Multi-class continuum traffic flow models : analysis and simulation methods. Thesis Delft University of Technology.

How to model and simulate traffic flow including different vehicles such as cars and trucks ? This dissertation answers this question by analyzing existing models and simulation methods and by developing new ones. The new model (Fastlane) describes traffic as a continuum flow while accounting for different types of vehicles. It is reformulated in Lagrangian coordinates. Using the reformulation, mathematical properties of the model are analyzed and efficient simulation methods are developed. (Author/publisher)

[1]  Warren F. Phillips,et al.  A kinetic model for traffic flow with continuum implications , 1979 .

[2]  Patrizia Bagnerini,et al.  A Multiclass Homogenized Hyperbolic Model of Traffic Flow , 2003, SIAM J. Math. Anal..

[3]  C. Daganzo A variational formulation of kinematic waves: basic theory and complex boundary conditions , 2005 .

[4]  R. Courant,et al.  On the Partial Difference Equations, of Mathematical Physics , 2015 .

[5]  Thijs Johan Muizelaar Non-recurrent traffic situations and traffic information: determining preferences and effects on route choice , 2011 .

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

[7]  Nima Zaerpour,et al.  Efficient Management of Compact Storage Systems , 2008 .

[8]  J. Lebacque THE GODUNOV SCHEME AND WHAT IT MEANS FOR FIRST ORDER TRAFFIC FLOW MODELS , 1996 .

[9]  B. van Arem,et al.  Gas-Kinetic Traffic Flow Modeling Including Continuous Driver Behavior Models , 2002 .

[10]  T. W. Schaap,et al.  Driving Behaviour in Unexpected Situations , 2012 .

[11]  Olga Huibregtse,et al.  Robust model-based optimization of evacuation guidance , 2013 .

[12]  S. Wong,et al.  Hyperbolicity and kinematic waves of a class of multi-population partial differential equations , 2006, European Journal of Applied Mathematics.

[13]  L. A. Pipes An Operational Analysis of Traffic Dynamics , 1953 .

[14]  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.

[15]  Erik S. Van Vleck,et al.  Partial Difference Equations. , 2005 .

[16]  Shing Chung Josh Wong,et al.  A multi-class traffic flow model: an extension of LWR model with heterogeneous drivers , 2002 .

[17]  K. Hasebe,et al.  Analysis of optimal velocity model with explicit delay , 1998, patt-sol/9805002.

[18]  F. Zheng Modelling urban travel times , 2011 .

[19]  C. Daganzo THE CELL TRANSMISSION MODEL.. , 1994 .

[20]  Dong Ngoduy Multiclass first-order modelling of traffic networks using discontinuous flow-density relationships , 2010 .

[21]  Bart van Arem,et al.  A multi-class macroscopic intersection model , 2012 .

[22]  Stef Smulders,et al.  Control of freeway traffic flow by variable speed signs , 1990 .

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

[24]  Nicola Bellomo,et al.  TRAFFIC, CROWDS, AND SWARMS , 2008 .

[25]  D. Helbing Traffic and related self-driven many-particle systems , 2000, cond-mat/0012229.

[26]  J. Lebacque First-Order Macroscopic Traffic Flow Models: Intersection Modeling, Network Modeling , 2005 .

[27]  S. Hoogendoorn,et al.  Lagrangian Formulation of Multiclass Kinematic Wave Model , 2010 .

[28]  Ludovic Leclercq,et al.  A mechanism to describe the formation and propagation of stop-and-go waves in congested freeway traffic , 2010, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[29]  R. B. Carmona Benitez The Design of a Large Scale Airline Network , 2012 .

[30]  D. Helbing,et al.  LETTER TO THE EDITOR: Macroscopic simulation of widely scattered synchronized traffic states , 1999, cond-mat/9901119.

[31]  Amir Gharehgozli,et al.  Developing New Methods for Efficient Container Stacking Operations , 2012 .

[32]  J.H.R. van Duin,et al.  Logistics Concept Development in Multi-Actor Environments , 2012 .

[33]  Gunnar Flötteröd,et al.  Operational macroscopic modeling of complex urban road intersections , 2011 .

[34]  Mohinder S. Grewal,et al.  Identification of Parameters in a Freeway Traffic Model , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[35]  Chantal C. Cantarelli,et al.  Cost Overruns in Large-scale Transport Infrastructure Projects - A theoretical and empirical exploration for the Netherlands and worldwide , 2011 .

