为了解析交通流速度与密度关系, 推导出了一组交通流参数物理意义明确且符合交通流特性的通用Logistic模型。从Logistic模型本质出发, 讨论速度变化率的表达形式, 结合交通流实际情况修正速度变化率并引入速度上确界概念, 建立了一系列Logistic模型;通过改变取值, 给出了模型参数变化对Logistic速度-密度曲线的影响, 并细致讨论了参数的物理意义及获取方法;最后分别采集区段和断面的全交通状态数据进行模型验证。结果表明:模型3对2组数据的拟合优度分别为0.931 3和0.970 4, 该模型能够很好地描述不同状态下的交通流特性。
Abstract
In order to characterize the speed-density relationship in traffic flow, a group of generalized logistic models were proposed with physically meaningful and explicit parameters, which can fit field data well. Starting from the initial concept of Logistic model, the expression of speed change rate was discussed in detail, and thus three models were derived by modifying the change rate of speed and introducing the supremum of speed. The influences of parameters on logistic speed-density curve were provided by changing one parameter each time while keeping the others fixed, and the physical meaning of parameters and the acquisition method were discussed in detail. Both section data and fixed-location data were validated for the practicality. The result shows that the goodness of fit of model 3 for the two groups of date is 0.931 3 and 0.970 4 respectively, and the proposed model characterize the speed-density relationship well under various traffic states.
关键词
交通工程 /
速度-密度关系 /
Logistic模型 /
交通流
{{custom_keyword}} /
Key words
traffic engineering /
speed-density relationship /
Logistic model /
traffic flow
{{custom_keyword}} /
中图分类号：
U491.112
{{custom_clc.code}}
({{custom_clc.text}})
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] 王殿海.交通流理论[M].北京:人民交通出版社, 2002. WANG Dian-hai.Traffic Flow Theory[M].Beijing:China Communications Press,2002.
[2] GAZIS D C.The Origins of Traffic Theory[J].Operations Research,2002,50(1):69-77.
[3] LIGHTHILL M J,WHITHAM G B.On Kinematic Waves.II.A Theory of Traffic Flow on Long Crowded Roads[J].Proceedings of the Royal Society of London Series A:Mathematical,Physical & Engineering Sciences,1955,229(1178):317-345.
[4] RICHARDS P I.Shock Waves on the Highway[J].Operations Research,1956,4(1):42-51.
[5] HERMAN R,PRIGOGINE I.A Two-fluid Approach to Town Traffic[J].Science,1979,204(4389):148-151.
[6] BERG P,WOODS A.Traveling Waves in an Optimal Velocity Model of Freeway Traffic[J].Physical Review E,2001,63(3):036107.
[7] DAGANZO C F.Requiem for Second-order Fluid Approximations of Traffic Flow[J].Transportation Research Part B,1995,29(4):277-286.
[8] JIANG R,WU Q S,ZHU Z J.A New Continuum Model for Traffic Flow and Numerical Tests[J].Transportation Research Part B,2002,36(5):405-419.
[9] 邵春福, 肖崇紫, 王博彬, 等.最小安全间距约束下拥挤交通流速度-密度关系模型[J].交通运输工程学报, 2015, 15(1):92-99. SHAO Chun-fu,XIAO Chong-zi,WANG Bo-bin,et al.Speed-density Relation Model of Congested Traffic Flow Under Minimum Safety Distance Constraint[J].Journal of Traffic and Transportation Engineering,2015,15(1):92-99.
[10] 王殿海, 金 盛.车辆跟驰行为建模的回顾与展望[J].中国公路学报, 2012, 25(1):115-127. WANG Dian-hai,JIN Sheng.Review and Outlook of Modeling of Car Following Behavior[J].China Journal of Highway and Transport,2012,25(1):115-127.
[11] HELBING D.Traffic and Related Self-driven Many-particle Systems[J].Reviews of Modern Physics,2001,73(4):1067-1141.
[12] HELBING D,TREIBER M.Jams,Waves,and Clusters[J].Science,1998,282(5396):2001-2003.
[13] KUHNE R D.Greenshiels' Legacy:Highway Traffic[J].Transportation Research Circular,2011(E-C149):3-10.
[14] LIEU H.Revised Monograph on Traffic Flow Theory[M].Washington DC:Federal Highway Administration,2003.
[15] 张亚平, 张起森.高速公路速度-流量模型研究[J].中国公路学报, 2000, 13(3):73-77. ZHANG Ya-ping,ZHANG Qi-sen.A Study of Models of Speed-flow for Freeways[J].China Journal of Highway and Transport,2000,13(3):73-77.
[16] 陈永恒, 葛 兴, 王殿海.城市干线典型路段速度-流量特性分析[J].吉林大学学报:工学版, 2006, 36(4):613-617. CHEN Yong-heng,GE Xing,WANG Dian-hai.Analysis on Speed-flow Characteristics at Typical Sections in Urban Arteries[J].Journal of Jilin University:Engineering and Technology Edition,2006,36(4):613-617.
[17] QU Xiao-bo,ZHANG Jin,WANG Shuai-an,et al.Modelling Follow up Time at a Single-lane Roundabout[J].Journal of Traffic and Transportation Engineering:English Edition,2014,1(2):97-102.
[18] WANG Hai-zhong,LI Jia,CHEN Qian-yong,et al.Logistic Modeling of the Equilibrium Speed-density Relationship[J].Transportation Research Part A,2011,45(6):554-566.
[19] MACNICHOLAS M J.A Simple and Pragmatic Representation of Traffic Flow[J].Transportation Research Circular,2011(E-C149):161-177.
[20] GOTTSCHALK P G,DUNN J R.The Five-parameter Logistic:A Characterization and Comparison with the Four-parameter Logistic[J].Analytical Biochemistry,2005,343(1):54-65.
[21] KESTING A.Traffic Flow Dynamics:Data,Models and Simulation[M].New York:Springer,2012.
[22] National Academy of Sciences.Highway Capacity Manual 2010[M].Washington DC:Transportation Research Board,2010.
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}
基金
国家自然科学基金重点项目(51338008);国家自然科学基金项目(51278454); 国家自然科学基金青年科学基金项目(61304191);中央高校基本科研业务费专项资金项目(2014G1321035)
{{custom_fund}}
{{custom_fund}}
PDF全文下载(565 KB)
