交通流动态随机演化模型研究
|
摘要
随机交通流模型是智能交通系统、交通工程设计、交通管理与控制等领域的应用基础，对丰富现代交通流理论体系具有重要意义。道路交通流具有复杂性、动态性和随机性特征，新一代智能交通系统对交通流理论提出更高要求，静态的、确定的交通流理论已不能满足动态随机建模需求。本文应用多元异构数据，建立基于车辆轨迹信息的随机交通流模型，揭示交通流复杂动态性和随机演化性的内在机理，克服传统模型在确定函数上增加随机扰动项的不足。论文的主要研究内容和研究成果表现在以下方面：
（1）数据挖掘：考虑道路交通流系统内部的复杂动态性和随机演化性，对交通流特性进行了定量研究和定性分析，为构建随机交通流模型奠定了基础。选取欧拉型（伯克利I80-W和北京G6-S高速公路感应线圈）和拉格朗日型（NGSIM车辆轨迹）实测数据，描述了拥堵车队扰动特性和交通流随机振荡时频特性，提出了车头时距/车头间距/瞬时速度的对数正态型经验概率分布模型。
（2）微观关联：基于实测车头时距/瞬时速度、车头间距/瞬时速度联合概率分布，建立马尔可夫微观车辆跟驰模型，研究概率分布与微观模型内在关联，利用转移概率矩阵描述驾驶员随机驾驶行为，更真实地反映交通流动态演化特征。
（3）宏观关联：将车头时距/车头间距/瞬时速度经验分布与流量/密度散布特性相结合，建立随机基本图模型，探讨概率分布与宏观模型内在关联，提出随机Newell条件，研究交通流半稳态区域的分布特性和概率边界计算方法。有助于指导交通系统设计、管理和控制。
（4）匝道瓶颈建模：考虑道路通行能力随机性和时变性，建立基于车头时距/间距分布的交通流崩溃概率模型，研究连续流设施瓶颈区通行能力随机特性和交通流崩溃机理，分析瓶颈拥堵形成、传播、消散规律。有助于采取主动交通管理措施、形成优化控制策略预防常发性拥堵，提高道路交通可靠性。
本文依托拉格朗日型和欧拉型检测数据，围绕车头时距/间距联合概率分布，提出一系列随机交通流模型，从微观和宏观两个层面揭示交通流随机特性内在影响因素和形成机理，可辅助构建城市主动交通管理系统。
Stochastic traffic flow modelling is the application foundation of Intelligent Trans-portation Systems (ITS), traffic engineering, traffic management and control and so on.It is of a certain significance to enrich the modern traffic flow theory. Road traffic flow iswith complex, dynamic and stochastic characteristics. The new generation of ITS bringsforward higher requirements to the traditional static and deterministic theory, so that itno longer satisfies the demands of dynamic and stochastic modelling. This dissertationinvestigates multiple heterogeneous data to establish stochastic traffic flow models basedon vehicle trajectory information, reveals the underlying mechanism of complexity andstochastic evolutions, and overcomes the deficiency of traditional models that added ran-dom disturbance terms to determinant functions. The main contents and results are asfollows:
(1) Data mining: we first analyze the characteristics of empirical traffic measure-ments to reveal the underlying mechanism of complexity, dynamic and stochastic evo-lutions quantitatively and qualitatively. This work lays the foundation to the stochastictraffic flow modelling. By using Eulerian measurements (e.g. inductive loop data offreeways I80-W in Berkeley and G6-S in Beijing) and Lagrangian measurements (e.g.vehicular trajectories of NGSIM dataset Highway101), we study shifted lognormal dis-tributions of headway/spacing/velocity, disturbances of congested platoons (jam queues)and time-frequency properties of traffic oscillations.
(2) Microscopic connection: based on the joint probability distributions of head-way/velocity and spacing/velocity, we propose a Markov model for road traffic by incor-porating the connection between empirical distributions and microscopic car-followingmodels. Applying the transition probability matrix to describe random choices of drivers,the results show that the stochastic model more veritably reflects the dynamic evolutioncharacteristics of traffic flow.
(3) Macroscopic connection: we propose a stochastic FD model through the con-nection between headway/spacing distributions and the macroscopic fundamental dia-gram (FD). We also study the stochastic Newell condition, wide scattering features andprobabilistic boundaries in flow-density plot, which compensate for the lack of analyticalderivation of the meta-stable2D region.
(4) On-ramp/off-ramp bottleneck modeling: we propose a traffic flow breakdownprobability model based on headway/spacing distributions. It assumes the stochastic anddynamic road capacity. We study the capacity of highway on-ramp bottlenecks and themechanism of traffic breakdown phenomena, analyze the formation, propagation and dis-sipation of bottleneck congestions, and use the spatial-temporal queueing model to derivephase transition conditions of5traffic jam patterns. This work is beneficial to take mea-sures in active traffic management (ATM), obtain optimal control strategies to preventrecurrent congestions and improve reliability.
This dissertation relies on Lagrangian and Eulerian measurements to study jointdistributions of headway/spacing/velocity, proposes a series of stochastic traffic flowmodels to reveal the potential impact factors and the formation mechanism of stochasticcharacteristics. This study assists in establishing urban ATM systems.
（1）数据挖掘：考虑道路交通流系统内部的复杂动态性和随机演化性，对交通流特性进行了定量研究和定性分析，为构建随机交通流模型奠定了基础。选取欧拉型（伯克利I80-W和北京G6-S高速公路感应线圈）和拉格朗日型（NGSIM车辆轨迹）实测数据，描述了拥堵车队扰动特性和交通流随机振荡时频特性，提出了车头时距/车头间距/瞬时速度的对数正态型经验概率分布模型。
（2）微观关联：基于实测车头时距/瞬时速度、车头间距/瞬时速度联合概率分布，建立马尔可夫微观车辆跟驰模型，研究概率分布与微观模型内在关联，利用转移概率矩阵描述驾驶员随机驾驶行为，更真实地反映交通流动态演化特征。
（3）宏观关联：将车头时距/车头间距/瞬时速度经验分布与流量/密度散布特性相结合，建立随机基本图模型，探讨概率分布与宏观模型内在关联，提出随机Newell条件，研究交通流半稳态区域的分布特性和概率边界计算方法。有助于指导交通系统设计、管理和控制。
（4）匝道瓶颈建模：考虑道路通行能力随机性和时变性，建立基于车头时距/间距分布的交通流崩溃概率模型，研究连续流设施瓶颈区通行能力随机特性和交通流崩溃机理，分析瓶颈拥堵形成、传播、消散规律。有助于采取主动交通管理措施、形成优化控制策略预防常发性拥堵，提高道路交通可靠性。
本文依托拉格朗日型和欧拉型检测数据，围绕车头时距/间距联合概率分布，提出一系列随机交通流模型，从微观和宏观两个层面揭示交通流随机特性内在影响因素和形成机理，可辅助构建城市主动交通管理系统。
Stochastic traffic flow modelling is the application foundation of Intelligent Trans-portation Systems (ITS), traffic engineering, traffic management and control and so on.It is of a certain significance to enrich the modern traffic flow theory. Road traffic flow iswith complex, dynamic and stochastic characteristics. The new generation of ITS bringsforward higher requirements to the traditional static and deterministic theory, so that itno longer satisfies the demands of dynamic and stochastic modelling. This dissertationinvestigates multiple heterogeneous data to establish stochastic traffic flow models basedon vehicle trajectory information, reveals the underlying mechanism of complexity andstochastic evolutions, and overcomes the deficiency of traditional models that added ran-dom disturbance terms to determinant functions. The main contents and results are asfollows:
(1) Data mining: we first analyze the characteristics of empirical traffic measure-ments to reveal the underlying mechanism of complexity, dynamic and stochastic evo-lutions quantitatively and qualitatively. This work lays the foundation to the stochastictraffic flow modelling. By using Eulerian measurements (e.g. inductive loop data offreeways I80-W in Berkeley and G6-S in Beijing) and Lagrangian measurements (e.g.vehicular trajectories of NGSIM dataset Highway101), we study shifted lognormal dis-tributions of headway/spacing/velocity, disturbances of congested platoons (jam queues)and time-frequency properties of traffic oscillations.
(2) Microscopic connection: based on the joint probability distributions of head-way/velocity and spacing/velocity, we propose a Markov model for road traffic by incor-porating the connection between empirical distributions and microscopic car-followingmodels. Applying the transition probability matrix to describe random choices of drivers,the results show that the stochastic model more veritably reflects the dynamic evolutioncharacteristics of traffic flow.
(3) Macroscopic connection: we propose a stochastic FD model through the con-nection between headway/spacing distributions and the macroscopic fundamental dia-gram (FD). We also study the stochastic Newell condition, wide scattering features andprobabilistic boundaries in flow-density plot, which compensate for the lack of analyticalderivation of the meta-stable2D region.
(4) On-ramp/off-ramp bottleneck modeling: we propose a traffic flow breakdownprobability model based on headway/spacing distributions. It assumes the stochastic anddynamic road capacity. We study the capacity of highway on-ramp bottlenecks and themechanism of traffic breakdown phenomena, analyze the formation, propagation and dis-sipation of bottleneck congestions, and use the spatial-temporal queueing model to derivephase transition conditions of5traffic jam patterns. This work is beneficial to take mea-sures in active traffic management (ATM), obtain optimal control strategies to preventrecurrent congestions and improve reliability.
This dissertation relies on Lagrangian and Eulerian measurements to study jointdistributions of headway/spacing/velocity, proposes a series of stochastic traffic flowmodels to reveal the potential impact factors and the formation mechanism of stochasticcharacteristics. This study assists in establishing urban ATM systems.
引文
[1]北京交通发展研究中心.2012年上半年交通运行监测报告.2012.
[2]吴建军.城市交通网络拓扑结构复杂性研究[博士学位论文].北京:北京交通大学,2008.
[3]李力,姜锐,贾斌,等.现代交通流理论与应用（卷1）：高速公路交通流.清华大学出版社,2011:86–87.
