连续型交通分配模型及其在交通规划中的应用
|
摘要
交通流分配模型和算法是交通规划的基础理论,分为连续型分配模型和离散型分配模型。本文根据连续型交通流分配模型适用于初始阶段和大范围规划的特点,在研究连续型交通流平衡模型的基础上,将其应用于道路选线、中央商务区(central business district, CBD)选址以及轨道交通规划等问题的分析,旨在规划更为合理的城市交通布局,避免交通需求与交通供给之间的矛盾,进而避免和减少交通拥堵的发生。本文的主要工作与创新点为：
1在研究跟驰状态中的车辆行驶时发现,前后两车间距和前车速度都会对后随车的行驶产生影响,尤其是当前车速度低于后车速度时影响较为明显。根据上述车辆行驶特性,结合我国城市中车辆行驶的最大限制速度,提出基于最大车速的广义力跟驰模型。将该模型用于模拟车辆经过信号交叉口的动态运动,并采用实际道路上车辆的跟车数据仿真跟车状态。结果表明,该模型不仅消除了以往模型存在的停车间距过大问题,而且仿真效果更接近实际的交通流特性。
2从交通规划及结构优化的角度出发,将交通流平衡分配模型与结构优化算法相结合,提出用户优化模型及其用户优化算法进行道路选线。在城市区域中,通过连续交通流平衡分配模型,描述通勤者的出行行为；采用渐进结构优化算法(evolutionary structural optimization, ESO)逐渐删除城市结构中流量水平较低的部分,并不断地更新剩余区域的流量水平,最终找到城市区域内流量密度最集中且均匀分布的地区,并将其作为初始设计阶段城市主干道的位置,采用数值实验和交通特征评价方法,证明了模型和算法的有效性。
3在现实城市交通系统中,用户可通过区域道路就近直接进入CBD,或先进入快速道路入口,然后通过快速路网到达目的CBD。根据这一行为特点,将用户到达CBD的总旅行费用分为连续区域道路旅行费用和快速路网旅行费用两部分,提出用户平衡的连续型交通分配模型。在数值实验中,仿真了城市增加CBD,整个区域内交通流密度分布的变化,及CBD上的用户量变化情况。将该模型用于分析西安市新建CBD——经开区的定位与建设,对于整个西安市特别是原钟楼地区CBD交通流的影响,定量地分析了新CBD对原CBD及其周边区域的分流作用。
4在公共交通方式中,公路交通的出行时间不仅会受到地面道路拥挤程度的影响,而且会受到车速和停靠站点上、下车乘客数的影响。与之相比,轨道交通则具有快捷和准时的特点。因此,不同交通方式下的用户会对同一目的地产生出行费用的感知偏差。根据这一情况,本文在快速路网旅行费用中加入感知偏差项,提出考虑感知偏差的交通流平衡分配模型,用以分析不同交通方式对交通流分布的影响。采用该模型分析了香港九广铁路西铁线的建成,使元朗地区人口数增长了4.5%。
Traffic assignment model and its algorithm are a fundamental theory of transport planning. In modeling traffic equilibrium problems for a transportation system, two different approaches, the discrete and the continuum modeling approach, are commonly adopted. The continuum modeling approach is mainly used for initial planning and macroscopic studies. This thesis aims to develop the continuum modeling approach for transport planning in order to avoid traffic congestion. The thesis focuses on the applications in road alignment, CBD location and rail transport. The main works are as follows:
1 Cars following states are studied, it is shown that velocity of following car depends on the following distance of the preceding car and velocity of preceding car. When the preceding car is slower than the following car, the effect is more obvious. Based on the characters, a new generalized force model which is based on the maximal velocity is proposed. The model is used to simulate the state which the cars pass the signalized intersection and the cars following state. The simulation results show that the new model can eliminate the large distance between cars on the red light and has better features than former model.
2 Traffic equilibrium and topology optimization are imported to route planning problem. A user-optimal model and algorithm for initial route planning are proposed based on transport planning and structural optimization theory. Continuum traffic equilibrium model is used to describe the commuters' behavior flexibly. Evolutionary structural optimization (ESO) is used to delete the low flow intensity parts step by step, update the flow intensity of remainder and get the parts in which flow intensity level is uniform and concentrated finally. Then the initial location of future artery is found. A numerical example and an appraisement method based on traffic performance are given to demonstrate the effectiveness of the proposed methodology.
3 In realistic traffic network, travelers can either travel directly to the CBD on the continuum (surface streets), or they can travel on the continuum and then exchange at an interchange (ramp) before moving to the CBD in the fast road network. According to this character, the total cost from a demand point to CBD includes travel cost of surface streets and travel cost of fast road network. A continuous model is proposed further. A numerical example is given to simulate changes in the traffic flow intensity and the users' number on CBD after adding a CBD in the city. The model is used to analyse the case of Xi'an quantificationally. When a new CBD is built in Jingkai Area, how the traffic flow in Bell Tower Area will change.
4 Road traffic time is affected by vehicle's velocity, boarding and debarking people number, and road congestion. On the contrary, rail transport mode is clocklike and rapid. So users who choose different traffic mode will perceive different traffic time. According to this character, a perceived bias is added into the travel cost of fast road network and a traffic equilibrium assignment model based on perceived bias is proposed. The model is used to study how the traffic mode affects the traffic flow distribution. The case of West Rail Line in Hong Kong is analysed the model.
