An Analysis of Traffic Flow

Harold Greenberg
Harold Greenberg
The Port of New York Authority, New York, New York
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The Port of New York Authority, New York, New York

Published Online:1 Feb 1959https://doi.org/10.1287/opre.7.1.79

Abstract

A model for traffic flow is developed by treating the traffic stream as a continuous fluid. Fluid dynamic principles are then used to derive relations between speed, density, and flow.

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  22 April 2019 | Mathematical Problems in Engineering, Vol. 2019, No. 1
- General‐Logistic‐Based Speed‐Density Relationship Model Incorporating the Effect of Heavy Vehicles
  25 February 2019 | Mathematical Problems in Engineering, Vol. 2019, No. 1
- A Driver's Mind
- Characteristics of traffic flow on urban expressway - A case study of Beijing
  21 December 2018
- Application of a Discontinuous Form of Macroscopic Gazis–Herman–Rothery Model to Steady-State Freeway Traffic Stream Observations
  9 October 2018 | Transportation Research Record: Journal of the Transportation Research Board, Vol. 2672, No. 20
- Exploring Characteristics and Fundamental Relations of Area-Wide Vessel Traffic Flow
- Adaptive neuro-fuzzy approach for modeling equilibrium speed–density relationship
  15 February 2018 | Transportmetrica A: Transport Science, Vol. 14, No. 9
- Road Speed Fusion Model Based on Wavelet Neural Network Optimized by Genetic Algorithm
- A Macroscopic Traffic Simulation Model to Mingle Manually Operated and Self-driving Cars
- On development of arterial fundamental diagrams based on surrogate density measures from adaptive traffic control systems utilizing stop-line detection
  Transportation Research Part C: Emerging Technologies, Vol. 94
- Vehicle routing algorithms based on a route reservation approach
  11 December 2018 | Journal of Physics: Conference Series, Vol. 1096
- Comparison of the one-equation LWR models for density and for speed
  11 October 2018 | IOP Conference Series: Materials Science and Engineering, Vol. 421
- Traffic Service Quantitative Analysis Method under Developing Country
- Shared Autonomous Taxi System and Utilization of Collected Travel-Time Information
  Journal of Advanced Transportation, Vol. 2018
- Questions regarding vehicle safety and the mathematical analysis of safety in large scale networks using positive dynamic systems and probability theory methods
- Research on evacuation control of panic crowds
- A Study on Congestion Toll Pricing: The Case of Beijing, China
  Journal of the Economic Geographical Society of Korea, Vol. 21, No. 2
- An extended car-following model considering the appearing probability of truck and driver's characteristics
  Physics Letters A, Vol. 382, No. 20
- Reproducible generation of experimental data sample for calibrating traffic flow fundamental diagram
  Transportation Research Part A: Policy and Practice, Vol. 111
- Dynamic traffic assignment of cooperative adaptive cruise control
  Transportation Research Part C: Emerging Technologies, Vol. 90
- An extended car-following model to describe connected traffic dynamics under cyberattacks
  Physica A: Statistical Mechanics and its Applications, Vol. 496
- A mixed-mode traffic assignment model with new time-flow impedance function
  22 January 2018 | International Journal of Modern Physics B, Vol. 32, No. 03
- Generalized velocity–density model based on microscopic traffic simulation
  12 April 2017 | Transport, Vol. 33, No. 2
- Research on Formation Mechanism and Recognition Technology of Traffic Congestion: Brief Review and New Development
  18 January 2018
- Neural-Network-Based Calibration of Macroscopic Traffic Flow Models
  26 July 2017
- COMPRAM Assessment and System Dynamics Modeling and Simulation of Car-Following Model for Degraded Roads
  26 July 2017
- Traffic Flow Theory
  17 May 2018
- Fundamentals of Traffic Dynamics
  13 April 2018
- Cellular Automaton Models in the Framework of Three-Phase Traffic Theory
  23 August 2018
- Modeling phase diagrams as stochastic processes with application in vehicular traffic flow
  Applied Mathematical Modelling, Vol. 53
- Scalable evacuation routing in a dynamic environment
  Computers, Environment and Urban Systems, Vol. 67
- Study of travel behavior of vessels in narrow waterways using AIS data – A case study in Sabine-Neches Waterways
  Ocean Engineering, Vol. 147
- Fundamental diagram of ship traffic in the Singapore Strait
  Ocean Engineering, Vol. 147
- A Distributed Traffic Control Strategy Based on Cell-Transmission Model
  IEEE Access, Vol. 6
- The study of monodisperse water-in-oil macroemulsion dynamics in a microfluidic chip
  23 November 2017 | Journal of Physics: Conference Series, Vol. 917
- The effect of distances between vehicles on time and speed in simulated traffic flow
  30 September 2017 | Roads and Bridges - Drogi i Mosty, Vol. 16, No. 3
- Don’t think of them as roads. Think of them as road transport markets
  Progress in Planning, Vol. 117
