On the Stochastic Fundamental Diagram for Freeway Traffic: Model Development, Analytical Properties, Validation, and Extensive Applications

[1]  B D Greenshields,et al.  A study of traffic capacity , 1935 .

[2]  M. Lighthill,et al.  On kinematic waves I. Flood movement in long rivers , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[3]  M J Lighthill,et al.  On kinematic waves II. A theory of traffic flow on long crowded roads , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[4]  H. Greenberg.  An Analysis of Traffic Flow , 1959 .

[5]  G. F. Newell.  Nonlinear Effects in the Dynamics of Car Following , 1961 .

[6]  L. C. Edie.  Car-Following and Steady-State Theory for Noncongested Traffic , 1961 .

[7]  L. Breiman.  The Poisson Tendency in Traffic Distribution , 1963 .

[8]  Frank A. Haight,et al.  Mathematical Theories of Traffic Flow , 2012 .

[9]  Joseph L. Schofer,et al.  A STATISTICAL ANALYSIS OF SPEED-DENSITY HYPOTHESES , 1965 .

[10]  Richard Cowan,et al.  A Road With no Overtaking , 1971 .

[11]  A. Soyster,et al.  A STOCHASTIC MODEL OF FLOW VERSUS CONCENTRATION APPLIED TO TRAFFIC ON HILLS , 1973 .

[12]  Richard Cowan,et al.  Useful headway models , 1975 .

[13]  D. Branston.  Models of Single Lane Time Headway Distributions , 1976 .

[14]  R D Kuehne,et al.  MACROSCOPIC FREEWAY MODEL FOR DENSE TRAFFIC - STOP-START WAVES AND INCIDENT DETECTION , 1984 .

[15]  Kerner,et al.  Structure and parameters of clusters in traffic flow. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[16]  J. M. D. Castillo,et al.  On the functional form of the speed-density relationship—I: General theory , 1995 .

[17]  J. M. D. Castillo,et al.  ON THE FUNCTIONAL FORM OF THE SPEED-DENSITY RELATIONSHIP--II: EMPIRICAL INVESTIGATION , 1995 .

[18]  H. M. Zhang.  A theory of nonequilibrium traffic flow , 1998 .

[19]  B. Kerner.  EXPERIMENTAL FEATURES OF SELF-ORGANIZATION IN TRAFFIC FLOW , 1998 .

[20]  Serge P. Hoogendoorn,et al.  New Estimation Technique for Vehicle-Type-Specific Headway Distributions , 1998 .

[21]  R. Mahnke,et al.  STOCHASTIC THEORY OF FREEWAY TRAFFIC , 1999 .

[22]  Michel Rascle,et al.  Resurrection of "Second Order" Models of Traffic Flow , 2000, SIAM J. Appl. Math..

[23]  H. M. Zhang,et al.  A Car-Following Theory for Multiphase Vehicular Traffic Flow , 2003 .

[24]  N. Geroliminis,et al.  Existence of urban-scale macroscopic fundamental diagrams: Some experimental findings - eScholarship , 2007 .

[25]  N. Geroliminis,et al.  An analytical approximation for the macropscopic fundamental diagram of urban traffic , 2008 .

[26]  Michael J MacNicholas,et al.  A Simple and Pragmatic Representation of Traffic Flow , 2011 .

[27]  Hesham Rakha,et al.  Derivation of Van Aerde Traffic Stream Model from Tandem-Queuing Theory , 2009 .

[28]  Serge P. Hoogendoorn,et al.  Investigating the Shape of the Macroscopic Fundamental Diagram Using Simulation Data , 2010 .

[29]  Houbing Song,et al.  Development and calibration of the Anisotropic Mesoscopic Simulation model for uninterrupted flow facilities , 2010 .

[30]  Henry X. Liu,et al.  A stochastic model of traffic flow: Theoretical foundations , 2011 .