1在研究跟驰状态中的车辆行驶时发现,前后两车间距和前车速度都会对后随车的行驶产生影响,尤其是当前车速度低于后车速度时影响较为明显。根据上述车辆行驶特性,结合我国城市中车辆行驶的最大限制速度,提出基于最大车速的广义力跟驰模型。将该模型用于模拟车辆经过信号交叉口的动态运动,并采用实际道路上车辆的跟车数据仿真跟车状态。结果表明,该模型不仅消除了以往模型存在的停车间距过大问题,而且仿真效果更接近实际的交通流特性。
2从交通规划及结构优化的角度出发,将交通流平衡分配模型与结构优化算法相结合,提出用户优化模型及其用户优化算法进行道路选线。在城市区域中,通过连续交通流平衡分配模型,描述通勤者的出行行为；采用渐进结构优化算法(evolutionary structural optimization, ESO)逐渐删除城市结构中流量水平较低的部分,并不断地更新剩余区域的流量水平,最终找到城市区域内流量密度最集中且均匀分布的地区,并将其作为初始设计阶段城市主干道的位置,采用数值实验和交通特征评价方法,证明了模型和算法的有效性。
3在现实城市交通系统中,用户可通过区域道路就近直接进入CBD,或先进入快速道路入口,然后通过快速路网到达目的CBD。根据这一行为特点,将用户到达CBD的总旅行费用分为连续区域道路旅行费用和快速路网旅行费用两部分,提出用户平衡的连续型交通分配模型。在数值实验中,仿真了城市增加CBD,整个区域内交通流密度分布的变化,及CBD上的用户量变化情况。将该模型用于分析西安市新建CBD——经开区的定位与建设,对于整个西安市特别是原钟楼地区CBD交通流的影响,定量地分析了新CBD对原CBD及其周边区域的分流作用。
4在公共交通方式中,公路交通的出行时间不仅会受到地面道路拥挤程度的影响,而且会受到车速和停靠站点上、下车乘客数的影响。与之相比,轨道交通则具有快捷和准时的特点。因此,不同交通方式下的用户会对同一目的地产生出行费用的感知偏差。根据这一情况,本文在快速路网旅行费用中加入感知偏差项,提出考虑感知偏差的交通流平衡分配模型,用以分析不同交通方式对交通流分布的影响。采用该模型分析了香港九广铁路西铁线的建成,使元朗地区人口数增长了4.5%。
Traffic assignment model and its algorithm are a fundamental theory of transport planning. In modeling traffic equilibrium problems for a transportation system, two different approaches, the discrete and the continuum modeling approach, are commonly adopted. The continuum modeling approach is mainly used for initial planning and macroscopic studies. This thesis aims to develop the continuum modeling approach for transport planning in order to avoid traffic congestion. The thesis focuses on the applications in road alignment, CBD location and rail transport. The main works are as follows:
1 Cars following states are studied, it is shown that velocity of following car depends on the following distance of the preceding car and velocity of preceding car. When the preceding car is slower than the following car, the effect is more obvious. Based on the characters, a new generalized force model which is based on the maximal velocity is proposed. The model is used to simulate the state which the cars pass the signalized intersection and the cars following state. The simulation results show that the new model can eliminate the large distance between cars on the red light and has better features than former model.
2 Traffic equilibrium and topology optimization are imported to route planning problem. A user-optimal model and algorithm for initial route planning are proposed based on transport planning and structural optimization theory. Continuum traffic equilibrium model is used to describe the commuters' behavior flexibly. Evolutionary structural optimization (ESO) is used to delete the low flow intensity parts step by step, update the flow intensity of remainder and get the parts in which flow intensity level is uniform and concentrated finally. Then the initial location of future artery is found. A numerical example and an appraisement method based on traffic performance are given to demonstrate the effectiveness of the proposed methodology.
3 In realistic traffic network, travelers can either travel directly to the CBD on the continuum (surface streets), or they can travel on the continuum and then exchange at an interchange (ramp) before moving to the CBD in the fast road network. According to this character, the total cost from a demand point to CBD includes travel cost of surface streets and travel cost of fast road network. A continuous model is proposed further. A numerical example is given to simulate changes in the traffic flow intensity and the users' number on CBD after adding a CBD in the city. The model is used to analyse the case of Xi'an quantificationally. When a new CBD is built in Jingkai Area, how the traffic flow in Bell Tower Area will change.
4 Road traffic time is affected by vehicle's velocity, boarding and debarking people number, and road congestion. On the contrary, rail transport mode is clocklike and rapid. So users who choose different traffic mode will perceive different traffic time. According to this character, a perceived bias is added into the travel cost of fast road network and a traffic equilibrium assignment model based on perceived bias is proposed. The model is used to study how the traffic mode affects the traffic flow distribution. The case of West Rail Line in Hong Kong is analysed the model.
引文
[1]邵春福.交通规划原理[M].中国铁道出版社,2004
[2]宋永昌主编.城市生态学[M].华东师范大学出版社,2000
[3]连爱萍.城市动态网络交通流分配及相关问题的研究[D].北京交通大学博士论文,2007
[4]孙家驷主编.道路勘测设计[M].人民交通出版社,1999
[5]H.Z. Guo and Y.J. Sun. Application of remote sensing technology in engineering geological survey of datong-Yuncheng highway (Huozhonu-Linfen part) [C]. ACRS/2001 22nd Asian Conference on Remote Sensing, Singapore, pp.639-642,2001.
[6]M. R. Delavar, F. Samadzadegan and P. Pahlavani. A GIS-Assisted optimal urban route finding approach based on genetic algorithms [J]. International Archives of Photogrammetry Remote Sensing and Spatial Information Sciences:2004,35(2): 305-308.
[7]H. Heldal. Supporting participation in planning new roads by using virtual reality systems [J]. Virtual Reality:2007,11:145-159,2007.