- On the stochastic fundamental diagram for freeway traffic: Model development, analytical properties, validation, and extensive applications
  Transportation Research Part B: Methodological, Vol. 104
- Stability analysis in Greenberg’s traffic model
  15 November 2017 | International Journal of Modern Physics C, Vol. 28, No. 10
- Estimation of Vehicular Speed and Passenger Car Equivalent Under Mixed Traffic Condition Using Artificial Neural Network
  23 May 2017 | Arabian Journal for Science and Engineering, Vol. 42, No. 9
- Modelling speed–flow relationships for bicycle traffic flow
  Proceedings of the Institution of Civil Engineers - Transport, Vol. 170, No. 4
- Traffic Velocity Estimation From Vehicle Count Sequences
  IEEE Transactions on Intelligent Transportation Systems, Vol. 18, No. 7
- Evaluating lane reservation problems by carbon emission approach
  Transportation Research Part D: Transport and Environment, Vol. 53
- A Novel Speed–Density Relationship Model Based on the Energy Conservation Concept
  IEEE Transactions on Intelligent Transportation Systems, Vol. 18, No. 5
- Observations on the fundamental diagram and their interpretation from the human factors perspective
  2 June 2016 | Transportmetrica B: Transport Dynamics, Vol. 5, No. 2
- A simulation tool as a support for teaching the concepts of urban traffic flow
  27 January 2017 | Computer Applications in Engineering Education, Vol. 25, No. 2
- Kriging-Based Approach for Estimation of Vehicular Speed and Passenger Car Units on an Urban Arterial
  Journal of Transportation Engineering, Part A: Systems, Vol. 143, No. 3
- Spatial fluctuation on speed-density relationship of pedestrian dynamics
  9 March 2017 | Journal of Statistical Mechanics: Theory and Experiment, Vol. 2017, No. 3
- A flexible traffic stream model and its three representations of traffic flow
  Transportation Research Part C: Emerging Technologies, Vol. 75
- Follow-the-Leader Approximations of Macroscopic Models for Vehicular and Pedestrian Flows
  11 April 2017
- Intelligent Traffic Congestion Prediction System Based on ANN and Decision Tree Using Big GPS Traces
  23 February 2017
- A heterogeneous traffic flow model consisting of two types of vehicles with different sensitivities
  Communications in Nonlinear Science and Numerical Simulation, Vol. 42
- Effect of Mixed Traffic on Capacity of Two-Lane Roads: Case Study on Indian Highways
  Procedia Engineering, Vol. 187
- Modelling of Bicycle Traffic in the Cities Using VISUM
  Procedia Engineering, Vol. 187
- Efficiency comparison of the routing algorithms used in centralized traffic management systems
  Procedia Engineering, Vol. 201
- On development of arterial fundamental diagrams based on surrogate density measures from adaptive traffic control systems utilizing stop-line detection
  Transportation Research Procedia, Vol. 23
- Eigenvalue and Eigenvector Analysis of Stability for a Line of Traffic
  8 September 2016 | Studies in Applied Mathematics, Vol. 138, No. 1
- Effects of Rain on Freeway Traffic in Southern California
  1 January 2017 | Transportation Research Record: Journal of the Transportation Research Board, Vol. 2616, No. 1
- Modeling Small Unmanned Aircraft System Traffic Flow Under External Force
  1 January 2017 | Transportation Research Record: Journal of the Transportation Research Board, Vol. 2626, No. 1
- Traveling waves for degenerate diffusive equations on networks
  Networks & Heterogeneous Media, Vol. 12, No. 3
- ON THE DIRICHLET-NEUMANN BOUNDARY PROBLEM FOR SCALAR CONSERVATION LAWS
  20 September 2016 | Mathematical Modelling and Analysis, Vol. 21, No. 5
- Outflow of traffic from the national capital Kuala Lumpur to the north, south and east coast highways using flow, speed and density relationships
  Journal of Traffic and Transportation Engineering (English Edition), Vol. 3, No. 6
- Integrated expression method for technical mapping of traffic parameters using RGB color model
  6 October 2016 | Journal of Advanced Transportation, Vol. 50, No. 6
- An efficient iterative link transmission model
  Transportation Research Part B: Methodological, Vol. 92
- Vehicle Longitudinal Control and Traffic Stream Modeling
  Daiheng Ni,
  John D. Leonard,
  Chaoqun Jia,
  Jianqiang Wang
  10 July 2015 | Transportation Science, Vol. 50, No. 3
- Simulation of Road Traffic Applying Model-Driven Engineering
  10 May 2015 | ADCAIJ: Advances in Distributed Computing and Artificial Intelligence Journal, Vol. 4, No. 2
- Roundabout System Capacity Estimation and Control Strategy with Origin-Destination Pattern
  Journal of Transportation Engineering, Vol. 142, No. 5
- Traffic Assignment Using a Density-Based Travel-Time Function for Intelligent Transportation Systems
  IEEE Transactions on Intelligent Transportation Systems, Vol. 17, No. 5
- Traffic simulation models calibration using speed–density relationship: An automated procedure based on genetic algorithm
  Expert Systems with Applications, Vol. 44
- Revised lattice Boltzmann model for traffic flow with equilibrium traffic pressure
  Physica A: Statistical Mechanics and its Applications, Vol. 443