[31]  H. M. Zhang,et al.  Fundamental Diagram of Traffic Flow , 2011 .

[32]  Daiheng Ni,et al.  Logistic modeling of the equilibrium speed-density relationship , 2011 .

[33]  Roberto Horowitz,et al.  Probabilistic Graphical Models of Fundamental Diagram Parameters for Simulations of Freeway Traffic , 2011 .

[34]  Nikolas Geroliminis,et al.  An empirical analysis on the arterial fundamental diagram , 2011 .

[35]  Gunes Dervisoglu.  Automatic Calibration of Freeway Models with Model-Based Sensor Fault Detection , 2012 .

[36]  Markos Papageorgiou,et al.  Exploiting the fundamental diagram of urban networks for feedback-based gating , 2012 .

[37]  Henry X. Liu,et al.  A stochastic model of traffic flow: Gaussian approximation and estimation , 2013 .

[38]  Markos Papageorgiou,et al.  Urban congestion gating control based on reduced operational network fundamental diagrams , 2013 .

[39]  Haizhong Wang,et al.  Stochastic modeling of the equilibrium speed-density relationship , 2013 .

[40]  Shimao Fan.  Data-fitted generic second order macroscopic traffic flow models , 2013 .

[41]  Benjamin Seibold,et al.  Data-Fitted First-Order Traffic Models and Their Second-Order Generalizations , 2013 .

[42]  Roberto Horowitz,et al.  Fundamental Diagram Calibration: A Stochastic Approach to Linear Fitting , 2014 .

[43]  Benjamin Coifman,et al.  Revisiting the empirical fundamental relationship , 2014 .

[44]  Markos Papageorgiou,et al.  Local Ramp Metering in the Presence of a Distant Downstream Bottleneck: Theoretical Analysis and Simulation Study , 2014, IEEE Transactions on Intelligent Transportation Systems.

[45]  Chen Wu,et al.  Effect of stochastic transition in the fundamental diagram of traffic flow , 2014, 1408.2902.

[46]  Jianfeng Zheng,et al.  A probabilistic stationary speed–density relation based on Newell’s simplified car-following model , 2014 .

[47]  Ludovic Leclercq,et al.  Macroscopic Fundamental Diagrams: A cross-comparison of estimation methods , 2014 .

[48]  Fang Zhou,et al.  Parsimonious shooting heuristic for trajectory control of connected automated traffic part I: Theoretical analysis with generalized time geography , 2015, ArXiv.

[49]  Lili Du,et al.  Coordinated online in-vehicle routing balancing user optimality and system optimality through information perturbation , 2015 .

[50]  Balaji Ponnu,et al.  Speed-spacing dependency on relative speed from the adjacent lane: New insights for car following models , 2015 .

[51]  Markos Papageorgiou,et al.  Controller Design for Gating Traffic Control in Presence of Time-delay in Urban Road Networks , 2015 .

[52]  Jin Zhang,et al.  On the fundamental diagram for freeway traffic: A novel calibration approach for single-regime models , 2015 .

[53]  Benjamin Coifman,et al.  An Overview of Empirical Flow-Density and Speed-Spacing Relationships: Evidence of Vehicle Length Dependency , 2015 .

[54]  Keith Redmill,et al.  Collecting ambient vehicle trajectories from an instrumented probe vehicle: High quality data for microscopic traffic flow studies , 2016 .

[55]  Marcello Montanino,et al.  Speed or spacing? Cumulative variables, and convolution of model errors and time in traffic flow models validation and calibration , 2016 .

[56]  Jia Hu,et al.  Parsimonious shooting heuristic for trajectory design of connected automated traffic part II: Computational issues and optimization , 2017 .

[57]  Xiaobo Qu,et al.  On the Impact of Cooperative Autonomous Vehicles in Improving Freeway Merging: A Modified Intelligent Driver Model-Based Approach , 2017, IEEE Transactions on Intelligent Transportation Systems.