[8]赵群毅,秦波,周一星.重庆市中央商务区的区位选择研究[J].地域研究与开发,2005,24(6)：56-60
[9]葛公文.区位与城市中央商务区产业定位的相关性研究——以西安南郊小寨地区为例[J].地域研究与开发,2005,24(6)：61-65
[10]金继晶,郑伯红.基于商务设施分布的CBD选址研究[J].华中建筑,2008,26(11)：80-83
[11]陈一新著,中央商务区CBD城市规划设计与实践[M],中国建筑工业出版社,2006
[12]Amaya Vega and Aisling Reynolds-Feighan. A methodological framework for the study of residential location and travel-to-work mode choice under central and suburban employment destination patterns [J]. Transportation Research Part A,2009,43(4): 401-419
[13]H.W. Ho, S.C. Wong, H. Yang and Becky P.Y. Loo. Cordon-based congestion pricing in a continuum traffic equilibrium system [J]. Transportation Research Part B,2005,39: 813-834
[14]Michael Kuby, Anthony Barranda and Christopher Upchurch. Factors influencing light-rail station boardings in the United States [J]. Transportation Research Part A,2004, 38:223-247
[15]Chaug-Ing Hsu and Shwu-Ping Guo. CBD oriented commuter's mode and residential location choices in an urban area with surface streets and rail transit lines [J]. Journal of Urban Planning and Development,2006,132(4):235-246
[16]Siu Kei Hwe, Raymond K. Cheung and Yat-wah Wan. Merging bus routes in Hong Kong's central business district:Analysis and models [J]. Transportation Research Part A, 2006,40:918-935
[17]Chandra R. Bhat, Sudeshna Sen and Naveen Eluru. The impact of demograghics, built environment attributes, vehicle characteristics, and gasoline prices on household vehicle holdings and use [J]. Transportation Research Part B,2009,43:1-18
[18]顾新.香港轨道交通规划与经营理念对深圳的启示[J].城市规划,2009,08：87-91
[19]任刚.交通管理措施下的交通分配模型与算法[M].东南大学出版社,2007
[20]Otto Anker Nielsen. A stochastic transit assignment model considering differences in passengers utility functions [J]. Transportation Research Part B 34 (2000):377-402
[21]William H. K. Lam, Yafeng Yin. An activity-based time-dependent traffic assignment model [J]. Transportation Research Part B,2001,35:549-574
[22]Robert B. Dial. A path-based user-equilibrium traffic assignment algorithm that obviates path storage and enumeration [J]. Transportation Research Part B,2006,40:917-936
[23]S.C. Wong, C. K. Lee and C. O. Tong. Finite element solution for the continuum traffic equilibrium problems [J]. International Journal for Numerical Methods in Engineering, 1998,43:1253-1273
[24]T. Sasaki, Y. Iida and H. Yang. User-equilibrium traffic assignment by continuum approximation of network flow [C]. Proceedings of 11th International Symposium on Transportation and traffic theory, Japan, Yokohama, Elsevier,1990:233-252.
[25]H. Yang, S. Yagar and Y. Iida. Traffic assignment in a congested discrete/continuous transportation system [J]. Transportation Research,1994,28B (2):161-174
[26]高自友,宋一凡,四兵锋.城市交通连续平衡网络设计：理论与方法[M].中国铁道出版社,2000
[27]H.W. Ho, S.C. Wong, Becky P.Y. Loo. Combined distribution and assignment model for a continuum traffic equilibrium problem with multiple user classes [J]. Transportation Research Part B,2006,40:633-650
[28]H.W. Ho, S.C. Wong.. Housing allocation problem in a continuum transportation system [J]. Transportmetrica,2007,3 (1):21-39
[29]M. Beckmann. A continuous model of transportation [J]. Econometrica,1952,20: 643-660.
[30]S.C. Dafermos. Continuum Modeling of transportation networks [J]. Transportation Research Part B,1980,14 (3):295-301
[31]J. Gwinner. On contimuum modeling of large dense network in urban road traffic [C]. In Mathematics in transport planning and control:proceedings of the third IMA International Conference on Mathematics in Transport Planning and Control held in United Kingdom 1-3 April 1998. edited by J.D. Griffiths,321-330. Amsterdam, and New York:Pergamon Publishing Company
[32]A. Angel, GM. Hyman. Urban velocity fields [J]. Environment and Planning,1970,2: 211-224.
[33]A. Angel, GM. Hyman. Urban spatial interaction [J]. Environment and Planning,1972,4: 99-118.
[34]陆化普.交通规划理论与方法[M].清华大学出版社,2006
[35]C.F. Daganzo. Network representation, continuum approximations and a solution to the spatial aggregation problem of traffic assignment [J]. Transportation Research B,1980.14 (3):229-239
[36]W. Tobler. Derivation of a spatially continuous transportation model [J]. Transportation Research A,1985,19(2):169-172
[37]Daniele, P. and Maugeri, A. Vector variational inequalities and modelling of a continuum traffic equilibrium problem, in F. Giannessi (ed.) Vector Variational Inequalities and Vector Equilibria[M]. Kluwer Academic Publishers, Netherlands.2000:97-111
[38]Daniele, P., Idone, G. and Maugeri, A. Variational Inequalities and the continuum model of transportation problem[J]. International Journal of Nonlinear Science and Numerical Simulation 2003, (4):11-16
[39]A. Nagurney. A mulitclass, multicriteria traffic network equilibrium model [J]. Mathematical and Computer Modelling,2000,30:393-411
[40]June Dong, Ding Zhang, Anna Nagurney. A supply chain network equilibrium model with random demands [J]. European Journal of Operational Research,2004,156:194-212
[41]Zhong Zhou, Anthony Chen, S.C. Wong. Alternative formulation of a combined trip generation, trip distribution, modal split, and trip assignment model [J]. European Journal of Operational Research,2009,198:129-138
[42]T.N. Lam and G.F. Newell. Flow dependent traffic assignment on a circular city [J]. Transportation Science,1967,1(4):318-361
[43]G. D'Este. Trip assignment to radial major roads [J]. Transportation Research B,1987, 21(6):433-442
[44]S.C. Wong. An alternative formulation of D'Este's trip assignment model [J]. Transportation Research Part B,1994,28 (3):187-196.
[45]D.E. Blumenfeld and G.H. Weiss. Routing in a circular city with two ring roads [J]. Transportation Research,1970,4(3):235-242.
[46]H.C.W.L. Williams and J.D. Ortuzar Salas. Some generalization and applications of the velocity field concept:Trip patterns in idealized cities [J]. Transportation Research,1976, 10:65-73
[47]N.R. Zitron. A continuous model of optimal--cost route in a circular city [J]. Journal of Optimization Theory and Application,1974,14:291-303.