- Travel Time Dynamics for Intelligent Transportation Systems: Theory and Applications
  IEEE Transactions on Intelligent Transportation Systems, Vol. 17, No. 2
- Equilibrium Traffic Flow Models
- General Motors Models
- The Field Theory
- Longitudinal Control Model
- The Unified Diagram
- Bibliography
- Assessing the Possibility of Presenting a Semi-Stochastic Speed-Density Function
  25 October 2016 | MATEC Web of Conferences, Vol. 81
- Analytical studies on an extended car following model for mixed traffic flow with slow and fast vehicles
  3 January 2016 | International Journal of Modern Physics C, Vol. 27, No. 01
- Exact Boundary Controllability for Free Traffic Flow with Lipschitz Continuous State
  Mathematical Problems in Engineering, Vol. 2016
- An Integrative Modelling Language for Agent-Based Simulation of Traffic
  IEICE Transactions on Information and Systems, Vol. E99.D, No. 2
- Modelling speed–density relationship in traffic streams
  Proceedings of the Institution of Civil Engineers - Transport, Vol. 168, No. 5
- Traffic Flow Characteristics at Different Sites on an Urban Expressway from Loop Counts
  21 September 2015
- Efficient parameter estimation in a macroscopic traffic flow model by discrete mollification
  24 July 2015 | Transportmetrica A: Transport Science, Vol. 11, No. 8
- Rigorous Derivation of Nonlinear Scalar Conservation Laws from Follow-the-Leader Type Models via Many Particle Limit
  30 January 2015 | Archive for Rational Mechanics and Analysis, Vol. 217, No. 3
- Impact of driving aggressiveness on the traffic stability based on an extended optimal velocity model
  7 May 2015 | Nonlinear Dynamics, Vol. 81, No. 4
- Specifications of Fundamental Diagrams for Dynamic Traffic Modeling
  Journal of Transportation Engineering, Vol. 141, No. 9
- An improved car-following model with two preceding cars' average speed
  3 May 2015 | International Journal of Modern Physics C, Vol. 26, No. 08
- Pedestrian Flow Characteristics Studies: A Review
  6 March 2015 | Transport Reviews, Vol. 35, No. 4
- Estimating cycleway capacity and bicycle equivalent unit for electric bicycles
  Transportation Research Part A: Policy and Practice, Vol. 77
- Nonlinear multivariate time–space threshold vector error correction model for short term traffic state prediction
  Transportation Research Part B: Methodological, Vol. 76
- Towards data-driven car-following models
  Transportation Research Part C: Emerging Technologies, Vol. 55
- Development of road traffic flow model for nighttime conditions
- An Improved Potential Field Based Method for Crowd Simulation
  5 August 2015 | International Journal of Software Engineering and Knowledge Engineering, Vol. 25, No. 03
- An improved car-following model considering headway changes with memory
  Physica A: Statistical Mechanics and its Applications, Vol. 421
- On the fundamental diagram for freeway traffic: A novel calibration approach for single-regime models
  Transportation Research Part B: Methodological, Vol. 73
- EVALUATION OF SPEED–FLOW CHARACTERISTICS ON TWO-LANE HIGHWAYS WITH MIXED TRAFFIC
  TRANSPORT, Vol. 32, No. 4
- Speed-Volume Relationship Model for Speed Estimation on Urban Roads in Intelligent Transportation Systems
- Simulation Optimization of Car-Following Models Using Flexible Techniques
  22 May 2015
- Road traffic noise mapping in Guangzhou using GIS and GPS
  Applied Acoustics, Vol. 87
- DATA-ORIENTED APPROACH IN TRANSPORT STUDIES
  Journal of Japan Society of Civil Engineers, Ser. D3 (Infrastructure Planning and Management), Vol. 71, No. 5
- Left-Lane Changes in Laterally Unbalanced Traffic
  28 April 2019 | Transportation Research Record: Journal of the Transportation Research Board, Vol. 2490, No. 1
- Analysis of Traffic Flow Speed-Density Relation Model Characteristics
  Journal of Highway and Transportation Research and Development (English Edition), Vol. 8, No. 4
- Data mining using regularized adaptive B‐splines regression with penalization for multi‐regime traffic stream models
  30 April 2013 | Journal of Advanced Transportation, Vol. 48, No. 7
- Asymmetric flux models for particle-size segregation in granular avalanches
  19 September 2014 | Journal of Fluid Mechanics, Vol. 757
- Some exact solutions to the Lighthill–Whitham–Richards–Payne traffic flow equations: II. Moderate congestion
  29 September 2014 | Journal of Physics A: Mathematical and Theoretical, Vol. 47, No. 41
- A probabilistic stationary speed–density relation based on Newell’s simplified car-following model
  Transportation Research Part B: Methodological, Vol. 68
- An extended car-following model at signalized intersections
  Physica A: Statistical Mechanics and its Applications, Vol. 407
- A traffic stream model for heterogeneous traffic conditions
  Proceedings of the Institution of Civil Engineers - Transport, Vol. 167, No. 4
- Research on Traffic Flow Characteristics of Urban Expressway
  4 July 2014 | Applied Mechanics and Materials, Vol. 587-589
- The impact of precipitation on speed–flow relationships along a UK motorway corridor