[4]史其信.“车联网”打造智能交通平台.第四届中国无线射频识别（RFID）技术发展国际研讨会,上海,2009.
[5]国务院发展研究中心国际技术经济研究所.中国射频识别（RFID）技术发展与应用报告.2009.
[6]钱小鸿,史其信,章建强,等.智慧交通.清华大学出版社,2011.
[7] Lighthill M J, Whitham G B. On Kinematic Waves. II. A Theory of Traffic Flow on LongCrowded Roads. Proceedings of the Royal Society of London. Series A, Mathematical andPhysical Sciences,1955,229(1178):317–345.
[8] Richards P I. Shockwaves on the highway. Operations Research,1956,4:42–51.
[9] JabariSE,LiuHX. Astochasticmodeloftrafficflow:Theoreticalfoundations. TransportationResearch, Part B,2012,46(1):156–174.
[10] Prigogine I, Herman R. Kinetic Theory of Vehicular Traffic. New York: American Elsevier,1971.
[11] Daganzo C F. The cell transmission model: A dynamic representation of highway traffic con-sistent with the hydrodynamic theory. Transportation Research, Part B,1994,28(4):269–287.
[12] Daganzo C F. A finite difference approximation of the kinematic wave model of traffic flow.Transportation Research, Part B,1995,29(4):261–276.
[13] Alecsandru C D. A Stochastic Mesoscopic Cell-Transmission Model for Operational Analysisof Large-scale Transportation Networks[D]. USA: Department of Civil and EnvironmentalEngineering, Louisiana State University and Agricultural and Mechanical College, May,2006.
[14] Daganzo C F. The cell transmission model, part II: Network traffic. Transportation Research,Part B,1995,29(2):79–93.
[15] Lebacque J P. The Godunov scheme and what it means for first order traffic flow model-s. Proceedings of International Symposium of Transportation and Traffic Theory, New York:Pergamon-Elservier,1996.
[16] Daganzo C F. The lagged cell transmission model. Proceedings of the14th InternationalSymposium of Transportation and Traffic Theory, Jerusalem, Israel,1999.147–171.
[17] Szeto W. Enhanced lagged cell-transmission model for dynamic traffic assignment. Trans-portation Research Record,2008,2085:76–85.
[18] Mu ozL,SunX,HorowitzR,etal. TrafficDensityEstimationwiththeCellTransmissionMod-el. Proceedings of American Control Conference, Denver, Colorado, USA,2003.3750–3755.
[19] Mu ozL,SunX,HorowitzR,etal. Piecewise-linearizedcelltransmissionmodelandparametercalibration methodology. Transportation Research Record,2006,1965:183–191.
[20] GomesG,HorowitzR. Optimalfreewayrampmeteringusingthe asymmetric celltransmissionmodel. Transportation Research, Part C,2006,14(4):244–262.
[21] Gomes G, Horowitz R, Kurzhanskiy A A, et al. Behavior of the cell transmission model andeffectiveness of ramp metering. Transportation Research, Part C,2008,16(4):485–513.
[22] BoelR,MihaylovaL. Acompositionalstochasticmodelforrealtimefreewaytrafficsimulation.Transportation Research, Part B,2006,40(4):319–334.
[23] Lo H K, Chang E, Chan Y C. Dynamic network traffic control. Transportation Research, PartA,2001,35(8):721–744.
[24] LoHK,SzetoWY. Acell-basedvariationalinequalityformulationofthedynamicuseroptimalassignment problem. Transportation Research, Part B,2002,36(5):421–443.
[25] Long J C, Gao Z Y, Ren H L, et al. Urban traffic congestion propagation and bottleneck iden-tification. Science in China Series F,2008,51(7):948–964.
[26] LongJC,GaoZY,ZhaoXM,etal. Urbantrafficjamsimulationbasedonthecelltransmissionmodel. Networks and Spatial Economics,2008,11(1):43–64.
[27] Chen X Q, Li R, Lu H, et al. Spatio-temporal Evolution of Traffic Congestions on Urban Free-ways. Proceedings of the2nd ASCE International Conference of Transportation Engineering,Chengdu, China,2009.
[28] Chen X Q, Shi J, Xie W J, et al. Perturbation and stability analysis of the multi-anticipativeintelligent driver model. International Journal of Modern Physics C,2010,21(5):647–668.
[29]陈喜群,杨新苗,李力,等.基于智能交通信息的预期与适应性元胞传输模型.控制理论与应用,2010,27(12):1591–1597.
[30] KurzhanskiyA. ModelingandSoftwareToolsforFreewayOperationalPlanning[D]. USA:De-partment of Electrical Engineering and Computer Science, University of California, Berkeley,2007.
[31]孙煦,陆化普,吴娟.北京市快速路速度—流量—密度关系研究.公路工程,2012,37(1):43–48.
[32]董春娇,邵春福,熊志华.基于优化SVM的城市快速路网交通流状态判别.北京交通大学学报,2011,35(6):13–17.
[33]董春娇,邵春福,马壮林,等.阻塞流状态下城市快速路交通流时空特性.交通运输工程学报,2012,12(3):73–79.
[34]董春娇,邵春福,诸葛承祥.混合状态下城市快速路交通流短时预测.物理学报,2012,61(1):44–52.
[35] Daganzo C F. Requiem for second-order fluid approximations of traffic flow. TransportationResearch, Part B,1995,29(4):277–286.
[36] Helbing D, Johansson A F. On the controversy around Daganzo’s requiem for and Aw-Rascle’s resurrection of second-order traffic flow models. The European Physical Journal B,2009,69:549–562.
[37] Payne H J. Models of freeway traffic and control. In: Bekey G A,(eds.). Proceedings ofMathematical models of public systems. La Jolla, CA: Simulation Council,1971:51–61.
[38] Whitham G B. Linear and nonlinear waves. New York: Wiley-interscience,1974.
[39] Phillips W F. A kinetic model for traffic flow with continuum implications. TransportationPlanning and Technology,1979,5(3):131–138.
[40] Zhang H M. A theory of nonequilibrium traffic flow. Transportation Research, Part B,1998,32(7):485–498.
[41] Aw A, Rascle M. Resurrection of “second order” models of traffic flow. SIAM Journal onApplied Mathematics,2000,60(3):916–938.
[42] Greenberg J M. Extensions and amplifications of a traffic model of Aw and Rascle. SIAMJournal on Applied Mathematics,2001,62(3):729–745.
[43] Zhang H M. A non-equilibrium traffic model devoid of gas-like behavior. TransportationResearch, Part B,2002,36(3):275–290.
[44] Jiang R, Wu Q S, Zhu Z J. Full velocity difference model for a car-following theory. PhysicalReview E,2001,64(1):017101.
[45] Jiang R, Wu Q S, Zhu Z J. A new continuum model for traffic flow and numerical tests.Transportation Research, Part B,2002,36(5):405–419.
[46] Xue Y, Dai S Q. Continuum traffic model with the consideration of two delay time scales.Physical Review E,2003,68(6):066123.
[47] Hoogendoorn S, Bovy P. State-of-the-art of Vehicular Traffic Flow Modelling. Proceedings ofthe Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering,2001,215(4):283–303.
[48] Leonard D R, Power P, Taylor N B. CONTRAM: Structure of the Model. Technical report,Transportation Research Laboratory (TRL), Crowthorn,1989.
[49] Jayakrishnan R, Mahmassani H S, Hu T Y. An evaluation tool for advanced traffic infor-mation and management systems in urban networks. Transportation Research, Part C,1994,2(3):129–147.
[50] Ben-Akiva M, Koutsopoulos H N, Antoniou C, et al. Traffic Simulation with DynaMIT. In:Barcelo J,(eds.). Proceedings of Fundamentals of Traffic Simulation. Springer,2010:.
[51] Aerde M, Rakha H. INTEGRATION Release2.30for Windows: User Guide. Technical report,Virginia Tech., Transportation Institute,2002.
[52] Burghout W, Koutsopoulos H, Andréasson I. Hybrid mesoscopic-microscopic traffic simula-tion. Transportation Research Record,2006,1934:218–225.
[53] Gawron C. Simulation-Based Traffic Assignment; Computing User Equilibria in Large StreetNetworks[D]. Germany: University of Cologne,1998.
[54] Snelder M. A Comparison between Dynameq and Indy. Technical report, CIRRELT Report,CIRRELT-2009-48,2009.
[55] Lin Y, Song H. DynaCHINA: A real-time traffic estimation and prediction system. IEEEPersvasive Computing,2006,5(4):65–72.
[56]商蕾,陆化普.城市微观交通仿真系统及其应用研究.系统仿真学报,2006,18(1):221–224.
[57]葛红霞.基于诱导信息的交通流动力学特性与非线性密度波研究[博士学位论文].上海:上海大学,2006.
[58] Pipes L A. An operational analysis of traffic dynamics. Journal of applied physics,1953,24(3):274–281.
[59] Gazis D C, Herman R, Rothery R. Nonlinear follow-the-leader models of traffic flow. Opera-tions Research,1961,9:545–567.
[60] Newell G F. Nonlinear effects in the dynamics of car following. Operations Research,1961,9(2):209–229.
[61] Bierley R L. Investigation of an intervehicle spacing display. Highway Research Record,1963,25:58–75.
[62] Leutzbach W, Wiedemann R. Development and applications of traffic simulation models at theKarlsruhe Institut für Verkehrswesen. Traffic engineering and control,1986,27(5):270–278.
[63] Sultan B, Brackstone M, McDonald M. Drivers’ use of deceleration and acceleration informa-tion in car-following process. Transportation Research Record,2004,1883:31–39.
[64] Bando M, Hasebe K, Nakayama A, et al. Dynamical model of traffic congestion and numericalsimulation. Physical Review E,1995,51(2):1035–1042.
[65] Helbing D, Tilch B. Generalized force model of traffic dynamics. Physical Review E,1998,58(1):133–138.
[66] Treiber M, Hennecke A, Helbing D. Congested traffic states in empirical observations andmicroscopic simulations. Physical Review E,2000,62(2):1805–1824.