[48]N.R. Zitron. A critical condition for the cost density in the circular city model [J]. Journal of Optimization Theory and Application,1978,24:507-512.
[49]R. J. Vaughan. A continuous analysis of the role of transportation and crowding costs in determining trip distribution and location in a linear city [J]. Transportation Research Part A,1985,19(2):89-107.
[50]R.J. Vaughan. "Optimum" distribution of population within a linear city [J]. Transportation Research,1975,9(1):25-29.
[51]D.E. Blumenfeld and G.H. Weiss. Some radial and direction-dependent models for densities of home and workspaces [J]. Transportation Research,1974,8:149-155
[52]D.P. Ballou, and J.S. Pipkin. A continuous model of traffic flow [J]. Geographical Analysis,1977,9:346-363.
[53]D.J. Buckley. Traffic assignment in a two-dimensional continuous representation of a traffic network with flow-dependent speeds [J]. Transportation Research Part B,1979, 13(2):167-179.
[54]E. J. Doyle, and R.J. Vaughan. Further aspects of rectangular routing in Smeed's city [J]. Transportation Research Part B,1981,15(3):149-157.
[55]R.W. Hall. Travel distance through transportation terminal on a rectangular grid [J]. Journal of the Operational Research Society,1984,35(12):1067-1078.
[56]A Taguchi and M. Iri. Continuum approximation to dense networks and its application to the analysis of urban road networks [J]. Mathematical Programming Study,1982, 20:178-217
[57]O.C. Zienkiewicz. and R.L. Taylor. The Finite Element Method.1989, McGraw-Hill International Editions.
[58]S.C. Wong, and S.H. Sun. A combined distribution and assignment model for facility location problem [J]. The Annals of Regional Science,2001,35:267-281.
[59]M. Beckmann, C.B. McGuire, and C.B. Winsten. Studies in the Economics of Transportation[M]. Yale University Press, New Haven.1956.
[60]H. Yang. A spatial price equilibrium model with congestion effects [J]. The Annals of Regional Science,1996,30:359-371
[61]D.E. Blumenfeld. Modeling the joint distribution of home and workplace location in a city [J]. Transportation Science,1977,11 (4):307-337.
[62]R.F. Love. A computational procedure for optimally locating a facility with respect to several rectangular region [J]. Journal of Regional Science,1972,12(2):233-242
[63]P.G. Wiles and B.V. Brunt. Optimal location of transshipment depots [J]. Transportation Research Part A 2001,35:745-771
[64]Y. Kitabatake, and T. Miyazaki. The location of sewage treatment plants on a continuous space:Theoretical and empirical analyses [J]. Environment and Planning A,1983, 15:1205-1217
[65]H. Tauchen, and A.D. Witte. An equilibrium model of office location and contract patterns [J]. Environment and Planning A,1983,15:1311-1326
[66]T. Tabuchi. Urban agglomeration economies in a linear city [J]. Regional Science and Urban Economics,1986,16:421-436
[67]J.Y.T. Wang, H. Yang and R. Lindsey. Locating and pricing park-and-ride facility in a linear monocentric city with deterministic model choice [J]. Transportation Research Part B,2004,38:709-731
[68]C.F. Daganzo. The length of tours in zones of different shapes [J]. Transportation Research B,1984a,18(2):135-145
[69]C.F. Daganzo. The distance traveled to visit N points with a maximum of C stops per vehicle:An analytical model and an application [J]. Transportation Science,1984b.18(4): 331-350.
[70]F. Robuste, C.F. Daganzo and R.R. Souleyrette Ⅱ. Implementing vehicle routing models [J]. Transportation Research B,1990,24:263-286
[71]G.F. Newell and C.F. Daganzo. Design of multiple-vehicle delivery tours-Ⅰa ring radial network [J]. Transportation Research B,1986a,20:345-363
[72]G.F. Newell and C.F. Daganzo. Design of multiple-vehicle delivery tours-Ⅱ other metrics [J]. Transportation Research B,1986b,20:365-376
[73]G.F. Newell. Design of multiple-vehicle delivery tours-III valuable goods [J]. Transportation Research B,1986,20:377-390
[74]D.E. Blumenfeld and M.J. Beckmann. Use of continuous space modeling to estimate freight distribution costs [J]. Transportation Research A,1985,19:173-187
[75]A. Langevin and F. Soumis. Design of multiple-vehicle delivery tours satisfying time constraints [J]. Transportation Research B,1989,23:123-138
[76]J.M. Del Castillo. A heuristics for the traveling salesman problem based on a continuous approximation [J]. Transportation Research B,1999,33:123-152
[77]A. Langevin, P. Mbaraga and J.F. Campbell. Continuous approximation models in freigh distribution:An overview [J]. Transportation Research B,1996,30(3):163-188
[78]J.F. Morrall, L.L. Ratnayake and P.N. Seneviratne. Comparison of central business district pedestrian characteristics in Canada and Sri Lanka [J]. Transportation Research Record,1991,1294:57-61
[79]Y Tanaboriboon and J.A. Guyano. Analysis of pedestrian movements in Bangkok [J]. Transportation Research Record,1991,1294:52-56
[80]M.R. Virkler and S. Elayadath. Pedestrian speed-flow-density relationships [J]. Transportation Research Record,1994,1438:51-58
[81]C.Y. Cheung and W.H.K. Lam. Pedestrian route choices between escalator and stairway in MTR station [J]. Journal of Transportation Engineering,1998,124(3):277-285