[36]  Ludovic Leclercq,et al.  The Hamilton-Jacobi Partial Differential Equation and the Three Representations of Traffic Flow , 2013 .

[37]  Ludovic Leclercq,et al.  The Lagrangian Coordinates and What it Means for First Order Traffic Flow Models , 2007 .

[38]  A. Klar,et al.  Congestion on Multilane Highways , 2002, SIAM J. Appl. Math..

[39]  Serge P. Hoogendoorn,et al.  State-of-the-art of vehicular traffic flow modelling , 2001 .

[40]  S Logghe,et al.  Multi-class kinematic wave theory of traffic flow , 2008 .

[41]  Dong Ngoduy,et al.  Multiclass first-order simulation model to explain non-linear traffic phenomena , 2007 .

[42]  Wen-Long Jin,et al.  An instantaneous kinematic wave theory of diverging traffic , 2013 .

[43]  R. Sollacher,et al.  Multi-anticipative car-following model , 1999 .

[44]  Serge P. Hoogendoorn,et al.  Fastlane: Traffic flow modeling and multi-class dynamic traffic management , 2012 .

[45]  Salissou Moutari,et al.  A Hybrid Lagrangian Model Based on the Aw--Rascle Traffic Flow Model , 2007, SIAM J. Appl. Math..

[46]  B S Kemer,et al.  THREE-PHASE TRAFFIC THEORY AND HIGHWAY CAPACITY , 2004 .

[47]  I. Lubashevsky,et al.  Probabilistic description of traffic breakdowns. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[48]  Carlos F. Daganzo,et al.  THE CELL TRANSMISSION MODEL, PART II: NETWORK TRAFFIC , 1995 .

[49]  Rinaldo M. Colombo,et al.  An $n$-populations model for traffic flow , 2003, European Journal of Applied Mathematics.

[50]  C. Buisson,et al.  Macroscopic Model and Its Numerical Solution for Two-Flow Mixed Traffic with Different Speeds and Lengths , 2003 .

[51]  Serge P. Hoogendoorn,et al.  Genealogy of traffic flow models , 2015, EURO J. Transp. Logist..

[52]  R. E. Wilson,et al.  Car-following models: fifty years of linear stability analysis – a mathematical perspective , 2011 .

[53]  P. Taneja,et al.  The Flexible Port , 2013 .

[54]  Jean-Baptiste Lesort,et al.  Mixing Microscopic and Macroscopic Representations of Traffic Flow: Hybrid Model Based on Lighthill–Whitham–Richards Theory , 2003 .

[55]  Reinhart D Kuhne,et al.  Greenshields’ Legacy: Highway Traffic , 2011 .

[56]  Dirk Helbing,et al.  Reply to comment on “On the controversy around Daganzo’s requiem for and Aw-Rascle’s resurrection of second-order traffic flow models” by H.M. Zhang , 2009 .

[57]  Dirk Helbing,et al.  Understanding widely scattered traffic flows, the capacity drop, and platoons as effects of variance-driven time gaps. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[58]  Dirk Helbing,et al.  MASTER: macroscopic traffic simulation based on a gas-kinetic, non-local traffic model , 2001 .

[59]  J Treiterer,et al.  THE HYSTERESIS PHENOMENON IN TRAFFIC FLOW , 1974 .

[60]  L. Leclercq A New Numerical Scheme for Bounding Acceleration in the LWR Model , 2007 .

[61]  Serge P. Hoogendoorn,et al.  Fastlane: New Multiclass First-Order Traffic Flow Model , 2008 .

[62]  Maarten Kroesen,et al.  Human Response to Aircraft Noise , 2011 .

[63]  Michael Z. F. Li A Generic Characterization of Equilibrium Speed-Flow Curves , 2008, Transp. Sci..

[64]  D. Gazis,et al.  Nonlinear Follow-the-Leader Models of Traffic Flow , 1961 .

[65]  Sven Vlassenroot,et al.  The acceptability of in-vehicle Intelligent Speed Assistance (ISA) systems : from trial support to public support. Thesis Delft University of Technology. , 2011 .

[66]  Vipin Tyagi,et al.  A review of mathematical models for the flow of traffic and some recent results , 2008 .

[67]  Dirk Cattrysse,et al.  A generic class of first order node models for dynamic macroscopic simulation of traffic flows , 2011 .

[68]  Boris S. Kerner,et al.  Cellular automata approach to three-phase traffic theory , 2002, cond-mat/0206370.