[67]王江锋,闫学东,邵春福,等.基于Min-Max方法和移动轨迹融合的车辆无线定位算法.汽车工程,2012,34(5):466–470.
[68] Lenz H, Wagner C K, Sollacher R. Multi-anticipative car-following model. The EuropeanPhysical Journal B,1999,7(2):331–335.
[69] SumaleeA,ZhongRX,PanTL,etal. Stochasticcelltransmissionmodel(SCTM):Astochasticdynamic traffic model for traffic state surveillance and assignment. Transportation Research,Part B,2011,45(3):507–533.
[70] WangY,PapageorgiouM. Real-timefreewaytrafficstateestimationbasedonextendedKalmanfilter: a general approach. Transportation Research, Part B,2005,39(2):141–167.
[71] WangY,PapageorgiouM,Messmer A. RENAISSANCE-A unifiedmacroscopic model-basedapproach to real-time freeway network traffic surveillance. Transportation Research, Part C,2006,14(3):190–212.
[72] Wang Y, Papageorgiou M, Messmer A, et al. An adaptive freeway traffic state estimator. Au-tomatica,2009,45(1):10–24.
[73] Papageorgiou M. Dynamic modeling, assignment, and route guidance in traffic networks.Transportation Research, Part B,1990,24(6):471–495.
[74] Wagner P. A time-discrete harmonic oscillator model of human car-following. The EuropeanPhysical Journal B,2011,84(4):713–718.
[75]黄乒花,孔令江,刘慕仁.一维元胞自动机随机交通流模型的研究.物理学报,2001,50(1):30–36.
[76]祝会兵.基于驾驶行为细致分析的交通流建模和模拟[博士学位论文].上海:上海大学,2008.
[77] Nagel K, Schreckenberg M. A cellular automaton model for freeway traffic. Journal dePhysique I,1992,2(12):2221–2229.
[78] Zhu H B, Ge H X, Dai S Q. A new cellular automaton model for traffic flow with differentprobability for drivers. International Journal of Modern Physics C,2007,18(5):773–782.
[79] EdieLC. Car-followingandsteady-statetheoryfornoncongestedtraffic. OperationsResearch,1961,9(1):66–76.
[80] Treiber M, Kesting A, Helbing D. Understanding widely scattered traffic flows, the capac-ity drop, and platoons as effects of variance-driven time gaps. Physical Review E,2006,74(1):016123.
[81] Wang H, Ni D, Chen Q Y, et al. Stochastic modeling of the equilibrium speed-density relation-ship. Journal of Advanced Transportation,2011,45(10):DOI:10.1002/atr.172.
[82] Ngoduy D. Multiclass first-order traffic model using stochastic fundamental diagrams. Trans-portmetrica,2011,7(2):111–125.
[83] Leclercq L. Calibration of flow-density relationships on urban streets. Transportation ResearchRecord,2005,1934:226–234.
[84]陈晓明,邵春福,熊志华.混合交通信号交叉口的通行能力可靠度.中国公路学报,2008,21(4):99–104.
[85] Brilon W, Geistefeldt J, Regler M. Reliability of freeway traffic flow: A stochastic conceptof capacity. Proceedings of the16th International Symposium of Transportation and TrafficTheory. College Park, Maryland,2005:125–144.
[86] Evans J L, Elefteriadou L, Gautam N. Probability of breakdown at freeway merges usingMarkov chains. Transportation Research, Part B,2001,35(3):237–254.
[87] Smilowitz K, Daganzo C. Reproducible features of congested highway traffic. Mathematicaland Computer Modelling,2002,35(5-6):509–515.
[88] KernerBS,KlenovSL. Probabilisticbreakdownphenomenonaton-rampbottlenecksinthree-phase traffic theory: Congestion nucleation in spatially non-homogeneous traffic. Physica A,2006,364:473–492.
[89] Kesting A, Treiber M, Helbing D. Enhanced intelligent driver model to access the impact ofdriving strategies on traffic capacity. Philosophical Transactions of the Royal Society A,2010,368(1928):4585–4605.
[90] Del Castillo J M. Propagation of perturbations in dense traffic flow: A model and its implica-tions. Transportation Research, Part B,2001,35(4):367–389.
[91] JostD,NagelK. Probabilistictrafficflowbreakdowninstochasticcarfollowingmodels. Trafficand Granular Flow’03,2003.87–103.
[92] Son B, Kim T, Kim H, et al. Probabilistic model of traffic breakdown with random propagationof disturbance for ITS application. Lecture Notes in Computer Science,2004,3215:45–51.
[93] BanksJ. Newapproachtobottleneckcapacityanalysis:Finalreport. CaliforniaPATHResearchReport,2006. UCB–ITS–PRR–2006–13.
[94] LuXY,SkabardonisA. FreewayTrafficShockwaveAnalysis:ExploringtheNGSIMTrajecto-ry Data. Proceedings of the86th Transportation Research Board Annual Meeting, Washington,D.C.,2007.
[95] Wang H, Wang W, Chen X, et al. Experimental features and characteristics of speed dispersionin urban freeway traffic. Transportation Research Record,2007,1999:150–160.
[96] Kim T, Zhang H M. A stochastic wave propagation model. Transportation Research, Part B,2008,42(7-8):619–634.
[97] Bassan S, Polus A, Faghri A. Time-dependent analysis of density fluctuations and breakdownthresholds on congested freeways. Transportation Research Record,2006,1965:40–47.
[98] Habib-Mattar C, Polus A, Cohen M A. Analysis of the breakdown process on congested free-ways. Transportation Research Record,2009,2124:58–66.
[99] Lorenz M, Elefteriadou L. Defining freeway capacity as a function of breakdown probability.Transportation Research Record,2001,1776:43–51.
[100] Mahnke R, Kühne R. Probabilistic description of traffic breakdown. Traffic and GranularFlow’05,2007.527–536.
[101] Chow A, Lu X Y, Qiu T. Empirical analysis of traffic breakdown probability distri-bution with respect to speed and occupancy. California PATH Working Paper,2009.UCB–ITS–PWP–2009–5.
[102]荣建,刘小明,任福田,等.基于可变跟驰时间和随机因素的通行能力理论计算模型.中国公路学报,2001,14(3):81–85.
[103]臧晓冬,周伟.基于车头间距变量的通行能力理论模型.公路交通科技,2010,27(2):103–107.
[104] Chen A, Zhou Z. The α-reliable mean-excess traffic equilibrium model with stochastic traveltimes. Transportation Research, Part B,2010,44(4):493–513.
[105]陆化普.交通规划理论与方法（第2版）.清华大学出版社,2006.
[106]陆化普.交通规划理论研究前沿.清华大学出版社,2007.
[107]卢宇.交通流混沌实时判定方法的研究[博士学位论文].天津:天津大学,2006.
[108]熊志华,邵春福.随机需求条件下道路网行程质量评估——行程时间可靠性.交通运输工程与信息学报,2006,4(2):40–44.
[109] Mahnke R, Pieret N. Stochastic master-equation approach to aggregation in freeway traffic.Physical Review E,1997,56(3):2666–2671.
[110] Mahnke R, Kaupu s J. Probabilistic description of traffic flow. Networks and Spatial Eco-nomics,2001,1(1):103–136.
[111] MahnkeR,Kaupu sJ,LubashevskyI. Probabilisticdescriptionoftrafficflow. PhysicsReports,2005,408(1-2):1–130.
[112] Kampen N G. Stochastic Processes in Physics and Chemistry. Third ed., Amsterdam: Elsevier,2007.
[113] Chowdhury D, Schadschneider A, Nishinari K. Stochastic Transport in Complex Systems:From Molecules to Vehicles. Oxford: Elsevier,2010.
[114] Kühne R, Mahnke R, Lubashevsky I, et al. Probabilistic description of traffic breakdowns.Physical Review E,2002,65:066125.
[115]李明,陆化普,聂聪.基于多元伽马分布的通行能力算法研究.公路工程,2009,34(4):136–140.
[116] Schuhl A. The probability theory applied to distribution of vehicles on two-lane highways.Poisson and Traffic, Eno Foundation, Saugatuck,1955.59–75.
[117] Dawson R F, Chimini L A. The hyperlang probability distribution: A generalized traffic head-way model. Highway Research Record, Highway Research Board, Washington, D.C.,1968,Characteristics of Traffic Flow(230):58–66.
[118] Buckley D J. A semi-poisson model of traffic flow. Transportation Science,1968,2(2):107–133.
[119] Wasielewski P. An integral equation for the semi-Poisson headway distribution model. Trans-portation Science,1974,8(3):237–247.
[120] Branston D. Models of single lane time headway distributions. Transportation Science,1976,10(2):125–148.
[121] Krbalek M, eba P, Wagner P. Headways in traffic flow: Remarks from a physical perspective.Physical Review E,2001,64(6):066119.
[122] Abul-Magd A Y. Modelling gap-size distribution of parked cars using random-matrix theory.Physica A,2006,368(2):536–540.
[123] Abul-Magd A Y. Modeling highway-traffic headway distributions using superstatistics. Phys-ical Review E,2007,76(5):057101.
[124] Jin X X, Zhang Y, Wang F, et al. Departure headways at signalized intersections: A log-normaldistribution model approach. Transportation Research, Part C,2009,17(3):318–327.
[125] WangF,LiL,HuJ,etal. AMarkovprocessinspiredCAmodelofhighwaytraffic. InternationalJournal of Modern Physics C,2009,20(1):117–131.
[126]王法,吉岩,李力,等.基于马尔科夫链间距模型的静态车队车距分布解释.交通与计算机,2008,26(3):19–22.
[127] Chen X Q, Li L, Zhang Y. A Markov model for headway/spacing distribution of road traffic.IEEE Transactions on Intelligent Transportation Systems,2010,11(4):773–785.
[128] ChenXQ,LiL,JiangR,etal. Ontheintrinsicconcordancebetweenthewidescatteringfeatureof synchronized flow and the empirical spacing distributions. Chinese Physics Letters,2010,27(7):074501.