[82]M.R. Virkler. Prediction and measurement of travel time along pedestrian routes [J]. Transportation Research Record,1998,1636:37-42
[83]R.L. Hughes. A continuum theory for the flow of pedestrians [J]. Transportation Research Part B,2002,36(6):507-535
[84]B.P. Hoogendoom. and P.H.L. Bovy. Nonlocal continuous-space microscopic simulation of pedestrian flows with local choice behavior [J]. Transportation Research Record,2001, 1776:201-210
[85]B.P.Hoogendoorn, P.H.L. Bovy and W. Daamen. Walking infrastructure design assignment by continuous space dynamic assignment modeling [J]. Journal of Advanced transportation,2004,38(1):69-92
[86]B.P. Hoogendorn and P.H.L. Bovy. Pedestrian route-choice and activity scheduling theory and models [J]. Transportation Research B,2004a,38:169-190
[87]B.P. Hoogendoorn and P.H.L. Bovy. Dynamic user-optimal assignment in continuous time and space [J]. Transportation Research B,2004b,38:571-592
[88]D.Helbing, I. Farkas and T. Vicsek. Simulating dynamic features of escape panic [J]. Nature,2000,407:487-490
[89]N Litinas and M. Ben-Akiva. Simplified transportation policy analysis using continuous distribution [J]. Transportation Research A,1982,16:431-445
[90]T. Puu. Catastrophic structure change in a continuous regional model [J]. Regional Science and Urban Economics,1981,11:317-333
[91]T. Puu. Continuous spatial modeling in economics [J]. Papers of the Regional Science Association,1985,56:21-36
[92]T. Puu. On traffic equilibrium, congestion tolls, and the allocation of transportation capacity in a congested urban area [J]. Environment and Planning A,1978a,10:29-36
[93]C.I. Hsu and S.P. Guo. Household-mode choice and residential-rent distribution in a metropolitan area with surface road and rail transit networks [J]. Environment and Planning A,2001,33:1547-1575
[94]S.C. Wong and H. Yang. Determining market areas captured by competitive facilities:A continuous equilibrium modeling approach [J]. Journal of Regional Science,1999, 39(1):51-72
[95]S.C. Wong, Y.C. Du, H.W. Ho and L.J. Sun. Simultaneous optimization formulation of a discrete-continuous transportation system [J]. Transportation Research Record,2003, 1857:11-20
[96]S.C. Wong, Y.C. Du, L.J. Sun and B.P.Y. Loo. Sensitivity analysis for a continuum traffic equilibrium problem [J]. Journal of Regional Science,2006,40:493-514
[97]H. Yang and S.C. Wong. A continuous equilibrium model for estimating market areas of competitive facility with elastic demand and market externality [J]. Transportation Science, 2000,34(2):216-227
[98]刘运通.交通系统仿真技术[M].人民交通出版社,2002
[99]L.A. Pipes. An operational analysis of traffic dynamics [J]. Journal of Applied Physics, 1953,24 (3):274-281
[100]R.E. Chandler, R. Herman, E. Montroll. Traffic dynamics:Studies in car following [J]. Operations Research,1958,6:165-184.
[101]Denos C. Gazis, Robert Herman, Richard W. Rothery. Nonlinear follow-the-leader models of traffic flow [J]. Operation Research,1961,9(4):545-567
[102]姜锐.交通流复杂动态特性的微观和宏观模式研究[D].中国科学技术大学博士论文,2003
[103]M. Bando, K. Hasebe. Dynamical model of traffic congestion and numerical simulation [J].Phys Rev E,1995,51:1035-1042
[104]Shunping Jia, Baohua Mao. Research on CFCM:Car following model using cloud model theory [J]. J Transpn Sys Eng & IT,2007,7(6):67-73
[105]Dirk Helbing, Benno Tilch. Generalized force model of traffic dynamics [J]. Phys Rev E,1998,58:133-138
[106]许世燕,贺昱曜,李渊.基于最大车速的广义力跟驰模型[J].长安大学学报(自然科学版),2007,27(1)：72-75
[107]贾洪飞,陈良等.应用五轮仪采集车辆跟驰过程描述参数[J].山东工程学院学报,2002.16(3),33-36
[108]许世燕,贺昱曜,李雪.用户优化选线模型及其收敛性研究[J].计算机工程与应用,2009,45(18)：35-37
[109]孙宝元等.现代执行器技术[M].吉林大学出版社,2003：47-48
[110]Shiyan Xu, Yuyao He. A user-optimal model for route planning problem[C]. Proceedings of 2008 IEEE International Conference on Automation and Logistics, Qingdao, China, Sept.1-3,2008. Washington, DC. USA:IEEE Computer Society,2008, 00:967-971.
[111]Shiyan Xu, Yuyao He. Model and algorithm for initial route planning[C]. Proceeding of the 2008 workshop on Power Electronics and Intelligent Transportation System. Guangzhou, China:IEEE Computer Society,2008:237-241
[112]王庆海.现代城市规划与管理(第二版)[M].中国建筑工业出版社,2007
[113]Shiyan Xu, Yuyao He, Xue Li. The relationship between location of new central business district and traffic flow [C]. Proceedings of 2009 IEEE International Conference on Automation and Logistics, Shenyang, China, Aug.5-7,2009. Washington, DC. USA: IEEE Computer Society,2009,00:1827-1831.
[114]西安市公安局交通管理支队,长安大学.西安市城市道路交通管理规划[R].西安：西安市公安局交通管理支队,2003
[115]张生瑞,严海.城市公共交通规划的理论与实践[M].中国铁道出版社,2007.
[2]宋永昌主编.城市生态学[M].华东师范大学出版社,2000
[3]连爱萍.城市动态网络交通流分配及相关问题的研究[D].北京交通大学博士论文,2007
[4]孙家驷主编.道路勘测设计[M].人民交通出版社,1999
[5]H.Z. Guo and Y.J. Sun. Application of remote sensing technology in engineering geological survey of datong-Yuncheng highway (Huozhonu-Linfen part) [C]. ACRS/2001 22nd Asian Conference on Remote Sensing, Singapore, pp.639-642,2001.
[6]M. R. Delavar, F. Samadzadegan and P. Pahlavani. A GIS-Assisted optimal urban route finding approach based on genetic algorithms [J]. International Archives of Photogrammetry Remote Sensing and Spatial Information Sciences:2004,35(2): 305-308.
