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Transport Theory and Statistical Physics Volume 25, 1996 - Issue 7
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Original Articles

A kinetic model for vehicular traffic derived from a stochastic microscopic model

R. Wegener Fachbereich Mathematik Universität, Kaiserslautern, 67663, Kaiserslautern Germany
&
A. Klar Fachbereich Mathematik Universität, Kaiserslautern, 67663, Kaiserslautern Germany
Pages 785-798 | Received 24 Apr 1995, Accepted 22 Feb 1996, Published online: 13 Sep 2006

Citations (34)

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K. T. Waldeer. (2004) Numerical Investigation of a Mesoscopic Vehicular Traffic Flow Model Based on a Stochastic Acceleration Process. Transport Theory and Statistical Physics 33:1, pages 31-46.
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K. T. Waldeer. (2004) A Vehicular Traffic Flow Model Based on a Stochastic Acceleration Process. Transport Theory and Statistical Physics 33:1, pages 7-30.
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Articles from other publishers (32)

Michael Herty, Gabriella Puppo & Giuseppe Visconti. (2023) Model of vehicle interactions with autonomous cars and its properties. Discrete and Continuous Dynamical Systems - B 28:2, pages 833.
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Elisa Iacomini. 2023. Advances in Numerical Methods for Hyperbolic Balance Laws and Related Problems. Advances in Numerical Methods for Hyperbolic Balance Laws and Related Problems 121 138 .
Aman Kumar Singh, Jarrett Meyer & Subramanian Ramakrishnan. (2022) On the emergence of traffic jams in a stochastic traffic flow driven by additive and multiplicative white Gaussian noise processes. Journal of Statistical Mechanics: Theory and Experiment 2022:12, pages 123401.
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Michael Herty & Elisa Iacomini. (2022) Uncertainty quantification in hierarchical vehicular flow models. Kinetic and Related Models 15:2, pages 239.
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Danial Rezaei, Iman Aghayan & Farhad Hadadi. (2021) Studying perturbations and wave propagations by lane closures on traffic characteristics based on a dynamic approach. Physica A: Statistical Mechanics and its Applications 566, pages 125654.
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Young-Pil Choi & Seok-Bae Yun. (2021) Existence and Hydrodynamic Limit for a Paveri-Fontana Type Kinetic Traffic Model. SIAM Journal on Mathematical Analysis 53:2, pages 2631-2659.
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Juan Calvo, Juanjo Nieto & Mohamed Zagour. (2019) Kinetic Model for Vehicular Traffic with Continuum Velocity and Mean Field Interactions. Symmetry 11:9, pages 1093.
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Michael Herty, Salissou Moutari & Giuseppe Visconti. (2018) Macroscopic Modeling of Multilane Motorways Using a Two-Dimensional Second-Order Model of Traffic Flow. SIAM Journal on Applied Mathematics 78:4, pages 2252-2278.
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Florent Berthelin, Thierry Goudon, Bastien Polizzi & Magali Ribot. (2017) Asymptotic problems and numerical schemes for traffic flows with unilateral constraints describing the formation of jams. Networks and Heterogeneous Media 12:4, pages 591-617.
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Giuseppe Visconti, Michael Herty, Gabriella Puppo & Andrea Tosin. (2017) Multivalued Fundamental Diagrams of Traffic Flow in the Kinetic Fokker--Planck Limit. Multiscale Modeling & Simulation 15:3, pages 1267-1293.
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Gabriella Puppo, Matteo Semplice, Andrea Tosin & Giuseppe Visconti. (2016) Kinetic models for traffic flow resulting in a reduced space of microscopic velocities. Kinetic and Related Models 10:3, pages 823-854.
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. 2016. Traffic Flow Theory. Traffic Flow Theory 379 386 .
Daiheng Ni. 2016. Traffic Flow Theory. Traffic Flow Theory 361 377 .
Luisa Fermo & Andrea Tosin. (2014) A fully-discrete-state kinetic theory approach to traffic flow on road networks. Mathematical Models and Methods in Applied Sciences 25:03, pages 423-461.
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Benedetto Piccoli & Andrea Tosin. 2009. Encyclopedia of Complexity and Systems Science. Encyclopedia of Complexity and Systems Science 1 37 .
Benedetto Piccoli & Andrea Tosin. 2011. Mathematics of Complexity and Dynamical Systems. Mathematics of Complexity and Dynamical Systems 1748 1770 .
Daiheng Ni. (2010) A spectrum of traffic flow modeling at multiple scales. A spectrum of traffic flow modeling at multiple scales.
Benedetto Piccoli & Andrea Tosin. 2009. Encyclopedia of Complexity and Systems Science. Encyclopedia of Complexity and Systems Science 9727 9749 .
MARCELLO DELITALA & ANDREA TOSIN. (2011) MATHEMATICAL MODELING OF VEHICULAR TRAFFIC: A DISCRETE KINETIC THEORY APPROACH. Mathematical Models and Methods in Applied Sciences 17:06, pages 901-932.
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Stephane Cordier, Lorenzo Pareschi & Giuseppe Toscani. (2005) On a Kinetic Model for a Simple Market Economy. Journal of Statistical Physics 120:1-2, pages 253-277.
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K.T. Waldeer. (2003) The direct simulation Monte Carlo method applied to a Boltzmann-like vehicular traffic flow model. Computer Physics Communications 156:1, pages 1-12.
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Alexandros Sopasakis. (2003) Formal Asymptotic Models of Vehicular Traffic. Model Closures. SIAM Journal on Applied Mathematics 63:5, pages 1561-1584.
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N. BELLOMO, M. DELITALA & V. COSCIA. (2011) ON THE MATHEMATICAL THEORY OF VEHICULAR TRAFFIC FLOW I: FLUID DYNAMIC AND KINETIC MODELLING. Mathematical Models and Methods in Applied Sciences 12:12, pages 1801-1843.
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N. Bellomo, A. Marasco & A. Romano. (2002) From the modelling of driver's behavior to hydrodynamic models and problems of traffic flow. Nonlinear Analysis: Real World Applications 3:3, pages 339-363.
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Dirk Helbing. (2001) Traffic and related self-driven many-particle systems. Reviews of Modern Physics 73:4, pages 1067-1141.
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B. S. Kerner. 2000. Traffic and Granular Flow ’99. Traffic and Granular Flow ’99 253 283 .
Axel Klar & Raimund Wegener. 2000. Modeling in Applied Sciences. Modeling in Applied Sciences 263 316 .
Paul Nelson & Alexandros Sopasakis. (1998) The prigogine-herman kinetic model predicts widely scattered traffic flow data at high concentrations. Transportation Research Part B: Methodological 32:8, pages 589-604.
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Axel Klar & Raimund Wegener. (1998) A Hierarchy of Models for Multilane Vehicular Traffic I: Modeling. SIAM Journal on Applied Mathematics 59:3, pages 983-1001.
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B. S. Kerner, S. L. Klenov & P. Konhäuser. (1997) Asymptotic theory of traffic jams. Physical Review E 56:4, pages 4200-4216.
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N Bellomo & M Lo Schiavo. (1997) From the Boltzmann equation to generalized kinetic models in applied sciences. Mathematical and Computer Modelling 26:7, pages 43-76.
Crossref
A. Klar & R. Wegener. (1997) Enskog-like kinetic models for vehicular traffic. Journal of Statistical Physics 87:1-2, pages 91-114.
Crossref

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