  15 September 2013 | Theoretical and Applied Climatology, Vol. 117, No. 1-2
- CASPER: Intelligent capacity-aware evacuation routing
  Computers, Environment and Urban Systems, Vol. 46
- Power-law in pedestrian crossing flow under the interference of vehicles at an un-signalized midblock crosswalk
  Physica A: Statistical Mechanics and its Applications, Vol. 406
- Modeling and optimization of road transport facility operations
  Journal of Facilities Management, Vol. 12, No. 3
- Flow rate and time mean speed predictions for the urban freeway network using state space models
  Transportation Research Part C: Emerging Technologies, Vol. 43
- A NEW CAR-FOLLOWING MODEL CONSIDERING ACCELERATION OF LEAD VEHICLE
  TRANSPORT, Vol. 31, No. 1
- Using high-resolution event-based data for traffic modeling and control: An overview
  Transportation Research Part C: Emerging Technologies, Vol. 42
- From asia to europe: Short-term traffic flow prediction between continents
- Architecture and Recipient Selection of Emergency Messaging for Ambulance Traveling
- Intelligent Control System on Traffic Flow under the Keep-Right-Except-to-Pass Rule
  1 May 2014 | Advanced Materials Research, Vol. 951
- SELECTED ISSUES IN MODELLING OF TRAFFIC FLOWS IN CONGESTED URBAN
  Archives of Transport, Vol. 29, No. 1
- A Modelling Framework for estimating Road Segment Based On-Board Vehicle Emissions
  18 March 2014 | IOP Conference Series: Earth and Environmental Science, Vol. 17
- Urban Traffic Analysis through an UAV
  Procedia - Social and Behavioral Sciences, Vol. 111
- Flow, Speed, Density, and Their Relationships
  15 September 2013
- Speed-Flow-Density Relationships: The Fundamental Basis of Uninterrupted Flow Analysis
- A Driver’s Mind
- Flow-Density Relationship for Discontinuous Flow on Urban Street Network
  1 January 2014 | Applied Mechanics and Materials, Vol. 505-506
- Compilation of References
- Asymptotic Analysis of Traffic Lights Performance Under Heavy Traffic Assumption
  16 May 2012 | Methodology and Computing in Applied Probability, Vol. 15, No. 4
- Behavioural foundations of two-fluid model for urban traffic
  Transportation Research Part C: Emerging Technologies, Vol. 35
- Road traffic networks: Optimal transport and incentives
- Some exact solutions to the Lighthill–Whitham–Richards–Payne traffic flow equations
  14 August 2013 | Journal of Physics A: Mathematical and Theoretical, Vol. 46, No. 36
- Intervehicle Communication: Cox-Fox Modeling
  IEEE Journal on Selected Areas in Communications, Vol. 31, No. 9
- Empirical Innovation of Computational Dual-Loop Models for Identifying Vehicle Classifications against Varied Traffic Conditions
  Computer-Aided Civil and Infrastructure Engineering, Vol. 28, No. 8
- Optimal concentrations in transport systems
  Journal of The Royal Society Interface, Vol. 10, No. 83
- Phase transition model of non-stationary traffic flow: Definition, properties and solution method
  Transportation Research Part B: Methodological, Vol. 52
- Modeling Emergency Messaging for Car Accident over Dichotomized Headway Model in Vehicular Ad-hoc Networks
  IEEE Transactions on Communications, Vol. 61, No. 2
- Stochastic modeling of the equilibrium speed–density relationship
  2 May 2011 | Journal of Advanced Transportation, Vol. 47, No. 1
- Traffic Analysis
  23 January 2016
- Equilibrium Traffic Models
- Regularized Nonlinear Solvers for IMEX Methods Applied to Diffusively Corrected Multispecies Kinematic Flow Models
  SIAM Journal on Scientific Computing, Vol. 35, No. 3
- Data-Fitted First-Order Traffic Models and Their Second-Order Generalizations
  1 January 2013 | Transportation Research Record: Journal of the Transportation Research Board, Vol. 2391, No. 1
- Connecting Networkwide Travel Time Reliability and the Network Fundamental Diagram of Traffic Flow
  1 January 2013 | Transportation Research Record: Journal of the Transportation Research Board, Vol. 2391, No. 1
- Viability approach to Hamilton-Jacobi-Moskowitz problem involving variable regulation parameters
  Networks & Heterogeneous Media, Vol. 8, No. 3
- Constructing set-valued fundamental diagrams from Jamiton solutions in second order traffic models
  Networks & Heterogeneous Media, Vol. 8, No. 3
- A Microscopic Analysis on the Fundamental Diagram and Driver Behavior
  Journal of the Korean Society of Road Engineers, Vol. 14, No. 6
- Parameters Calibration of Traffic Simulation Model Based on Data Mining
  Journal of Transportation Systems Engineering and Information Technology, Vol. 12, No. 6
- Piecewise linear car-following modeling
  Transportation Research Part C: Emerging Technologies, Vol. 25
- Cost-Benefit Analysis and the Optimal Timing of Road Infrastructures
  Journal of Infrastructure Systems, Vol. 18, No. 4
- Modeling of intervehicle communication
- Modelling motorway merge: The current practice in the UK and towards establishing general principles
  Transport Policy, Vol. 24
- On sequential data assimilation for scalar macroscopic traffic flow models
  Physica D: Nonlinear Phenomena, Vol. 241, No. 17