[7]H. Heldal. Supporting participation in planning new roads by using virtual reality systems [J]. Virtual Reality:2007,11:145-159,2007.
[8]赵群毅,秦波,周一星.重庆市中央商务区的区位选择研究[J].地域研究与开发,2005,24(6)：56-60
[9]葛公文.区位与城市中央商务区产业定位的相关性研究——以西安南郊小寨地区为例[J].地域研究与开发,2005,24(6)：61-65
[10]金继晶,郑伯红.基于商务设施分布的CBD选址研究[J].华中建筑,2008,26(11)：80-83
[11]陈一新著,中央商务区CBD城市规划设计与实践[M],中国建筑工业出版社,2006
[12]Amaya Vega and Aisling Reynolds-Feighan. A methodological framework for the study of residential location and travel-to-work mode choice under central and suburban employment destination patterns [J]. Transportation Research Part A,2009,43(4): 401-419
[13]H.W. Ho, S.C. Wong, H. Yang and Becky P.Y. Loo. Cordon-based congestion pricing in a continuum traffic equilibrium system [J]. Transportation Research Part B,2005,39: 813-834
[14]Michael Kuby, Anthony Barranda and Christopher Upchurch. Factors influencing light-rail station boardings in the United States [J]. Transportation Research Part A,2004, 38:223-247
[15]Chaug-Ing Hsu and Shwu-Ping Guo. CBD oriented commuter's mode and residential location choices in an urban area with surface streets and rail transit lines [J]. Journal of Urban Planning and Development,2006,132(4):235-246
[16]Siu Kei Hwe, Raymond K. Cheung and Yat-wah Wan. Merging bus routes in Hong Kong's central business district:Analysis and models [J]. Transportation Research Part A, 2006,40:918-935
[17]Chandra R. Bhat, Sudeshna Sen and Naveen Eluru. The impact of demograghics, built environment attributes, vehicle characteristics, and gasoline prices on household vehicle holdings and use [J]. Transportation Research Part B,2009,43:1-18
[18]顾新.香港轨道交通规划与经营理念对深圳的启示[J].城市规划,2009,08：87-91
[19]任刚.交通管理措施下的交通分配模型与算法[M].东南大学出版社,2007
[20]Otto Anker Nielsen. A stochastic transit assignment model considering differences in passengers utility functions [J]. Transportation Research Part B 34 (2000):377-402
[21]William H. K. Lam, Yafeng Yin. An activity-based time-dependent traffic assignment model [J]. Transportation Research Part B,2001,35:549-574
[22]Robert B. Dial. A path-based user-equilibrium traffic assignment algorithm that obviates path storage and enumeration [J]. Transportation Research Part B,2006,40:917-936
[23]S.C. Wong, C. K. Lee and C. O. Tong. Finite element solution for the continuum traffic equilibrium problems [J]. International Journal for Numerical Methods in Engineering, 1998,43:1253-1273
[24]T. Sasaki, Y. Iida and H. Yang. User-equilibrium traffic assignment by continuum approximation of network flow [C]. Proceedings of 11th International Symposium on Transportation and traffic theory, Japan, Yokohama, Elsevier,1990:233-252.
[25]H. Yang, S. Yagar and Y. Iida. Traffic assignment in a congested discrete/continuous transportation system [J]. Transportation Research,1994,28B (2):161-174
[26]高自友,宋一凡,四兵锋.城市交通连续平衡网络设计：理论与方法[M].中国铁道出版社,2000
[27]H.W. Ho, S.C. Wong, Becky P.Y. Loo. Combined distribution and assignment model for a continuum traffic equilibrium problem with multiple user classes [J]. Transportation Research Part B,2006,40:633-650
[28]H.W. Ho, S.C. Wong.. Housing allocation problem in a continuum transportation system [J]. Transportmetrica,2007,3 (1):21-39
[29]M. Beckmann. A continuous model of transportation [J]. Econometrica,1952,20: 643-660.
[30]S.C. Dafermos. Continuum Modeling of transportation networks [J]. Transportation Research Part B,1980,14 (3):295-301
[31]J. Gwinner. On contimuum modeling of large dense network in urban road traffic [C]. In Mathematics in transport planning and control:proceedings of the third IMA International Conference on Mathematics in Transport Planning and Control held in United Kingdom 1-3 April 1998. edited by J.D. Griffiths,321-330. Amsterdam, and New York:Pergamon Publishing Company
[32]A. Angel, GM. Hyman. Urban velocity fields [J]. Environment and Planning,1970,2: 211-224.
[33]A. Angel, GM. Hyman. Urban spatial interaction [J]. Environment and Planning,1972,4: 99-118.
[34]陆化普.交通规划理论与方法[M].清华大学出版社,2006
[35]C.F. Daganzo. Network representation, continuum approximations and a solution to the spatial aggregation problem of traffic assignment [J]. Transportation Research B,1980.14 (3):229-239
[36]W. Tobler. Derivation of a spatially continuous transportation model [J]. Transportation Research A,1985,19(2):169-172
[37]Daniele, P. and Maugeri, A. Vector variational inequalities and modelling of a continuum traffic equilibrium problem, in F. Giannessi (ed.) Vector Variational Inequalities and Vector Equilibria[M]. Kluwer Academic Publishers, Netherlands.2000:97-111
[38]Daniele, P., Idone, G. and Maugeri, A. Variational Inequalities and the continuum model of transportation problem[J]. International Journal of Nonlinear Science and Numerical Simulation 2003, (4):11-16
[39]A. Nagurney. A mulitclass, multicriteria traffic network equilibrium model [J]. Mathematical and Computer Modelling,2000,30:393-411
[40]June Dong, Ding Zhang, Anna Nagurney. A supply chain network equilibrium model with random demands [J]. European Journal of Operational Research,2004,156:194-212
[41]Zhong Zhou, Anthony Chen, S.C. Wong. Alternative formulation of a combined trip generation, trip distribution, modal split, and trip assignment model [J]. European Journal of Operational Research,2009,198:129-138
[42]T.N. Lam and G.F. Newell. Flow dependent traffic assignment on a circular city [J]. Transportation Science,1967,1(4):318-361
[43]G. D'Este. Trip assignment to radial major roads [J]. Transportation Research B,1987, 21(6):433-442
[44]S.C. Wong. An alternative formulation of D'Este's trip assignment model [J]. Transportation Research Part B,1994,28 (3):187-196.