[129] Rached Z, Alajaji F, Campbell L L. The Kullback-Leibler divergence rate between Markovsources. IEEE Transactions on Information Theory,2004,50(5):917–921.
[130] DengK,SunY,MehtaPG,etal. AnInformation-theoreticFrameworktoAggregateAMarkovChain. Proceedings of American Control Conference, St. Louis, MO, USA,2009.
[131] Deng K, Mehta P G, Meyn S P. A Simulation-based Method for Aggregating Markov Chains.Proceedings of IEEE Conference of Decision and Control, Shanghai, China,2009.
[132] Deng K, Mehta P G, Meyn S P. Optimal Kullback-Leibler aggregation via the Spectral Theoryof Markov Chains. IEEE Transactions on Automatic Control,2011,56(12):2793–2808.
[133] Meyn S P, Tweedie R L. Markov Chains and Stochastic Stability.2nd ed., Cambridge: Cam-bridge University Press,2005.
[134]王进.短期交通流预测模型和方法研究[博士学位论文].北京:清华大学,2005.
[135]刘诗序,关宏志,严海.网络交通流动态演化的混沌现象及其控制.物理学报,2012,61(9):58–67.
[136] Herrera J C, Bayen A M. Incorporation of Lagrangian measurements in freeway traffic stateestimation. Transportation Research, Part B,2010,44(4):460–481.
[137] NGSIM. Next generation simulation. http://ngsim.fhwa.dot.gov,2006..
[138] Chiabaut N, Buisson C, Leclercq L. Fundamental diagram estimation through passing ratemeasurements in congestion. IEEE Transactions on Intelligent Transportation Systems,2009,10(2):355–359.
[139] Chiabaut N, Leclercq L, Buisson C. From heterogeneous drivers to macroscopic patterns incongestion. Transportation Research, Part B,2010,44(2):299–308.
[140] Yeo H. Asymmetric Microscopic Driving Behavior Theory[D]. USA: Department of Civil andEnvironmental Engineering, University of California, Berkeley,2008.
[141] Kesting A, Treiber M, Helbing D. General lane-changing model MOBIL for car-followingmodels. Transportation Research Record,2007,1999:86–94.
[142] Thiemann C, Treiber M, Kesting A. Estimating acceleration and lane-changing dynamic-s from Next Generation Simulation trajectory data. Transportation Research Record,2008,2088:90–101.
[143] Hamdar S, Mahmassani H. From existing accident-free car-following models to colliding ve-hicles: exploration and assessment. Transportation Research Record,2008,2088:45–56.
[144] Toledo T, Zohar D. Modeling duration of lane changes. Transportation Research Record,2007,1999:71–78.
[145] Kesting A, Treiber M. Calibrating car-following models by using trajectory data methodolog-ical study. Transportation Research Record,2008,2088:148–156.
[146] Leclercq L, Chiabaut N, Laval J, et al. Relaxation phenomenon after lane changing: Experi-mental validation with NGSIM data set. Transportation Research Record,2007,1999:79–85.
[147] Ossen S, Hoogendoorn S, Gorte B. Interdriver differences in car-following: A vehicletrajectory-based study. Transportation Research Record,2006,1965:121–129.
[148] Young C, Rice J. Estimating velocity fields on a freeway from low-resolution videos. IEEETransactions on Intelligent Transportation Systems,2006,7(4):463–469.
[149] Nelsen R B. An Introduction to Copulas. Springer Verlag,2006.
[150] Chandler R, Herman R, Montroll E. Traffic dynamics: Studies in car following. OperationsResearch,1958,6:165–184.
[151] Gipps P G. A behavioural car-following model for computer simulation. Transportation Re-search, Part B,1981,15(2):105–111.
[152] Kühne R D. Freeway speed distribution and acceleration noise: Calculations from a stochasticcontinuum theory and comparison with measurements. In: Gartner N H, Wilson N H M,(eds.).Proceedings of Proceedings of the10th International Symposium on Transportation and TrafficTheory. New York: Elsevier,1987:119–137.
[153] Kerner B S, Rehborn H. Experimental features and characteristics of traffic jams. PhysicalReview E,1996,53(2):R1297.
[154] KernerBS,RehbornH. Experimentalpropertiesofcomplexityintrafficflow. PhysicalReviewE,1996,53(5):R4275.
[155] Helbing D, Hennecke A, Treiber M. Phase diagram of traffic states in the presence of inhomo-geneities. Physical Review Letters,1999,82(21):4360.
[156] Cassidy M J, Bertini R L. Some traffic features at freeway bottlenecks. Transportation Re-search, Part B,1999,33(1):25–42.
[157] Bertini R L, Leal M T. Empirical study of traffic features at a freeway lane drop. Journal ofTransportation Engineering-ASCE,2005,131(6):397–407.
[158] Li X P, Peng F, Ouyang Y. Measurement and estimation of traffic oscillation properties. Trans-portation Research, Part B,2010,44(1):1–14.
[159] PeMS. California performance measurement system. http://pems.dot.ca.gov,2011..
[160] Sugiyama Y, Fukui M, Kikuchi M, et al. Traffic jams without bottlenecks-Experimentalevidence for the physical mechanism of the formation of a jam. New Journal of Physics,2008,10:033001.
[161] Panwai S, Dia H. Comparative evaluation of microscopic car-following behavior. IEEE Trans-actions on Intelligent Transportation Systems,2005,6(3):314–325.
[162] Lee D N. A theory of visual control of braking based on information about time-to-collision.Perception,1976,5(4):437–459.
[163] Lee D N. General Tau theory: Evolution to date. Perception,2009,38(6):837–850.
[164] Frost B J. Lee’s Tau operator. Perception,2009,38(6):852–853.
[165] Deco G, Scarano L, Soto-Faraco S. Weber’s law in decision making: Integrating behav-ioral data in humans with a neurophysiological model. The Journal of Neuroscience,2007,27(42):11192–11200.
[166] Michaels R M. Perceptual factors in car following. Proceedings of the Second InternationalSymposium on the Theory of Road Traffic Flow, Paris:OECD,1963.44–59.
[167] Boer E R. Car following from the driver’s perspective. Transportation Research, Part F,1999,2(4):201–206.
[168] Forbes T W. Human factor consideration in traffic flow theory. Highway Research Record,1963,15:60–66.
[169] Kullback S, Leibler R A. On information and sufficiency. The Annals of Mathematical Statis-tics,1951,22(1):79–86.
[170] Juang B, Rabiner L. A probabilistic distance measure for hidden Markov models. AT&TTechnical Journal,1985,62(2):391–408.
[171] Vidyasagar M. Kullback-Leibler divergence rate between probability distributions on sets ofdifferent cardinalities. Proceedings of the49th IEEE Conference on Decision and Control,Atlanta, GA, USA,2010.
[172] Newell G F. A simplified car-following theory: A lower order model. Transportation Research,Part B,2002,36(3):195–205.
[173] Newell G F. Instability in dense highway traffic: A review. In: Almond J,(eds.). Proceedingsof the2nd International Symposium of Transportation and Traffic Theory. London, UK: Or-ganization for Economic Cooperation and Developmen,1965:73–83.
[174] Yeo H, Skabardonis A. Understanding stop-and-go traffic in view of asymmetric traffic the-ory. In: Lam W, Wong S, Lo H,(eds.). Proceedings of the18th International Symposium ofTransportation and Traffic Theory. Hong Kong, China: Pergamon-Elservier,2009:99–115.
[175] Ben Slimane S. Bounds on the distribution of a sum of independent lognormal random vari-ables. IEEE Transactions on Communications,2001,49(6):975–978.
[176] Beaulieu N C, Rajwani F. Highly accurate simple closed-form approximations to lognormalsum distributions and densities. IEEE Communications Letters,2004,8(12):709–711.
[177] Beaulieu N C, Xie Q. An optimal lognormal approximation to lognormal sum distributions.IEEE Transactions on Vehicular Technology,2004,53(2):479–489.
[178] Lam C L J, Le-Ngoc T. Estimation of typical sum of lognormal random variables using logshifted gamma approximation. IEEE Communications Letters,2006,10(4):234–235.
[179] Mehta N B, Wu J, Molisch A F, et al. Approximating a sum of random variables with a log-normal. IEEE Transactions on Wireless Communications,2007,6(7):2690–2699.
[180] Nadarajah S. A review of results on sums of random variables. Acta Applicandae Mathemati-cae,2008,103(2):131–140.
[181] Zhao L, Ding J. Least squares approximations to lognormal sum distributions. IEEE Transac-tions on Vehicular Technology,2007,56(2):991–997.
[182] Romeo M, Da Costa V, Bardou F. Broad distribution effects in sums of lognormal randomvariables. The European Physical Journal B,2003,32(4):513–525.
[183] WangC,CoifmanB. Theeffectoflane-changemaneuversonasimplifiedcar-followingtheory.IEEE Transactions on Intelligent Transportation Systems,2008,9(3):523–535.
[184] Li L, Wang F, Jiang R, et al. A new car-following model yielding log-normal type headwaysdistributions. Chinese Physics B,2010,19(2):020513.
[185] Hoeffding W. Probability inequalities for sums of bounded random variables. Journal of theAmerican Statistical Association,1963,58(301):13–30.
[186] PeMS. California performance measurement system. http://pems.eecs.berkeley.edu,2005..
[187] Rice J, Zwet E. A simple and effective method for predicting travel times on freeways. IEEETransactions on Intelligent Transportation Systems,2004,5(3):200–207.
[188] Coifman B, Dhoorjaty S, Lee Z H. Estimating median velocity instead of mean velocity atsingle loop detectors. Transportation Research, Part C,2003,11(3-4):211–222.
[189] DaileyDJ. Astatisticalalgorithmforestimatingspeedfromsingleloopvolumeandoccupancymeasurements. Transportation Research, Part B,1999,33(5):313–322.
[190] Li B. On the recursive estimation of vehicular speed using data from a single inductance loopdetector: A Bayesian approach. Transportation Research, Part B,2009,43(4):391–402.
[191] Li B. Bayesian inference for vehicle speed and vehicle length using dual-loop detector data.Transportation Research, Part B,2010,44(1):108–119.