[69]  Serge P. Hoogendoorn,et al.  Discontinuities in the Lagrangian formulation of the kinematic wave model , 2013 .

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

[71]  R. Ansorge What does the entropy condition mean in traffic flow theory , 1990 .

[72]  Ludovic Leclercq,et al.  A Multiclass Car-Following Rule Based on the LWR Model , 2009 .

[73]  Mike McDonald,et al.  Car-following: a historical review , 1999 .

[74]  Hani S. Mahmassani,et al.  A Porous Flow Model for Disordered Heterogeneous Traffic Streams , 2012 .

[75]  Michael Schreckenberg,et al.  A cellular automaton model for freeway traffic , 1992 .

[76]  Dirk Helbing,et al.  Reconstructing the spatio-temporal traffic dynamics from stationary detector data , 2002 .

[77]  Serge P. Hoogendoorn,et al.  Network-Wide Traffic State Estimation Using Loop Detector and Floating Car Data , 2014, J. Intell. Transp. Syst..

[78]  J. Lebacque,et al.  Generic Second Order Traffic Flow Modelling , 2007 .

[79]  James M. Greenberg,et al.  Extensions and Amplifications of a Traffic Model of Aw and Rascle , 2000, SIAM J. Appl. Math..

[80]  H. M. Zhang New Perspectives on Continuum Traffic Flow Models , 2001 .

[81]  K. Kockelman Changes in Flow-Density Relationship Due to Environmental, Vehicle, and Driver Characteristics , 1998 .

[82]  Serge P. Hoogendoorn,et al.  Dynamic First-Order Modeling of Phase-Transition Probabilities , 2009 .

[83]  L. Ludovic,et al.  The Lagrangian Coordinates Applied to the LWR Model , 2008 .

[84]  Benjamin Coifman,et al.  Extended bottlenecks, the fundamental relationship, and capacity drop on freeways , 2011 .

[85]  Nicola Bellomo,et al.  On the Modeling of Traffic and Crowds: A Survey of Models, Speculations, and Perspectives , 2011, SIAM Rev..

[86]  H. M. Zhang A mathematical theory of traffic hysteresis , 1999 .

[87]  Rainer Wiedemann,et al.  SIMULATION DES STRASSENVERKEHRSFLUSSES. , 1974 .

[88]  I. Prigogine,et al.  A Boltzmann-Like Approach for Traffic Flow , 1960 .

[89]  Axel Klar,et al.  Derivation of Continuum Traffic Flow Models from Microscopic Follow-the-Leader Models , 2002, SIAM J. Appl. Math..

[90]  Av van der Vlies,et al.  Rail transport risks and urban planning : solving deadlock situations between urban planning and rail transport of hazardous materials in The Netherlands. Thesis Radboud Universiteit Nijmegen. , 2011 .

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

[92]  G. F. Newell A simplified theory of kinematic waves in highway traffic, part I: General theory , 1993 .

[93]  Solomon Kidane Zegeye,et al.  Model-Based Traffic Control for Sustainable Mobility , 2011 .

[94]  Dirk Helbing,et al.  Delays, inaccuracies and anticipation in microscopic traffic models , 2006 .

[95]  J. P. Lebacque Intersection Modeling, Application to Macroscopic Network Traffic Flow Models and Traffic Management , 2005 .

[96]  Stephane Chanut,et al.  A First-Order Macroscopic Traffic Flow Model for Mixed Traffic Including Moving Bottleneck Effects , 2005 .

[97]  Carlos F. Daganzo,et al.  A BEHAVIORAL THEORY OF MULTI-LANE TRAFFIC FLOW. PART I, LONG HOMOGENEOUS FREEWAY SECTIONS , 1999 .

[98]  H. M. Zhang Comment on “On the controversy around Daganzo’s requiem for and Aw-Rascle’s resurrection of second-order traffic flow models" by D. Helbing and A.F. Johansson , 2009 .

[99]  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.

[100]  R. LeVeque Finite Volume Methods for Hyperbolic Problems: Characteristics and Riemann Problems for Linear Hyperbolic Equations , 2002 .

[101]  Elise Miller-Hooks,et al.  A Porous Flow Approach to Modeling Heterogeneous Traffic in Disordered Systems , 2011 .

[102]  Dirk Helbing,et al.  Numerical simulation of macroscopic traffic equations , 1999, Comput. Sci. Eng..