[45]D.E. Blumenfeld and G.H. Weiss. Routing in a circular city with two ring roads [J]. Transportation Research,1970,4(3):235-242.
[46]H.C.W.L. Williams and J.D. Ortuzar Salas. Some generalization and applications of the velocity field concept:Trip patterns in idealized cities [J]. Transportation Research,1976, 10:65-73
[47]N.R. Zitron. A continuous model of optimal--cost route in a circular city [J]. Journal of Optimization Theory and Application,1974,14:291-303.
[48]N.R. Zitron. A critical condition for the cost density in the circular city model [J]. Journal of Optimization Theory and Application,1978,24:507-512.
[49]R. J. Vaughan. A continuous analysis of the role of transportation and crowding costs in determining trip distribution and location in a linear city [J]. Transportation Research Part A,1985,19(2):89-107.
[50]R.J. Vaughan. "Optimum" distribution of population within a linear city [J]. Transportation Research,1975,9(1):25-29.
[51]D.E. Blumenfeld and G.H. Weiss. Some radial and direction-dependent models for densities of home and workspaces [J]. Transportation Research,1974,8:149-155
[52]D.P. Ballou, and J.S. Pipkin. A continuous model of traffic flow [J]. Geographical Analysis,1977,9:346-363.
[53]D.J. Buckley. Traffic assignment in a two-dimensional continuous representation of a traffic network with flow-dependent speeds [J]. Transportation Research Part B,1979, 13(2):167-179.
[54]E. J. Doyle, and R.J. Vaughan. Further aspects of rectangular routing in Smeed's city [J]. Transportation Research Part B,1981,15(3):149-157.
[55]R.W. Hall. Travel distance through transportation terminal on a rectangular grid [J]. Journal of the Operational Research Society,1984,35(12):1067-1078.
[56]A Taguchi and M. Iri. Continuum approximation to dense networks and its application to the analysis of urban road networks [J]. Mathematical Programming Study,1982, 20:178-217
[57]O.C. Zienkiewicz. and R.L. Taylor. The Finite Element Method.1989, McGraw-Hill International Editions.
[58]S.C. Wong, and S.H. Sun. A combined distribution and assignment model for facility location problem [J]. The Annals of Regional Science,2001,35:267-281.
[59]M. Beckmann, C.B. McGuire, and C.B. Winsten. Studies in the Economics of Transportation[M]. Yale University Press, New Haven.1956.
[60]H. Yang. A spatial price equilibrium model with congestion effects [J]. The Annals of Regional Science,1996,30:359-371
[61]D.E. Blumenfeld. Modeling the joint distribution of home and workplace location in a city [J]. Transportation Science,1977,11 (4):307-337.
[62]R.F. Love. A computational procedure for optimally locating a facility with respect to several rectangular region [J]. Journal of Regional Science,1972,12(2):233-242
[63]P.G. Wiles and B.V. Brunt. Optimal location of transshipment depots [J]. Transportation Research Part A 2001,35:745-771
[64]Y. Kitabatake, and T. Miyazaki. The location of sewage treatment plants on a continuous space:Theoretical and empirical analyses [J]. Environment and Planning A,1983, 15:1205-1217
[65]H. Tauchen, and A.D. Witte. An equilibrium model of office location and contract patterns [J]. Environment and Planning A,1983,15:1311-1326
[66]T. Tabuchi. Urban agglomeration economies in a linear city [J]. Regional Science and Urban Economics,1986,16:421-436
[67]J.Y.T. Wang, H. Yang and R. Lindsey. Locating and pricing park-and-ride facility in a linear monocentric city with deterministic model choice [J]. Transportation Research Part B,2004,38:709-731
[68]C.F. Daganzo. The length of tours in zones of different shapes [J]. Transportation Research B,1984a,18(2):135-145
[69]C.F. Daganzo. The distance traveled to visit N points with a maximum of C stops per vehicle:An analytical model and an application [J]. Transportation Science,1984b.18(4): 331-350.
