael Schachtebeck, Anita Schobel, Sebastian Stiller, Andre Prigge, Computing delay resistant railway timetables, Computers and Operations Research, v.37 n.5, May, 2010,857-868
[95]Goran Vuk. Transport impacts of the Copenhagen Metro, Journal of Transport Geography. Journal of Transport Geography, Volume 13, Issue 3,223-233
[96]S.B.A. Anas, T.J. Quinlan, S.D. Walker. Service differentiated drop code unit for metro ring optical networks. IET optoelectronics,2010, vol.4, no.1,46-50
[97]N.Bilgin, T.Dincer, H.Copur. The performance prediction of impact hammers from Schmidt hammer rebound values in Istanbul metro tunnel drivages. Tunnelling and Underground Space Technology, Volume 17, Issue 3, Page 237
[98]Brian L. Mishara. Railway and Metro Suicides:Understanding the Problem and Prevention Potential. Crisis:The Journal of Crisis Intervention and Suicide Prevention. Volume 14, Number 3, September 2007,203-221
[99]Zuehre Sue; Mehmet Caliskan. Acoustical Design and Noise Control in Metro Stations:Case Studies of the Ankara Metro System. Building Acoustics. Volume 14, Number 3, September 2007, 203-221
[100]J.C.Golias. Analysis of traffic corridor impacts from the introduction of the new Athens Metro system. Journal of Transport Geography, Volume 10, Issue 2,91-97
[101]Mohamed El Hosseiny Abdel Salam. Regional line of the Cairo metro. Tunnelling and Underground Space Technology, Volume 4, Issue 3,279-283
[102]Daniel J. Graham, Amado Crotte, Richard J. Anderson. A dynamic panel analysis of urban metro demand. Transportation Research Part E:Logistics and Transportation Review, Volume 45, Issue 5,787-794
[103]覃煜,晏克非.轨道交通枢纽换乘效率DEA非均一评价模型[J].长安大学学报：自然科学版,2002.22(4)：48-51、54
[104]徐玖平,李军.多目标决策的理论与方法[M].北京：清华大学出版社,2005
[105]余露.香港快速轨道交通运营的成功模式研究[J].规划与设计,2007(3)：27-31
[106]北京城市轨道交通线网调整.北京规划建设,2006(5)：152-153
[107]赵丽珍.关于综合运输枢纽概念及其分类[J].综合运输,2005(12)：23-24
[108]李得伟,韩宝明,刘殿仁.城市综合交通一体化枢纽布设研究[J].综合运输,2006(3) 60-63
[109]胡运权.运筹学教程[M].北京：清华大学出版社,1998
[110]潘有成.基于PopFuzzy的综合交通枢纽客运站布局影响评价研究[J].重庆交通学院学报,2004.23(5)：102-105
[111]杨东奇,李一军.基于DEA的城市管理绩效评价研究[J].中国软科学,2006(2)：146-149
[112]Taho Yang, Chunwei Kuo. A hierarchical AHP/DEA methodology for the facilities layout design problem. European Journal of Operational Research 147, pp 128-136
[113]杨敏王炜陈学武李文勇.基于DEA/AHP方法的大运量快速交通方式选择决策[J].公路交通科技,2006.23(7)：111-115
[114]刘华.铁路和城市轨道行车组织设计的差异[J].铁道标准设计,2000(7)：67-68
[115]王春娥.基于C均值聚类算法的交通时段划分方法研究[J].盐城工学院学报：自然科学版,2009.22(4)：73-76
[116]四兵锋,赵小梅,高自友.综合运输体系下的客运流量分离模型及算法研究[J].铁道学报,2004.26(6)：14-19
[117]四兵锋,高自友.综合运输体系下铁路客运市场的优化策略模型及算法[J].铁道学报,2005.27(5)：6-10
[118]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
[119]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
[120]梁青槐.德国城市轨道交通规划思路与运营经验[J].都市快轨交通,2005.18(5)：82-84
[121]王振海.欧洲城市轨道交通及对中国的借鉴意义[J].地铁与轻轨,2003(5)：57-61
[122]Assis W o.etal.Generation of optimal schedules for metro lines using model predietive control[J]. Automatiea,2004 (40):1397-1404
[123]Castelli L, Pesenti R, Ukovieh W. Scheduling multimodal transportation systems[J]. European Journal of Operational Researeh,2004 (155):603-615
[124]郭鹏,徐瑞华.城市轨道交通客流量增长的系统动力学研究[J].都市快轨交通,2006.19(6)：38-41
[125]郑丽娟.基于城市轨道交通网络运营的客流分布预测研究[D].同济大学,2008