- Green- function for the highway vehicular traffic flow modeling and analysis
  IFAC Proceedings Volumes, Vol. 45, No. 24
- Dual influences on vehicle speed in special-use lanes and critique of US regulation
  Transportation Research Part A: Policy and Practice, Vol. 46, No. 7
- Acquisition of traffic flow density using multi-source data fusion
- A Review of Properties of Flow–Density Functions
  Transport Reviews, Vol. 32, No. 1
- Phase Transition Model Based on Driver Reaction Time and Sensitivity
  1 January 2012 | Transportation Research Record: Journal of the Transportation Research Board, Vol. 2316, No. 1
- Advance-F automatic car-following model and its traffic characteristics
  24 November 2011 | International Journal of Automotive Technology, Vol. 12, No. 6
- Design and Implementation of An Agent-Based Simulation for Emergency Response and Crisis Management
  1 December 2011 | Journal of Algorithms & Computational Technology, Vol. 5, No. 4
- On the fundamental diagram and supply curves for congested urban networks
  Transportation Research Part A: Policy and Practice, Vol. 45, No. 9
- On the modelling and management of traffic
  23 February 2011 | ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 45, No. 5
- Assuring Accuracy on Low Penetration Rate Mobile Phone-Based Traffic State Estimation System
- The Characteristics of Breakdown and the Development of Breakdown Probability Models at Freeway Merging Areas
  Journal of Transport Research, Vol. 18, No. 3
- Stochastic Models of Transport Flows
  Communications in Statistics - Theory and Methods, Vol. 40, No. 16
- Car-following theory of steady-state traffic flow using time-to-collision
  1 August 2011 | Journal of Zhejiang University-SCIENCE A, Vol. 12, No. 8
- A Unified Perspective on Traffic Flow Theory, Part II: The Unified Diagram
  26 April 2012
- Logistic modeling of the equilibrium speed–density relationship
  Transportation Research Part A: Policy and Practice, Vol. 45, No. 6
- The Optimum Road Length in the Container Port
  1 July 2011 | Advanced Materials Research, Vol. 280
- Analysis and modelling of traffic flow under variable speed limits
  Transportation Research Part C: Emerging Technologies, Vol. 19, No. 2
- Establishing speed–flow–density relationships for exclusive motorcycle lanes
  Transportation Planning and Technology, Vol. 34, No. 3
- Traffic flow headway distribution and capacity analysis using urban arterial road data
- Vehicular Traffic III: Other CA Models
- Vehicular Traffic IV: Non-CA Approaches
- Transport on Networks
- Pedestrian Dynamics
- Traffic Phenomena in Biology
- Guide to the Literature
- Bibliography
- On the Fundamental Diagram and Supply Curves for Congested Urban Networks
  Procedia - Social and Behavioral Sciences, Vol. 17
- An empirical analysis on the arterial fundamental diagram
  Transportation Research Part B: Methodological, Vol. 45, No. 1
- A General Phase Transition Model for Vehicular Traffic
  SIAM Journal on Applied Mathematics, Vol. 71, No. 1
- Development of Extreme Value Distribution Method for Estimation of Expressway Capacity
  1 January 2011 | Transportation Research Record: Journal of the Transportation Research Board, Vol. 2260, No. 1
- Traffic Flow Condition Classification for Short Sections Using Single Microwave Sensor
  19 September 2010 | EURASIP Journal on Advances in Signal Processing, Vol. 2010, No. 1
- Stochasticity of freeway operational capacity and chance-constrained ramp metering
  Transportation Research Part C: Emerging Technologies, Vol. 18, No. 5
- An adaptive time gap car-following model
  Transportation Research Part B: Methodological, Vol. 44, No. 8-9
- Traffic Stream Modeling under Heterogeneous Traffic Conditions
  26 April 2012
- Traffic Flow Capacity Model for Urban Expressways
  26 April 2012
- Optimal routing of vehicles with communication capabilities in disasters
  25 September 2008 | Computational Management Science, Vol. 7, No. 2
- Data mining-based adaptive regression for developing equilibrium speed–density relationships
  Canadian Journal of Civil Engineering, Vol. 37, No. 3
- Models, Traffic Models, Simulation, and Traffic Simulation
  28 June 2010
- Multi-agent systems for simulating traffic behaviors
  3 July 2009 | Chinese Science Bulletin, Vol. 55, No. 3
- A novel self-organizing fuzzy rule-based system for modelling traffic flow behaviour
  Expert Systems with Applications, Vol. 36, No. 10
- The Relationship of Speed-Flow-Density for the Mix Traffic Flow on Beijing Urban Expressway
  26 April 2012
- Validation of Van Aerde's simplified steadystate car-following and traffic stream model
  7 September 2013 | Transportation Letters, Vol. 1, No. 3
- A simplified behavioral vehicle longitudinal motion model
  7 September 2013 | Transportation Letters, Vol. 1, No. 2
- References
  19 February 2010
- Modelling of Traffic Flow from an Engineer’s Perspective
- Traffic Speed-Flow Model for the Mix Traffic Flow on Beijing Urban Expressway
- On Discovering Road Traffic Information Using Virtual Reality Simulations