[70]F. Robuste, C.F. Daganzo and R.R. Souleyrette Ⅱ. Implementing vehicle routing models [J]. Transportation Research B,1990,24:263-286
[71]G.F. Newell and C.F. Daganzo. Design of multiple-vehicle delivery tours-Ⅰa ring radial network [J]. Transportation Research B,1986a,20:345-363
[72]G.F. Newell and C.F. Daganzo. Design of multiple-vehicle delivery tours-Ⅱ other metrics [J]. Transportation Research B,1986b,20:365-376
[73]G.F. Newell. Design of multiple-vehicle delivery tours-III valuable goods [J]. Transportation Research B,1986,20:377-390
[74]D.E. Blumenfeld and M.J. Beckmann. Use of continuous space modeling to estimate freight distribution costs [J]. Transportation Research A,1985,19:173-187
[75]A. Langevin and F. Soumis. Design of multiple-vehicle delivery tours satisfying time constraints [J]. Transportation Research B,1989,23:123-138
[76]J.M. Del Castillo. A heuristics for the traveling salesman problem based on a continuous approximation [J]. Transportation Research B,1999,33:123-152
[77]A. Langevin, P. Mbaraga and J.F. Campbell. Continuous approximation models in freigh distribution:An overview [J]. Transportation Research B,1996,30(3):163-188
[78]J.F. Morrall, L.L. Ratnayake and P.N. Seneviratne. Comparison of central business district pedestrian characteristics in Canada and Sri Lanka [J]. Transportation Research Record,1991,1294:57-61
[79]Y Tanaboriboon and J.A. Guyano. Analysis of pedestrian movements in Bangkok [J]. Transportation Research Record,1991,1294:52-56
[80]M.R. Virkler and S. Elayadath. Pedestrian speed-flow-density relationships [J]. Transportation Research Record,1994,1438:51-58
[81]C.Y. Cheung and W.H.K. Lam. Pedestrian route choices between escalator and stairway in MTR station [J]. Journal of Transportation Engineering,1998,124(3):277-285
[82]M.R. Virkler. Prediction and measurement of travel time along pedestrian routes [J]. Transportation Research Record,1998,1636:37-42
[83]R.L. Hughes. A continuum theory for the flow of pedestrians [J]. Transportation Research Part B,2002,36(6):507-535
[84]B.P. Hoogendoom. and P.H.L. Bovy. Nonlocal continuous-space microscopic simulation of pedestrian flows with local choice behavior [J]. Transportation Research Record,2001, 1776:201-210
[85]B.P.Hoogendoorn, P.H.L. Bovy and W. Daamen. Walking infrastructure design assignment by continuous space dynamic assignment modeling [J]. Journal of Advanced transportation,2004,38(1):69-92
[86]B.P. Hoogendorn and P.H.L. Bovy. Pedestrian route-choice and activity scheduling theory and models [J]. Transportation Research B,2004a,38:169-190
[87]B.P. Hoogendoorn and P.H.L. Bovy. Dynamic user-optimal assignment in continuous time and space [J]. Transportation Research B,2004b,38:571-592
[88]D.Helbing, I. Farkas and T. Vicsek. Simulating dynamic features of escape panic [J]. Nature,2000,407:487-490
[89]N Litinas and M. Ben-Akiva. Simplified transportation policy analysis using continuous distribution [J]. Transportation Research A,1982,16:431-445
[90]T. Puu. Catastrophic structure change in a continuous regional model [J]. Regional Science and Urban Economics,1981,11:317-333
[91]T. Puu. Continuous spatial modeling in economics [J]. Papers of the Regional Science Association,1985,56:21-36
[92]T. Puu. On traffic equilibrium, congestion tolls, and the allocation of transportation capacity in a congested urban area [J]. Environment and Planning A,1978a,10:29-36
[93]C.I. Hsu and S.P. Guo. Household-mode choice and residential-rent distribution in a metropolitan area with surface road and rail transit networks [J]. Environment and Planning A,2001,33:1547-1575
[94]S.C. Wong and H. Yang. Determining market areas captured by competitive facilities:A continuous equilibrium modeling approach [J]. Journal of Regional Science,1999, 39(1):51-72
[95]S.C. Wong, Y.C. Du, H.W. Ho and L.J. Sun. Simultaneous optimization formulation of a discrete-continuous transportation system [J]. Transportation Research Record,2003, 1857:11-20
[96]S.C. Wong, Y.C. Du, L.J. Sun and B.P.Y. Loo. Sensitivity analysis for a continuum traffic equilibrium problem [J]. Journal of Regional Science,2006,40:493-514
[97]H. Yang and S.C. Wong. A continuous equilibrium model for estimating market areas of competitive facility with elastic demand and market externality [J]. Transportation Science, 2000,34(2):216-227
[98]刘运通.交通系统仿真技术[M].人民交通出版社,2002
[99]L.A. Pipes. An operational analysis of traffic dynamics [J]. Journal of Applied Physics, 1953,24 (3):274-281
[100]R.E. Chandler, R. Herman, E. Montroll. Traffic dynamics:Studies in car following [J]. Operations Research,1958,6:165-184.
[101]Denos C. Gazis, Robert Herman, Richard W. Rothery. Nonlinear follow-the-leader models of traffic flow [J]. Operation Research,1961,9(4):545-567
[102]姜锐.交通流复杂动态特性的微观和宏观模式研究[D].中国科学技术大学博士论文,2003
[103]M. Bando, K. Hasebe. Dynamical model of traffic congestion and numerical simulation [J].Phys Rev E,1995,51:1035-1042
[104]Shunping Jia, Baohua Mao. Research on CFCM:Car following model using cloud model theory [J]. J Transpn Sys Eng & IT,2007,7(6):67-73
[105]Dirk Helbing, Benno Tilch. Generalized force model of traffic dynamics [J]. Phys Rev E,1998,58:133-138
[106]许世燕,贺昱曜,李渊.基于最大车速的广义力跟驰模型[J].长安大学学报(自然科学版),2007,27(1)：72-75
[107]贾洪飞,陈良等.应用五轮仪采集车辆跟驰过程描述参数[J].山东工程学院学报,2002.16(3),33-36
[108]许世燕,贺昱曜,李雪.用户优化选线模型及其收敛性研究[J].计算机工程与应用,2009,45(18)：35-37
[109]孙宝元等.现代执行器技术[M].吉林大学出版社,2003：47-48
[110]Shiyan Xu, Yuyao He. A user-optimal model for route planning problem[C]. Proceedings of 2008 IEEE International Conference on Automation and Logistics, Qingdao, China, Sept.1-3,2008. Washington, DC. USA:IEEE Computer Society,2008, 00:967-971.
[111]Shiyan Xu, Yuyao He. Model and algorithm for initial route planning[C]. Proceeding of the 2008 workshop on Power Electronics and Intelligent Transportation System. Guangzhou, China:IEEE Computer Society,2008:237-241
[112]王庆海.现代城市规划与管理(第二版)[M].中国建筑工业出版社,2007
[113]Shiyan Xu, Yuyao He, Xue Li. The relationship between location of new central business district and traffic flow [C]. Proceedings of 2009 IEEE International Conference on Automation and Logistics, Shenyang, China, Aug.5-7,2009. Washington, DC. USA: IEEE Computer Society,2009,00:1827-1831.
[114]西安市公安局交通管理支队,长安大学.西安市城市道路交通管理规划[R].西安：西安市公安局交通管理支队,2003
[115]张生瑞,严海.城市公共交通规划的理论与实践[M].中国铁道出版社,2007.