[192] Soriguera F, Robusté F. Estimation of traffic stream space mean speed from time aggregationsof double loop detector data. Transportation Research, Part C,2011,19(1):115–129.
[193] Forhes W. Human factor considerations in traffic flow theory. Highway Research Board,1963,15:60–66.
[194] Petrov V V. Sums of independent random variables. New York: Springer,1975.
[195] Transportation Research Board of the National Academies. Highway Capacity Manual2010,Volume1: Concepts, Chapter1,2and4; Volume2: Uninterrupted flow.2010.
[196] Elefteriadou L, Roess R, McShane W. Probabilistic nature of breakdown at freeway mergejunctions. Transportation Research Record,1995,1484:80–89.
[197] Persaud B, Yagar S, Tsui D, et al. Breakdown-related capacity for freeway with ramp metering.Transportation Research Record,2001,1748:110–115.
[198] Elefteriadou L, Lertworawanich P. Defining, measuring and estimating freeway capacity. Pro-ceedingsofthe82ndTransportationResearchBoardAnnualMeeting,Washington,D.C.,2003.
[199] Brilon W, Geistefeldt J, Zurlinden H. Implementing the concept of reliability for highwaycapacity analysis. Transportation Research Record,2001,2027:1–8.
[200] Ozbay K, Ozguven E E. A comparative methodology for estimating the capacity of a freewaysection. Proceedings of the10th International IEEE Conference on Intelligent TransportationSystems, Seattle, WA, USA,2007.
[201] Shawky M, Nakamura H. Characteristics of breakdown phenomenon in merging sections ofurban expressways in Japan. Transportation Research Record,2007,2012:11–19.
[202] Geistefeldt J, Brilon W. A comparative assessment of stochastic capacity estimation meth-ods. In: Lam W, Wong S, Lo H,(eds.). Proceedings of the18th International Symposium ofTransportation and Traffic Theory. Hong Kong, China: Springer,2009:.
[203] Shladover S E, Lu X Y, Cody D, et al. Effects of cooperative adaptive cruise control on traf-fic flow: testing drivers’ choices of following distances. Simulation Modelling Practice andTheory,2010. UCB–ITS–PRR–2010–2, California PATH, Institute of Transportation Studies,University of California, Berkeley.
[204] Kondyli A, Elefteriadou L. Modeling driver behavior at freeway-ramp merges. TransportationResearch Record,2011,2249:29–37.
[205] Elefteriadou L, Kondyli A, Brilon W, et al. Ramp metering enhancements for postponingfreeway-flow breakdown. Proceedings of the90th Transportation Research Board AnnualMeeting, Washington, D.C.,2011.
[206] Kondyli A, Soria I, Duret A, et al. Sensitivity analysis of CORSIM with respect to the processoffreewayflowbreakdownatbottlenecklocations. SimulationModellingPracticeandTheory,2011,22:197–206.
[207] Kaplan E L, Meier P. Nonparametric estimation from incomplete observations. Journal of theAmerican Statistical Association,1958,53:457–481.
[208] Daganzo C F. A simple traffic analysis procedure. Networks and Spatial Economics,2001,1(1):77–101.
[209] Duret A, Buisson C, Chiabaut N. Estimating individual speed-spacing relationship and assess-ing ability of Newell’s car-following model to reproduce trajectories. Transportation ResearchRecord,2008,2088:188–197.
[210] Kalos M, Whitlock P. Monte Carlo Methods.2nd ed., Wiley-VCH,2008.
[211] Kerner B S. The Physics of Traffic: Empirical Freeway Pattern Features, Engineering Appli-cations, and Theory. New York: Springer-Verlog,2004.
[212] Kerner B S. Introduction to Modern Traffic Flow Theory and Control: the Long Road to Three-phase Traffic Theory. Berlin: Springer-Verlag Berlin Heidelberg,2009.
[213] Sch nhof M, Helbing D. Empirical features of congested traffic states and their implicationsfor traffic modeling. Transportation Science,2007,41(2):135–166.
[214] Helbing D, Treiber M, Kesting A, et al. Theoretical vs. empirical classification and predictionof congested traffic states. The European Physical Journal B,2009,69:583–598.
[215] Treiber M, Kesting A, Helbing D. Three-phase traffic theory and two-phase models with afundamental diagram in the light of empirical stylized facts. Transportation Research, Part B,2010,44(8-9):983–1000.
[216] Lu L, Su Y, Yun T, et al. A comparison of phase transitions produced by PARAMICS, Trans-Modeler and VISSIM. IEEE Intelligent Transportation Systems Magazine,2010,2(3):19–24.
[217] Helbing D. Derivation of non-local macroscopic traffic equations and consistent traffic pres-sures from microscopic car-following models. The European Physical Journal B,2009,69(6):1–10.
[218] Daganzo C F. A variational formulation of kinematic waves: Solution methods. TransportationResearch, Part B,2005,39(10):934–950.
[2]吴建军.城市交通网络拓扑结构复杂性研究[博士学位论文].北京:北京交通大学,2008.
[3]李力,姜锐,贾斌,等.现代交通流理论与应用（卷1）：高速公路交通流.清华大学出版社,2011:86–87.
[4]史其信.“车联网”打造智能交通平台.第四届中国无线射频识别（RFID）技术发展国际研讨会,上海,2009.
[5]国务院发展研究中心国际技术经济研究所.中国射频识别（RFID）技术发展与应用报告.2009.
[6]钱小鸿,史其信,章建强,等.智慧交通.清华大学出版社,2011.
[7] Lighthill M J, Whitham G B. On Kinematic Waves. II. A Theory of Traffic Flow on LongCrowded Roads. Proceedings of the Royal Society of London. Series A, Mathematical andPhysical Sciences,1955,229(1178):317–345.
[8] Richards P I. Shockwaves on the highway. Operations Research,1956,4:42–51.
[9] JabariSE,LiuHX. Astochasticmodeloftrafficflow:Theoreticalfoundations. TransportationResearch, Part B,2012,46(1):156–174.
[10] Prigogine I, Herman R. Kinetic Theory of Vehicular Traffic. New York: American Elsevier,1971.
[11] Daganzo C F. The cell transmission model: A dynamic representation of highway traffic con-sistent with the hydrodynamic theory. Transportation Research, Part B,1994,28(4):269–287.
[12] Daganzo C F. A finite difference approximation of the kinematic wave model of traffic flow.Transportation Research, Part B,1995,29(4):261–276.
[13] Alecsandru C D. A Stochastic Mesoscopic Cell-Transmission Model for Operational Analysisof Large-scale Transportation Networks[D]. USA: Department of Civil and EnvironmentalEngineering, Louisiana State University and Agricultural and Mechanical College, May,2006.
[14] Daganzo C F. The cell transmission model, part II: Network traffic. Transportation Research,Part B,1995,29(2):79–93.
[15] Lebacque J P. The Godunov scheme and what it means for first order traffic flow model-s. Proceedings of International Symposium of Transportation and Traffic Theory, New York:Pergamon-Elservier,1996.
[16] Daganzo C F. The lagged cell transmission model. Proceedings of the14th InternationalSymposium of Transportation and Traffic Theory, Jerusalem, Israel,1999.147–171.
[17] Szeto W. Enhanced lagged cell-transmission model for dynamic traffic assignment. Trans-portation Research Record,2008,2085:76–85.
[18] Mu ozL,SunX,HorowitzR,etal. TrafficDensityEstimationwiththeCellTransmissionMod-el. Proceedings of American Control Conference, Denver, Colorado, USA,2003.3750–3755.
[19] Mu ozL,SunX,HorowitzR,etal. Piecewise-linearizedcelltransmissionmodelandparametercalibration methodology. Transportation Research Record,2006,1965:183–191.
[20] GomesG,HorowitzR. Optimalfreewayrampmeteringusingthe asymmetric celltransmissionmodel. Transportation Research, Part C,2006,14(4):244–262.
[21] Gomes G, Horowitz R, Kurzhanskiy A A, et al. Behavior of the cell transmission model andeffectiveness of ramp metering. Transportation Research, Part C,2008,16(4):485–513.
[22] BoelR,MihaylovaL. Acompositionalstochasticmodelforrealtimefreewaytrafficsimulation.Transportation Research, Part B,2006,40(4):319–334.
[23] Lo H K, Chang E, Chan Y C. Dynamic network traffic control. Transportation Research, PartA,2001,35(8):721–744.
[24] LoHK,SzetoWY. Acell-basedvariationalinequalityformulationofthedynamicuseroptimalassignment problem. Transportation Research, Part B,2002,36(5):421–443.
[25] Long J C, Gao Z Y, Ren H L, et al. Urban traffic congestion propagation and bottleneck iden-tification. Science in China Series F,2008,51(7):948–964.
[26] LongJC,GaoZY,ZhaoXM,etal. Urbantrafficjamsimulationbasedonthecelltransmissionmodel. Networks and Spatial Economics,2008,11(1):43–64.
[27] Chen X Q, Li R, Lu H, et al. Spatio-temporal Evolution of Traffic Congestions on Urban Free-ways. Proceedings of the2nd ASCE International Conference of Transportation Engineering,Chengdu, China,2009.
[28] Chen X Q, Shi J, Xie W J, et al. Perturbation and stability analysis of the multi-anticipativeintelligent driver model. International Journal of Modern Physics C,2010,21(5):647–668.
[29]陈喜群,杨新苗,李力,等.基于智能交通信息的预期与适应性元胞传输模型.控制理论与应用,2010,27(12):1591–1597.
[30] KurzhanskiyA. ModelingandSoftwareToolsforFreewayOperationalPlanning[D]. USA:De-partment of Electrical Engineering and Computer Science, University of California, Berkeley,2007.
[31]孙煦,陆化普,吴娟.北京市快速路速度—流量—密度关系研究.公路工程,2012,37(1):43–48.
[32]董春娇,邵春福,熊志华.基于优化SVM的城市快速路网交通流状态判别.北京交通大学学报,2011,35(6):13–17.