- Fundamental Diagram Modelling and Analysis Based NGSIM Data
  IFAC Proceedings Volumes, Vol. 42, No. 15
- Traffic flow model based on the green- function
- Fully adaptive multiresolution schemes for strongly degenerate parabolic equations in one space dimension
  27 May 2008 | ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 42, No. 4
- Calibration of traffic dynamics models with data mining
- A Generic Characterization of Equilibrium Speed-Flow Curves
  Michael Z. F. Li,
  24 March 2008 | Transportation Science, Vol. 42, No. 2
- Analysis of Work Zone Traffic Behavior for Planning Applications
  Transportation Planning and Technology, Vol. 31, No. 2
- Fully adaptive multiresolution schemes for strongly degenerate parabolic equations with discontinuous flux
  17 August 2007 | Journal of Engineering Mathematics, Vol. 60, No. 3-4
- Movement Nature of Speed-Flow Relationship on Congested Expressway
  Journal of Transportation Engineering, Vol. 134, No. 3
- Motorist conquest in big cities: The case of Budapest
  Acta Oeconomica, Vol. 58, No. 1
- Stability of Traffic Flow Behavior with Distributed Delays Modeling the Memory Effects of the Drivers
  SIAM Journal on Applied Mathematics, Vol. 68, No. 3
- A Comparative Methodology for Estimating the Capacity of a Freeway Section
- Characterization of road traffic flow from measured data of speed and time-headway -relationship between density ( k ), flow rate ( q ) and speed (V )-
- A slow-to-start traffic model related to a M / M /1 queue
  5 July 2007 | Journal of Statistical Mechanics: Theory and Experiment, Vol. 2007, No. 07
- A Microscopic Simulation Model for Incident Modeling in Urban Networks
  Transportation Planning and Technology, Vol. 30, No. 2-3
- Development of Improved and Efficient Traffic Flow Model
  15 July 2015 | International Journal of Modelling and Simulation, Vol. 27, No. 1
- Calibration Procedure for Gipps Car-Following Model
  1 January 2007 | Transportation Research Record: Journal of the Transportation Research Board, Vol. 1999, No. 1
- Models of vehicular traffic: An engineering perspective
  Physica A: Statistical Mechanics and its Applications, Vol. 372, No. 1
- Weak formulation of boundary conditions for scalar conservation laws: an application to highway traffic modelling
  8 September 2006 | International Journal of Robust and Nonlinear Control, Vol. 16, No. 16
- Mixed Initial-Boundary Value Problems for Scalar Conservation Laws: Application to the Modeling of Transportation Networks
- Prediction and Identification of Urban Traffic Flow Based on Features
- Estimation of Traffic Dynamics Models with Machine-Learning Methods
  1 January 2006 | Transportation Research Record: Journal of the Transportation Research Board, Vol. 1965, No. 1
- A car-following theory for multiphase vehicular traffic flow
  Transportation Research Part B: Methodological, Vol. 39, No. 5
- Online Calibration of Traffic Prediction Models
  1 January 2005 | Transportation Research Record: Journal of the Transportation Research Board, Vol. 1934, No. 1
- A CONTEMPORARY REASSESSMENT OF GM CAR-FOLLOWING MODEL USING RTK GPS DATA
  Doboku Gakkai Ronbunshu, Vol. 2005, No. 793
- Freeway Traffic Stream Modeling Based on Principal Curves and Its Analysis
  IEEE Transactions on Intelligent Transportation Systems, Vol. 5, No. 4
- A flow metamodel for delivery agents over a spatial area
  IIE Transactions, Vol. 36, No. 11
- Traffic flow: models and numerics
- SAFETY-BASED CAPACITY ANALYSIS FOR CHINESE HIGHWAYS
  IATSS Research, Vol. 28, No. 1
- Mathematical modelling of traffic flows on controlled roads
  Journal of Applied Mathematics and Mechanics, Vol. 68, No. 6
- Dynamics of traffic flow with real-time traffic information
  30 January 2004 | Physical Review E, Vol. 69, No. 1
- On-line calibration of traffic prediction models
- An empirical study on gap time and its relation to the fundamental diagram of traffic flow
- Evaluation of Interstate Highway Capacity for Short-Term Work Zone Lane Closures
  1 January 2004 | Transportation Research Record: Journal of the Transportation Research Board, Vol. 1877, No. 1
- ON A DIFFUSIVELY CORRECTED KINEMATIC-WAVE TRAFFIC FLOW MODEL WITH CHANGING ROAD SURFACE CONDITIONS
  21 November 2011 | Mathematical Models and Methods in Applied Sciences, Vol. 13, No. 12
- A theoretical probe of a German experiment on stationary moving traffic jams
  Transportation Research Part B: Methodological, Vol. 37, No. 3
- Distributed Ramp Model
- Distributed Modeling and Problem Formulation
- Optimal Velocity Model and its Applications
- References
- A Note on the Entropy Solutions of the Hydrodynamic Model of Traffic Flow
  Shane Velan,
  Michael Florian,
  1 November 2002 | Transportation Science, Vol. 36, No. 4
- A multi-class traffic flow model – an extension of LWR model with heterogeneous drivers
  Transportation Research Part A: Policy and Practice, Vol. 36, No. 9
- The role of speed–flow relationship in congestion pricing implementation with an application to Singapore
  Transportation Research Part B: Methodological, Vol. 36, No. 8