[103]  Jorge A. Laval Hysteresis in traffic flow revisited: An improved measurement method , 2011 .

[104]  D. Helbing,et al.  Cellular Automata Simulating Experimental Properties of Traffic Flow , 1998, cond-mat/9812300.

[105]  Carlos F. Daganzo,et al.  Lane-changing in traffic streams , 2006 .

[106]  B. Kerner,et al.  A microscopic model for phase transitions in traffic flow , 2002 .

[107]  M Cremer,et al.  A fast simulation model for traffic flow on the basis of Boolean operations , 1986 .

[108]  Anthony T. Chronopoulos,et al.  Traffic flow simulation through high order traffic modelling , 1993 .

[109]  Gordon F. Newell,et al.  A SIMPLIFIED THEORY OF KINEMATIC WAVES IN HIGHWAY TRAFFIC, PART III: MULTI-DESTINATION FLOWS , 1993 .

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

[111]  Gordon F. Newell,et al.  A simplified car-following theory: a lower order model , 2002 .

[112]  Luc J. J. Wismans,et al.  Towards sustainable dynamic traffic management , 2012 .

[113]  E. Montroll,et al.  Traffic Dynamics: Studies in Car Following , 1958 .

[114]  Wilhelm Leutzbach,et al.  Introduction to the Theory of Traffic Flow , 1987 .

[115]  Dirk Helbing,et al.  Three-phase traffic theory and two-phase models with a fundamental diagram in the light of empirical stylized facts , 2010, 1004.5545.

[116]  H. M. Zhang,et al.  Anisotropic property revisited––does it hold in multi-lane traffic? , 2003 .

[117]  A. Schadschneider,et al.  Empirical test for cellular automaton models of traffic flow. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[118]  Ihor Lubashevsky,et al.  Probabilistic Description of Traffic Breakdown , 2002 .

[119]  Yufei Yuan,et al.  Lagrangian Multi-Class Traffic State Estimation , 2013 .

[120]  Swaroop Darbha,et al.  A dynamical systems approach based on averaging to model the macroscopic flow of freeway traffic , 2008 .

[121]  Boris S. Kerner,et al.  Introduction to Modern Traffic Flow Theory and Control: The Long Road to Three-Phase Traffic Theory , 2009 .

[122]  Thomas Schreiter,et al.  Vehicle-Class-Specific Control of Freeway Traffic , 2013 .

[123]  Soyoung Ahn,et al.  Driver Turn-Taking Behavior in Congested Freeway Merges , 2004 .

[124]  C. Daganzo Requiem for second-order fluid approximations of traffic flow , 1995 .

[125]  D. Helbing Fundamentals of traffic flow , 1997, cond-mat/9806080.

[126]  R. M. Michaels,et al.  Perceptual Factors in Car-Following , 1963 .

[127]  D. Helbing,et al.  On the controversy around Daganzo’s requiem for and Aw-Rascle’s resurrection of second-order traffic flow models , 2008, 0805.3402.

[128]  Helbing,et al.  Congested traffic states in empirical observations and microscopic simulations , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[129]  Boris S. Kerner,et al.  Deterministic microscopic three-phase traffic flow models , 2006 .

[130]  Dirk Helbing,et al.  Evaluation of Single Vehicle Data in Dependence of the Vehicle-Type, Lane, and Site , 2000 .

[131]  Jorge A. Laval,et al.  Microscopic modeling of the relaxation phenomenon using a macroscopic lane-changing model , 2008 .

[132]  Serge P. Hoogendoorn,et al.  Generic gas-kinetic traffic systems modeling with applications to vehicular traffic flow , 2001 .

[133]  D. Helbing,et al.  DERIVATION, PROPERTIES, AND SIMULATION OF A GAS-KINETIC-BASED, NONLOCAL TRAFFIC MODEL , 1999, cond-mat/9901240.

[134]  Robert Herman,et al.  Traffic Dynamics: Analysis of Stability in Car Following , 1959 .

[135]  Gábor Stépán,et al.  Traffic jams: dynamics and control , 2010, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[136]  Serge P. Hoogendoorn,et al.  Sinks and Sources in Lagrangian Coordinates: Derivation, Interpretation and Simulation Results , 2011 .

[137]  Ludovic Leclercq,et al.  Moving Bottlenecks in Lighthill-Whitham-Richards Model: A Unified Theory , 2004 .