[33]董春娇,邵春福,马壮林,等.阻塞流状态下城市快速路交通流时空特性.交通运输工程学报,2012,12(3):73–79.
[34]董春娇,邵春福,诸葛承祥.混合状态下城市快速路交通流短时预测.物理学报,2012,61(1):44–52.
[35] Daganzo C F. Requiem for second-order fluid approximations of traffic flow. TransportationResearch, Part B,1995,29(4):277–286.
[36] Helbing D, Johansson A F. On the controversy around Daganzo’s requiem for and Aw-Rascle’s resurrection of second-order traffic flow models. The European Physical Journal B,2009,69:549–562.
[37] Payne H J. Models of freeway traffic and control. In: Bekey G A,(eds.). Proceedings ofMathematical models of public systems. La Jolla, CA: Simulation Council,1971:51–61.
[38] Whitham G B. Linear and nonlinear waves. New York: Wiley-interscience,1974.
[39] Phillips W F. A kinetic model for traffic flow with continuum implications. TransportationPlanning and Technology,1979,5(3):131–138.
[40] Zhang H M. A theory of nonequilibrium traffic flow. Transportation Research, Part B,1998,32(7):485–498.
[41] Aw A, Rascle M. Resurrection of “second order” models of traffic flow. SIAM Journal onApplied Mathematics,2000,60(3):916–938.
[42] Greenberg J M. Extensions and amplifications of a traffic model of Aw and Rascle. SIAMJournal on Applied Mathematics,2001,62(3):729–745.
[43] Zhang H M. A non-equilibrium traffic model devoid of gas-like behavior. TransportationResearch, Part B,2002,36(3):275–290.
[44] Jiang R, Wu Q S, Zhu Z J. Full velocity difference model for a car-following theory. PhysicalReview E,2001,64(1):017101.
[45] Jiang R, Wu Q S, Zhu Z J. A new continuum model for traffic flow and numerical tests.Transportation Research, Part B,2002,36(5):405–419.
[46] Xue Y, Dai S Q. Continuum traffic model with the consideration of two delay time scales.Physical Review E,2003,68(6):066123.
[47] Hoogendoorn S, Bovy P. State-of-the-art of Vehicular Traffic Flow Modelling. Proceedings ofthe Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering,2001,215(4):283–303.
[48] Leonard D R, Power P, Taylor N B. CONTRAM: Structure of the Model. Technical report,Transportation Research Laboratory (TRL), Crowthorn,1989.
[49] Jayakrishnan R, Mahmassani H S, Hu T Y. An evaluation tool for advanced traffic infor-mation and management systems in urban networks. Transportation Research, Part C,1994,2(3):129–147.
[50] Ben-Akiva M, Koutsopoulos H N, Antoniou C, et al. Traffic Simulation with DynaMIT. In:Barcelo J,(eds.). Proceedings of Fundamentals of Traffic Simulation. Springer,2010:.
[51] Aerde M, Rakha H. INTEGRATION Release2.30for Windows: User Guide. Technical report,Virginia Tech., Transportation Institute,2002.
[52] Burghout W, Koutsopoulos H, Andréasson I. Hybrid mesoscopic-microscopic traffic simula-tion. Transportation Research Record,2006,1934:218–225.
[53] Gawron C. Simulation-Based Traffic Assignment; Computing User Equilibria in Large StreetNetworks[D]. Germany: University of Cologne,1998.
[54] Snelder M. A Comparison between Dynameq and Indy. Technical report, CIRRELT Report,CIRRELT-2009-48,2009.
[55] Lin Y, Song H. DynaCHINA: A real-time traffic estimation and prediction system. IEEEPersvasive Computing,2006,5(4):65–72.
[56]商蕾,陆化普.城市微观交通仿真系统及其应用研究.系统仿真学报,2006,18(1):221–224.
[57]葛红霞.基于诱导信息的交通流动力学特性与非线性密度波研究[博士学位论文].上海:上海大学,2006.
[58] Pipes L A. An operational analysis of traffic dynamics. Journal of applied physics,1953,24(3):274–281.
[59] Gazis D C, Herman R, Rothery R. Nonlinear follow-the-leader models of traffic flow. Opera-tions Research,1961,9:545–567.
[60] Newell G F. Nonlinear effects in the dynamics of car following. Operations Research,1961,9(2):209–229.
[61] Bierley R L. Investigation of an intervehicle spacing display. Highway Research Record,1963,25:58–75.
[62] Leutzbach W, Wiedemann R. Development and applications of traffic simulation models at theKarlsruhe Institut für Verkehrswesen. Traffic engineering and control,1986,27(5):270–278.
[63] Sultan B, Brackstone M, McDonald M. Drivers’ use of deceleration and acceleration informa-tion in car-following process. Transportation Research Record,2004,1883:31–39.
[64] Bando M, Hasebe K, Nakayama A, et al. Dynamical model of traffic congestion and numericalsimulation. Physical Review E,1995,51(2):1035–1042.
[65] Helbing D, Tilch B. Generalized force model of traffic dynamics. Physical Review E,1998,58(1):133–138.
[66] Treiber M, Hennecke A, Helbing D. Congested traffic states in empirical observations andmicroscopic simulations. Physical Review E,2000,62(2):1805–1824.
[67]王江锋,闫学东,邵春福,等.基于Min-Max方法和移动轨迹融合的车辆无线定位算法.汽车工程,2012,34(5):466–470.
[68] Lenz H, Wagner C K, Sollacher R. Multi-anticipative car-following model. The EuropeanPhysical Journal B,1999,7(2):331–335.
[69] SumaleeA,ZhongRX,PanTL,etal. Stochasticcelltransmissionmodel(SCTM):Astochasticdynamic traffic model for traffic state surveillance and assignment. Transportation Research,Part B,2011,45(3):507–533.
[70] WangY,PapageorgiouM. Real-timefreewaytrafficstateestimationbasedonextendedKalmanfilter: a general approach. Transportation Research, Part B,2005,39(2):141–167.
[71] WangY,PapageorgiouM,Messmer A. RENAISSANCE-A unifiedmacroscopic model-basedapproach to real-time freeway network traffic surveillance. Transportation Research, Part C,2006,14(3):190–212.
[72] Wang Y, Papageorgiou M, Messmer A, et al. An adaptive freeway traffic state estimator. Au-tomatica,2009,45(1):10–24.
[73] Papageorgiou M. Dynamic modeling, assignment, and route guidance in traffic networks.Transportation Research, Part B,1990,24(6):471–495.
[74] Wagner P. A time-discrete harmonic oscillator model of human car-following. The EuropeanPhysical Journal B,2011,84(4):713–718.
[75]黄乒花,孔令江,刘慕仁.一维元胞自动机随机交通流模型的研究.物理学报,2001,50(1):30–36.
[76]祝会兵.基于驾驶行为细致分析的交通流建模和模拟[博士学位论文].上海:上海大学,2008.
[77] Nagel K, Schreckenberg M. A cellular automaton model for freeway traffic. Journal dePhysique I,1992,2(12):2221–2229.
[78] Zhu H B, Ge H X, Dai S Q. A new cellular automaton model for traffic flow with differentprobability for drivers. International Journal of Modern Physics C,2007,18(5):773–782.
[79] EdieLC. Car-followingandsteady-statetheoryfornoncongestedtraffic. OperationsResearch,1961,9(1):66–76.
[80] Treiber M, Kesting A, Helbing D. Understanding widely scattered traffic flows, the capac-ity drop, and platoons as effects of variance-driven time gaps. Physical Review E,2006,74(1):016123.
[81] Wang H, Ni D, Chen Q Y, et al. Stochastic modeling of the equilibrium speed-density relation-ship. Journal of Advanced Transportation,2011,45(10):DOI:10.1002/atr.172.
[82] Ngoduy D. Multiclass first-order traffic model using stochastic fundamental diagrams. Trans-portmetrica,2011,7(2):111–125.
[83] Leclercq L. Calibration of flow-density relationships on urban streets. Transportation ResearchRecord,2005,1934:226–234.
[84]陈晓明,邵春福,熊志华.混合交通信号交叉口的通行能力可靠度.中国公路学报,2008,21(4):99–104.
[85] Brilon W, Geistefeldt J, Regler M. Reliability of freeway traffic flow: A stochastic conceptof capacity. Proceedings of the16th International Symposium of Transportation and TrafficTheory. College Park, Maryland,2005:125–144.
[86] Evans J L, Elefteriadou L, Gautam N. Probability of breakdown at freeway merges usingMarkov chains. Transportation Research, Part B,2001,35(3):237–254.
[87] Smilowitz K, Daganzo C. Reproducible features of congested highway traffic. Mathematicaland Computer Modelling,2002,35(5-6):509–515.
[88] KernerBS,KlenovSL. Probabilisticbreakdownphenomenonaton-rampbottlenecksinthree-phase traffic theory: Congestion nucleation in spatially non-homogeneous traffic. Physica A,2006,364:473–492.
[89] Kesting A, Treiber M, Helbing D. Enhanced intelligent driver model to access the impact ofdriving strategies on traffic capacity. Philosophical Transactions of the Royal Society A,2010,368(1928):4585–4605.
[90] Del Castillo J M. Propagation of perturbations in dense traffic flow: A model and its implica-tions. Transportation Research, Part B,2001,35(4):367–389.
[91] JostD,NagelK. Probabilistictrafficflowbreakdowninstochasticcarfollowingmodels. Trafficand Granular Flow’03,2003.87–103.
[92] Son B, Kim T, Kim H, et al. Probabilistic model of traffic breakdown with random propagationof disturbance for ITS application. Lecture Notes in Computer Science,2004,3215:45–51.
[93] BanksJ. Newapproachtobottleneckcapacityanalysis:Finalreport. CaliforniaPATHResearchReport,2006. UCB–ITS–PRR–2006–13.
[94] LuXY,SkabardonisA. FreewayTrafficShockwaveAnalysis:ExploringtheNGSIMTrajecto-ry Data. Proceedings of the86th Transportation Research Board Annual Meeting, Washington,D.C.,2007.