- Some Recent Developments in Continuum Vehicular Traffic Flow Theory 1
  8 February 2016
- Traveling-wave solutions of the diffusively corrected kinematic-wave model
  Mathematical and Computer Modelling, Vol. 35, No. 5-6
- Traffic Dynamics of the Leaf‐Cutting Ant, Atta cephalotes
  The American Naturalist, Vol. 159, No. 3
- Traffic Flow Theories
- Calibrating Simulation Models for Advanced Traveler Information Systems/Advanced Traffic Management Systems Applications
  Journal of Transportation Engineering, Vol. 128, No. 1
- Traffic and related self-driven many-particle systems
  7 December 2001 | Reviews of Modern Physics, Vol. 73, No. 4
- Modeling traffic's flow-density relation: Accommodation of multiple flow regimes and traveler types
  Transportation, Vol. 28, No. 4
- Urban Traffic Flow
- Traffic analysis
  25 October 2005
- Some recent developments in traffic flow theory
- Modeling of Nonlinear Stochastic Dynamic Traffic Flow
  1 January 2001 | Transportation Research Record: Journal of the Transportation Research Board, Vol. 1771, No. 1
- Multi-value cellular automaton models and metastable states in a congested phase
  19 October 2000 | Journal of Physics A: Mathematical and General, Vol. 33, No. 43
- ANALYSIS OF BOTTLENECK PHENOMENA AT BASIC FREEWAY SEGMENTS
  Doboku Gakkai Ronbunshu, Vol. 2000, No. 660
- Synchronized traffic flow from a modified Lighthill-Whitman model
  1 June 2000 | Physical Review E, Vol. 61, No. 6
- COMPLEXITY IN A CRITICAL TRAFFIC FLOW
  20 November 2011 | International Journal of Modern Physics C, Vol. 11, No. 02
- Kinetic Traffic Flow Models
- Irregular traffic flow on a ring road
  Journal of Applied Mathematics and Mechanics, Vol. 64, No. 4
- References
  24 October 2011
- A mathematical theory of traffic hysteresis
  Transportation Research Part B: Methodological, Vol. 33, No. 1
- A new deterministic CA model for traffic flow with multiple states
  1 January 1999 | Journal of Physics A: Mathematical and General, Vol. 32, No. 1
- Traffic Flow Theory
- Modeling Heterogeneous Traffic Flow
  1 January 1999 | Transportation Research Record: Journal of the Transportation Research Board, Vol. 1678, No. 1
- Numerical Simulation and Analysis of Traffic Flow
  1 January 1999 | Transportation Research Record: Journal of the Transportation Research Board, Vol. 1678, No. 1
- On the Integration of Car-following Equations
  23 February 2016
- A generalised stability criterion for motorway traffic
  Transportation Research Part B: Methodological, Vol. 32, No. 2
- On the integration of car-following equations
- Changes in Flow-Density Relationship Due to Environmental, Vehicle, and Driver Characteristics
  1 January 1998 | Transportation Research Record: Journal of the Transportation Research Board, Vol. 1644, No. 1
- Freeway ramp metering using artificial neural networks
  Transportation Research Part C: Emerging Technologies, Vol. 5, No. 5
- A Novel Traffic Stream Model Deriving from a Bimodal Kinetic Equilibrium 1
  IFAC Proceedings Volumes, Vol. 30, No. 8
- Introduction to traffic flow theory
- Traffic flow modeling and control using artificial neural networks
  IEEE Control Systems, Vol. 16, No. 5
- The relationship between speed, flow and density of a highway traffic stream
- T
- On the functional form of the speed-density relationship—I: General theory
  Transportation Research Part B: Methodological, Vol. 29, No. 5
- On deterministic developments of traffic stream models
  Transportation Research Part B: Methodological, Vol. 29, No. 4
- A Mathematical Model of Traffic Flow on a Network of Unidirectional Roads
  SIAM Journal on Mathematical Analysis, Vol. 26, No. 4
- A Local Neural Network Controller for Freeway Ramp Metering
  IFAC Proceedings Volumes, Vol. 27, No. 12
- Multiple agent hybrid control: carrier manifolds and chattering approximations to optimal control
- Continuum modelling of traffic dynamics for congested freeways
  Transportation Research Part B: Methodological, Vol. 27, No. 4
- Car-following as a tool in road traffic simulation
- Kinematic Wave Theory
- Non-linear analysis of a traffic flow
  ZAMP Zeitschrift f�r angewandte Mathematik und Physik, Vol. 40, No. 6
- The relationship between speed, flow and density of a highway traffic stream
- Jams and superjams: a systems approach to congested traffic networks
  Civil Engineering Systems, Vol. 5, No. 4
- The Motion of Several Vehicles on a Road
- The characteristics of congested flow on a freeway across lanes, space, and time
  Transportation Research Part A: General, Vol. 22, No. 1
- Mathematische Modelle des Verkehrsablaufs
- On the dynamics and evolution of some sociotechnical systems
  Bulletin of the American Mathematical Society, Vol. 16, No. 1
- Empirical analysis of freeway flow-density relationships
  Transportation Research Part A: General, Vol. 20, No. 3
- Thermodynamic treatment of nonphysical systems: Formalism and an example (Single-lane traffic)
  Journal of Statistical Physics, Vol. 42, No. 3-4
- A Critical View of Driver Behavior Models: What Do We Know, What Should We Do?