[138]  M. Dicke-Ogenia,et al.  Psychological Aspects of Travel Information Presentation , 2012 .

[139]  Soyoung Ahn,et al.  Empirical macroscopic evaluation of freeway merge-ratios , 2010 .

[140]  R. E. Wilson,et al.  Mechanisms for spatio-temporal pattern formation in highway traffic models , 2008, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[141]  Serge P. Hoogendoorn,et al.  Multi-anticipation and heterogeneity in car-following empirics and a first exploration of their implications , 2006, 2006 IEEE Intelligent Transportation Systems Conference.

[142]  Lily Elefteriadou,et al.  Development of Passenger Car Equivalents for Freeways, Two-Lane Highways, and Arterials , 1997 .

[143]  S. Hoogendoorn,et al.  Anisotropy in generic multi-class traffic flow models , 2013 .

[144]  Dong Ngoduy,et al.  Multiclass first-order traffic model using stochastic fundamental diagrams , 2011 .

[145]  J. M. D. Castillo Three new models for the flow–density relationship: derivation and testing for freeway and urban data , 2012 .

[146]  Gordon F. Newell,et al.  INSTABILITY IN DENSE HIGHWAY TRAFFIC: A REVIEW. , 1965 .

[147]  Carlos F. Daganzo,et al.  In Traffic Flow, Cellular Automata = Kinematic Waves , 2004 .

[148]  S. L. Paveri-Fontana,et al.  On Boltzmann-like treatments for traffic flow: A critical review of the basic model and an alternative proposal for dilute traffic analysis , 1975 .

[149]  H. C. Dickinson,et al.  THE PHOTOGRAPHIC METHOD OF STUDYING TRAFFIC BEHAVIOR , 1934 .

[150]  Markos Papageorgiou,et al.  SOME REMARKS ON MACROSCOPIC TRAFFIC FLOW MODELLING , 1998 .

[151]  Carlos F. Daganzo,et al.  A SIMPLE PHYSICAL PRINCIPLE FOR THE SIMULATION OF FREEWAYS WITH SPECIAL LANES AND PRIORITY VEHICLES , 1997 .

[152]  Serge P. Hoogendoorn,et al.  Real-Time Lagrangian Traffic State Estimator for Freeways , 2012, IEEE Transactions on Intelligent Transportation Systems.

[153]  C. Daganzo A variational formulation of kinematic waves: Solution methods , 2005 .

[154]  F. Knight Some Fallacies in the Interpretation of Social Cost , 1924 .

[155]  Wen-Long Jin,et al.  The Inhomogeneous Kinematic Wave Traffic Flow Model as a Resonant Nonlinear System , 2003, Transp. Sci..

[156]  Serge P. Hoogendoorn,et al.  New Generic Multiclass Kinematic Wave Traffic Flow Model , 2014 .

[157]  Martin Treiber,et al.  Verkehrsdynamik und -simulation - Daten, Modelle und Anwendungen der Verkehrsflussdynamik , 2010 .

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

[159]  J P Lebacque,et al.  A TWO PHASE EXTENSION OF THE LRW MODEL BASED ON THE BOUNDEDNESS OF TRAFFIC ACCELERATION , 2002 .

[160]  M. Cassidy,et al.  Some traffic features at freeway bottlenecks , 1999 .

[161]  윤태영,et al.  Transportation Research Board of the National Academies , 2015 .

[162]  Ludovic Leclercq,et al.  "A Note on the Entropy Solutions of the Hydrodynamic Model of Traffic Flow" Revisited , 2011, Transp. Sci..

[163]  D. Buckley A Semi-Poisson Model of Traffic Flow , 1968 .

[164]  C. Vuik,et al.  Assessment of multi class kinematic wave models , 2012 .

[165]  Kerner,et al.  Experimental features and characteristics of traffic jams. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[166]  Haris N. Koutsopoulos,et al.  Hybrid Mesoscopic-Microscopic Traffic Simulation , 2004 .

[167]  Tamás Máhr,et al.  Vehicle Routing under Uncertainty , 2011 .

[168]  P. G. Gipps,et al.  A behavioural car-following model for computer simulation , 1981 .

[169]  Boris S. Kerner,et al.  Phase Transitions in Traffic Flow , 2000 .

[170]  S. P. Hoogendoorn,et al.  Multiclass continuum modelling of multilane traffic flow , 1999 .

[171]  Nakayama,et al.  Dynamical model of traffic congestion and numerical simulation. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.