[95] Wang H, Wang W, Chen X, et al. Experimental features and characteristics of speed dispersionin urban freeway traffic. Transportation Research Record,2007,1999:150–160.
[96] Kim T, Zhang H M. A stochastic wave propagation model. Transportation Research, Part B,2008,42(7-8):619–634.
[97] Bassan S, Polus A, Faghri A. Time-dependent analysis of density fluctuations and breakdownthresholds on congested freeways. Transportation Research Record,2006,1965:40–47.
[98] Habib-Mattar C, Polus A, Cohen M A. Analysis of the breakdown process on congested free-ways. Transportation Research Record,2009,2124:58–66.
[99] Lorenz M, Elefteriadou L. Defining freeway capacity as a function of breakdown probability.Transportation Research Record,2001,1776:43–51.
[100] Mahnke R, Kühne R. Probabilistic description of traffic breakdown. Traffic and GranularFlow’05,2007.527–536.
[101] Chow A, Lu X Y, Qiu T. Empirical analysis of traffic breakdown probability distri-bution with respect to speed and occupancy. California PATH Working Paper,2009.UCB–ITS–PWP–2009–5.
[102]荣建,刘小明,任福田,等.基于可变跟驰时间和随机因素的通行能力理论计算模型.中国公路学报,2001,14(3):81–85.
[103]臧晓冬,周伟.基于车头间距变量的通行能力理论模型.公路交通科技,2010,27(2):103–107.
[104] Chen A, Zhou Z. The α-reliable mean-excess traffic equilibrium model with stochastic traveltimes. Transportation Research, Part B,2010,44(4):493–513.
[105]陆化普.交通规划理论与方法（第2版）.清华大学出版社,2006.
[106]陆化普.交通规划理论研究前沿.清华大学出版社,2007.
[107]卢宇.交通流混沌实时判定方法的研究[博士学位论文].天津:天津大学,2006.
[108]熊志华,邵春福.随机需求条件下道路网行程质量评估——行程时间可靠性.交通运输工程与信息学报,2006,4(2):40–44.
[109] Mahnke R, Pieret N. Stochastic master-equation approach to aggregation in freeway traffic.Physical Review E,1997,56(3):2666–2671.
[110] Mahnke R, Kaupu s J. Probabilistic description of traffic flow. Networks and Spatial Eco-nomics,2001,1(1):103–136.
[111] MahnkeR,Kaupu sJ,LubashevskyI. Probabilisticdescriptionoftrafficflow. PhysicsReports,2005,408(1-2):1–130.
[112] Kampen N G. Stochastic Processes in Physics and Chemistry. Third ed., Amsterdam: Elsevier,2007.
[113] Chowdhury D, Schadschneider A, Nishinari K. Stochastic Transport in Complex Systems:From Molecules to Vehicles. Oxford: Elsevier,2010.
[114] Kühne R, Mahnke R, Lubashevsky I, et al. Probabilistic description of traffic breakdowns.Physical Review E,2002,65:066125.
[115]李明,陆化普,聂聪.基于多元伽马分布的通行能力算法研究.公路工程,2009,34(4):136–140.
[116] Schuhl A. The probability theory applied to distribution of vehicles on two-lane highways.Poisson and Traffic, Eno Foundation, Saugatuck,1955.59–75.
[117] Dawson R F, Chimini L A. The hyperlang probability distribution: A generalized traffic head-way model. Highway Research Record, Highway Research Board, Washington, D.C.,1968,Characteristics of Traffic Flow(230):58–66.
[118] Buckley D J. A semi-poisson model of traffic flow. Transportation Science,1968,2(2):107–133.
[119] Wasielewski P. An integral equation for the semi-Poisson headway distribution model. Trans-portation Science,1974,8(3):237–247.
[120] Branston D. Models of single lane time headway distributions. Transportation Science,1976,10(2):125–148.
[121] Krbalek M, eba P, Wagner P. Headways in traffic flow: Remarks from a physical perspective.Physical Review E,2001,64(6):066119.
[122] Abul-Magd A Y. Modelling gap-size distribution of parked cars using random-matrix theory.Physica A,2006,368(2):536–540.
[123] Abul-Magd A Y. Modeling highway-traffic headway distributions using superstatistics. Phys-ical Review E,2007,76(5):057101.
[124] Jin X X, Zhang Y, Wang F, et al. Departure headways at signalized intersections: A log-normaldistribution model approach. Transportation Research, Part C,2009,17(3):318–327.
[125] WangF,LiL,HuJ,etal. AMarkovprocessinspiredCAmodelofhighwaytraffic. InternationalJournal of Modern Physics C,2009,20(1):117–131.
[126]王法,吉岩,李力,等.基于马尔科夫链间距模型的静态车队车距分布解释.交通与计算机,2008,26(3):19–22.
[127] Chen X Q, Li L, Zhang Y. A Markov model for headway/spacing distribution of road traffic.IEEE Transactions on Intelligent Transportation Systems,2010,11(4):773–785.
[128] ChenXQ,LiL,JiangR,etal. Ontheintrinsicconcordancebetweenthewidescatteringfeatureof synchronized flow and the empirical spacing distributions. Chinese Physics Letters,2010,27(7):074501.
[129] Rached Z, Alajaji F, Campbell L L. The Kullback-Leibler divergence rate between Markovsources. IEEE Transactions on Information Theory,2004,50(5):917–921.
[130] DengK,SunY,MehtaPG,etal. AnInformation-theoreticFrameworktoAggregateAMarkovChain. Proceedings of American Control Conference, St. Louis, MO, USA,2009.
[131] Deng K, Mehta P G, Meyn S P. A Simulation-based Method for Aggregating Markov Chains.Proceedings of IEEE Conference of Decision and Control, Shanghai, China,2009.
[132] Deng K, Mehta P G, Meyn S P. Optimal Kullback-Leibler aggregation via the Spectral Theoryof Markov Chains. IEEE Transactions on Automatic Control,2011,56(12):2793–2808.
[133] Meyn S P, Tweedie R L. Markov Chains and Stochastic Stability.2nd ed., Cambridge: Cam-bridge University Press,2005.
[134]王进.短期交通流预测模型和方法研究[博士学位论文].北京:清华大学,2005.
[135]刘诗序,关宏志,严海.网络交通流动态演化的混沌现象及其控制.物理学报,2012,61(9):58–67.
[136] Herrera J C, Bayen A M. Incorporation of Lagrangian measurements in freeway traffic stateestimation. Transportation Research, Part B,2010,44(4):460–481.
[137] NGSIM. Next generation simulation. http://ngsim.fhwa.dot.gov,2006..
[138] Chiabaut N, Buisson C, Leclercq L. Fundamental diagram estimation through passing ratemeasurements in congestion. IEEE Transactions on Intelligent Transportation Systems,2009,10(2):355–359.
[139] Chiabaut N, Leclercq L, Buisson C. From heterogeneous drivers to macroscopic patterns incongestion. Transportation Research, Part B,2010,44(2):299–308.
[140] Yeo H. Asymmetric Microscopic Driving Behavior Theory[D]. USA: Department of Civil andEnvironmental Engineering, University of California, Berkeley,2008.
[141] Kesting A, Treiber M, Helbing D. General lane-changing model MOBIL for car-followingmodels. Transportation Research Record,2007,1999:86–94.
[142] Thiemann C, Treiber M, Kesting A. Estimating acceleration and lane-changing dynamic-s from Next Generation Simulation trajectory data. Transportation Research Record,2008,2088:90–101.
[143] Hamdar S, Mahmassani H. From existing accident-free car-following models to colliding ve-hicles: exploration and assessment. Transportation Research Record,2008,2088:45–56.
[144] Toledo T, Zohar D. Modeling duration of lane changes. Transportation Research Record,2007,1999:71–78.
[145] Kesting A, Treiber M. Calibrating car-following models by using trajectory data methodolog-ical study. Transportation Research Record,2008,2088:148–156.
[146] Leclercq L, Chiabaut N, Laval J, et al. Relaxation phenomenon after lane changing: Experi-mental validation with NGSIM data set. Transportation Research Record,2007,1999:79–85.
[147] Ossen S, Hoogendoorn S, Gorte B. Interdriver differences in car-following: A vehicletrajectory-based study. Transportation Research Record,2006,1965:121–129.
[148] Young C, Rice J. Estimating velocity fields on a freeway from low-resolution videos. IEEETransactions on Intelligent Transportation Systems,2006,7(4):463–469.
[149] Nelsen R B. An Introduction to Copulas. Springer Verlag,2006.
[150] Chandler R, Herman R, Montroll E. Traffic dynamics: Studies in car following. OperationsResearch,1958,6:165–184.
[151] Gipps P G. A behavioural car-following model for computer simulation. Transportation Re-search, Part B,1981,15(2):105–111.
[152] Kühne R D. Freeway speed distribution and acceleration noise: Calculations from a stochasticcontinuum theory and comparison with measurements. In: Gartner N H, Wilson N H M,(eds.).Proceedings of Proceedings of the10th International Symposium on Transportation and TrafficTheory. New York: Elsevier,1987:119–137.
[153] Kerner B S, Rehborn H. Experimental features and characteristics of traffic jams. PhysicalReview E,1996,53(2):R1297.
[154] KernerBS,RehbornH. Experimentalpropertiesofcomplexityintrafficflow. PhysicalReviewE,1996,53(5):R4275.
[155] Helbing D, Hennecke A, Treiber M. Phase diagram of traffic states in the presence of inhomo-geneities. Physical Review Letters,1999,82(21):4360.
[156] Cassidy M J, Bertini R L. Some traffic features at freeway bottlenecks. Transportation Re-search, Part B,1999,33(1):25–42.
[157] Bertini R L, Leal M T. Empirical study of traffic features at a freeway lane drop. Journal ofTransportation Engineering-ASCE,2005,131(6):397–407.
[158] Li X P, Peng F, Ouyang Y. Measurement and estimation of traffic oscillation properties. Trans-portation Research, Part B,2010,44(1):1–14.
[159] PeMS. California performance measurement system. http://pems.dot.ca.gov,2011..