- Hierarchical optimal control of urban traffic networks
  27 April 2007 | International Journal of Control, Vol. 40, No. 4
- Analysis of interrupted traffic flow by finite difference methods
  Transportation Research Part B: Methodological, Vol. 18, No. 4-5
- The asymptotic behaviour of simple kinematic waves of finite volume
  Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, Vol. 387, No. 1793
- Car-Following Models
- Numerical solutions of shock curves of hyperbolic 1-conservation laws
  Mathematical Modelling, Vol. 4, No. 4
- Dynamik und StabilitÄt des Stra\enverkehrs: Ein katastrophentheoretischer Beitrag zur K-Versicherung
  Blätter der DGVFM, Vol. 15, No. 1
- Modelling and analysis of traffic queue dynamics at signalized intersections
  Transportation Research Part A: General, Vol. 13, No. 5
- Perturbation strategies for optimal traffic reassignment
  IEEE Transactions on Automatic Control, Vol. 24, No. 1
- A generalized congestion function for highway travel
  Journal of Urban Economics, Vol. 5, No. 1
- Highway traffic kinematics and the characteristic relation
  28 March 2007 | Transportation Planning and Technology, Vol. 4, No. 2
- Highway congestion and congestion tolls
  Journal of Urban Economics, Vol. 4, No. 3
- A new approach to traffic behaviour: II. Individual car and traffic flow
  International Journal of Man-Machine Studies, Vol. 8, No. 6
- Remarks on the Relationship between Mean-Speed and Concentration in Traffic Flow
  Journal of the Physical Society of Japan, Vol. 38, No. 4
- Entrance ramp control for travel-rate maximization in expressways
  Transportation Research, Vol. 8, No. 6
- Composite car following models
  Transportation Research, Vol. 8, No. 2
- The relationship between speed, flow and density of a highway traffic stream
- Transport behaviour at high densities
  Transportation Research, Vol. 7, No. 4
- Further research on car-following models
  Transportation Research, Vol. 6, No. 3
- The economics of heavily congested roads
  Transportation Research, Vol. 5, No. 4
- Zur Dynamik des Stra�enverkehrs
  Die Naturwissenschaften, Vol. 57, No. 8
- The Asymptotic Approach to Traffic Dynamics
  IEEE Transactions on Systems Science and Cybernetics, Vol. 5, No. 4
- Vehicle accelerations in the hydrodynamic theory of traffic flow
  Transportation Research, Vol. 3, No. 2
- Determining the length of the approach lanes required at signal-controlled intersections on through highways
  Transportation Research, Vol. 2, No. 3
- Topics in the hydrodynamic theory of traffic flow
  Transportation Research, Vol. 2, No. 2
- A Contribution to Theory of Traffic Flow
  1 February 1968
- Study of Automobile Accidents Through Digital Simulation
  1 February 1968
- Improvement of traffic flow and safety by longitudinal control
  Transportation Research, Vol. 1, No. 3
- Mathematical Theory of Automobile Traffic
  Science, Vol. 157, No. 3786
- Car following models and the fundamental diagram of road traffic
  Transportation Research, Vol. 1, No. 1
- Wave theories of traffic flow
  Journal of the Franklin Institute, Vol. 280, No. 1
- A Development of a Conceptual Framework of the Driving Task
  1 August 1964 | Human Factors: The Journal of the Human Factors and Ergonomics Society, Vol. 6, No. 4
- Chapter 3 Fundamental Characteristics of Road Traffic
- Data Acquisition for Traffic Flow Research
  1 January 1962
- Human Factors in Highway Design, Operation and Safety Problems
  1 February 1960 | Human Factors: The Journal of the Human Factors and Ergonomics Society, Vol. 2, No. 1
- Fluctuation Phenomena and Stochastic Processes
  Nature, Vol. 184, No. 4685

Volume 7, Issue 1

January-February 1959

Pages 1-139

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Harold Greenberg, (1959) An Analysis of Traffic Flow. Operations Research 7(1):79-85.

https://doi.org/10.1287/opre.7.1.79

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An Analysis of Traffic Flow

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Volume 7, Issue 1

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