[160] Sugiyama Y, Fukui M, Kikuchi M, et al. Traffic jams without bottlenecks-Experimentalevidence for the physical mechanism of the formation of a jam. New Journal of Physics,2008,10:033001.
[161] Panwai S, Dia H. Comparative evaluation of microscopic car-following behavior. IEEE Trans-actions on Intelligent Transportation Systems,2005,6(3):314–325.
[162] Lee D N. A theory of visual control of braking based on information about time-to-collision.Perception,1976,5(4):437–459.
[163] Lee D N. General Tau theory: Evolution to date. Perception,2009,38(6):837–850.
[164] Frost B J. Lee’s Tau operator. Perception,2009,38(6):852–853.
[165] Deco G, Scarano L, Soto-Faraco S. Weber’s law in decision making: Integrating behav-ioral data in humans with a neurophysiological model. The Journal of Neuroscience,2007,27(42):11192–11200.
[166] Michaels R M. Perceptual factors in car following. Proceedings of the Second InternationalSymposium on the Theory of Road Traffic Flow, Paris:OECD,1963.44–59.
[167] Boer E R. Car following from the driver’s perspective. Transportation Research, Part F,1999,2(4):201–206.
[168] Forbes T W. Human factor consideration in traffic flow theory. Highway Research Record,1963,15:60–66.
[169] Kullback S, Leibler R A. On information and sufficiency. The Annals of Mathematical Statis-tics,1951,22(1):79–86.
[170] Juang B, Rabiner L. A probabilistic distance measure for hidden Markov models. AT&TTechnical Journal,1985,62(2):391–408.
[171] Vidyasagar M. Kullback-Leibler divergence rate between probability distributions on sets ofdifferent cardinalities. Proceedings of the49th IEEE Conference on Decision and Control,Atlanta, GA, USA,2010.
[172] Newell G F. A simplified car-following theory: A lower order model. Transportation Research,Part B,2002,36(3):195–205.
[173] Newell G F. Instability in dense highway traffic: A review. In: Almond J,(eds.). Proceedingsof the2nd International Symposium of Transportation and Traffic Theory. London, UK: Or-ganization for Economic Cooperation and Developmen,1965:73–83.
[174] Yeo H, Skabardonis A. Understanding stop-and-go traffic in view of asymmetric traffic the-ory. In: Lam W, Wong S, Lo H,(eds.). Proceedings of the18th International Symposium ofTransportation and Traffic Theory. Hong Kong, China: Pergamon-Elservier,2009:99–115.
[175] Ben Slimane S. Bounds on the distribution of a sum of independent lognormal random vari-ables. IEEE Transactions on Communications,2001,49(6):975–978.
[176] Beaulieu N C, Rajwani F. Highly accurate simple closed-form approximations to lognormalsum distributions and densities. IEEE Communications Letters,2004,8(12):709–711.
[177] Beaulieu N C, Xie Q. An optimal lognormal approximation to lognormal sum distributions.IEEE Transactions on Vehicular Technology,2004,53(2):479–489.
[178] Lam C L J, Le-Ngoc T. Estimation of typical sum of lognormal random variables using logshifted gamma approximation. IEEE Communications Letters,2006,10(4):234–235.
[179] Mehta N B, Wu J, Molisch A F, et al. Approximating a sum of random variables with a log-normal. IEEE Transactions on Wireless Communications,2007,6(7):2690–2699.
[180] Nadarajah S. A review of results on sums of random variables. Acta Applicandae Mathemati-cae,2008,103(2):131–140.
[181] Zhao L, Ding J. Least squares approximations to lognormal sum distributions. IEEE Transac-tions on Vehicular Technology,2007,56(2):991–997.
[182] Romeo M, Da Costa V, Bardou F. Broad distribution effects in sums of lognormal randomvariables. The European Physical Journal B,2003,32(4):513–525.
[183] WangC,CoifmanB. Theeffectoflane-changemaneuversonasimplifiedcar-followingtheory.IEEE Transactions on Intelligent Transportation Systems,2008,9(3):523–535.
[184] Li L, Wang F, Jiang R, et al. A new car-following model yielding log-normal type headwaysdistributions. Chinese Physics B,2010,19(2):020513.
[185] Hoeffding W. Probability inequalities for sums of bounded random variables. Journal of theAmerican Statistical Association,1963,58(301):13–30.
[186] PeMS. California performance measurement system. http://pems.eecs.berkeley.edu,2005..
[187] Rice J, Zwet E. A simple and effective method for predicting travel times on freeways. IEEETransactions on Intelligent Transportation Systems,2004,5(3):200–207.
[188] Coifman B, Dhoorjaty S, Lee Z H. Estimating median velocity instead of mean velocity atsingle loop detectors. Transportation Research, Part C,2003,11(3-4):211–222.
[189] DaileyDJ. Astatisticalalgorithmforestimatingspeedfromsingleloopvolumeandoccupancymeasurements. Transportation Research, Part B,1999,33(5):313–322.
[190] Li B. On the recursive estimation of vehicular speed using data from a single inductance loopdetector: A Bayesian approach. Transportation Research, Part B,2009,43(4):391–402.
[191] Li B. Bayesian inference for vehicle speed and vehicle length using dual-loop detector data.Transportation Research, Part B,2010,44(1):108–119.
[192] Soriguera F, Robusté F. Estimation of traffic stream space mean speed from time aggregationsof double loop detector data. Transportation Research, Part C,2011,19(1):115–129.
[193] Forhes W. Human factor considerations in traffic flow theory. Highway Research Board,1963,15:60–66.
[194] Petrov V V. Sums of independent random variables. New York: Springer,1975.
[195] Transportation Research Board of the National Academies. Highway Capacity Manual2010,Volume1: Concepts, Chapter1,2and4; Volume2: Uninterrupted flow.2010.
[196] Elefteriadou L, Roess R, McShane W. Probabilistic nature of breakdown at freeway mergejunctions. Transportation Research Record,1995,1484:80–89.
[197] Persaud B, Yagar S, Tsui D, et al. Breakdown-related capacity for freeway with ramp metering.Transportation Research Record,2001,1748:110–115.
[198] Elefteriadou L, Lertworawanich P. Defining, measuring and estimating freeway capacity. Pro-ceedingsofthe82ndTransportationResearchBoardAnnualMeeting,Washington,D.C.,2003.
[199] Brilon W, Geistefeldt J, Zurlinden H. Implementing the concept of reliability for highwaycapacity analysis. Transportation Research Record,2001,2027:1–8.
[200] Ozbay K, Ozguven E E. A comparative methodology for estimating the capacity of a freewaysection. Proceedings of the10th International IEEE Conference on Intelligent TransportationSystems, Seattle, WA, USA,2007.
[201] Shawky M, Nakamura H. Characteristics of breakdown phenomenon in merging sections ofurban expressways in Japan. Transportation Research Record,2007,2012:11–19.
[202] Geistefeldt J, Brilon W. A comparative assessment of stochastic capacity estimation meth-ods. In: Lam W, Wong S, Lo H,(eds.). Proceedings of the18th International Symposium ofTransportation and Traffic Theory. Hong Kong, China: Springer,2009:.
[203] Shladover S E, Lu X Y, Cody D, et al. Effects of cooperative adaptive cruise control on traf-fic flow: testing drivers’ choices of following distances. Simulation Modelling Practice andTheory,2010. UCB–ITS–PRR–2010–2, California PATH, Institute of Transportation Studies,University of California, Berkeley.
[204] Kondyli A, Elefteriadou L. Modeling driver behavior at freeway-ramp merges. TransportationResearch Record,2011,2249:29–37.
[205] Elefteriadou L, Kondyli A, Brilon W, et al. Ramp metering enhancements for postponingfreeway-flow breakdown. Proceedings of the90th Transportation Research Board AnnualMeeting, Washington, D.C.,2011.
[206] Kondyli A, Soria I, Duret A, et al. Sensitivity analysis of CORSIM with respect to the processoffreewayflowbreakdownatbottlenecklocations. SimulationModellingPracticeandTheory,2011,22:197–206.
[207] Kaplan E L, Meier P. Nonparametric estimation from incomplete observations. Journal of theAmerican Statistical Association,1958,53:457–481.
[208] Daganzo C F. A simple traffic analysis procedure. Networks and Spatial Economics,2001,1(1):77–101.
[209] Duret A, Buisson C, Chiabaut N. Estimating individual speed-spacing relationship and assess-ing ability of Newell’s car-following model to reproduce trajectories. Transportation ResearchRecord,2008,2088:188–197.
[210] Kalos M, Whitlock P. Monte Carlo Methods.2nd ed., Wiley-VCH,2008.
[211] Kerner B S. The Physics of Traffic: Empirical Freeway Pattern Features, Engineering Appli-cations, and Theory. New York: Springer-Verlog,2004.
[212] Kerner B S. Introduction to Modern Traffic Flow Theory and Control: the Long Road to Three-phase Traffic Theory. Berlin: Springer-Verlag Berlin Heidelberg,2009.
[213] Sch nhof M, Helbing D. Empirical features of congested traffic states and their implicationsfor traffic modeling. Transportation Science,2007,41(2):135–166.
[214] Helbing D, Treiber M, Kesting A, et al. Theoretical vs. empirical classification and predictionof congested traffic states. The European Physical Journal B,2009,69:583–598.
[215] Treiber M, Kesting A, Helbing D. Three-phase traffic theory and two-phase models with afundamental diagram in the light of empirical stylized facts. Transportation Research, Part B,2010,44(8-9):983–1000.
[216] Lu L, Su Y, Yun T, et al. A comparison of phase transitions produced by PARAMICS, Trans-Modeler and VISSIM. IEEE Intelligent Transportation Systems Magazine,2010,2(3):19–24.
[217] Helbing D. Derivation of non-local macroscopic traffic equations and consistent traffic pres-sures from microscopic car-following models. The European Physical Journal B,2009,69(6):1–10.
[218] Daganzo C F. A variational formulation of kinematic waves: Solution methods. TransportationResearch, Part B,2005,39(10):934–950.