Kinematic Wave and Cellular Automaton Models for Traffic Flow PDF Download
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Author: Jeffrey Kent Wiens
Publisher:
ISBN:
Category : Cellular automata
Languages : en
Pages : 0
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Book Description
We apply both cellular automaton (CA) and kinematic wave (KW) models to simulating vehicle traffic. We investigate three different CA models and show how each choice affects the fundamental diagram, which is a plot of the traffic flux versus density. Based on these CA simulations as well as empirical observations in the literature, we propose that the fundamental diagram can be approximated by a piecewise linear function having a discontinuity at a single point. We then construct a KW model that consists of a hyperbolic conservation law for the traffic density with this this discontinuous, non-convex function as the traffic flux function. We then derive the exact solution of the corresponding Riemann problem analytically for general piecewise constant initial data, which requires use of a mollifier to smooth out the discontinuity in the flux function. Another necessary component of the analytical solution is the construction of a convex hull for the mollified problem, which is then considered in the limit as the support of the mollifier goes to zero. Finally, the Riemann solution is used to construct a high resolution finite volume scheme for the KW model, which we use to simulate various traffic scenarios and draw comparisons with not only the CA model but also the analytical solution of the KW problem.
Author: Jeffrey Kent Wiens
Publisher:
ISBN:
Category : Cellular automata
Languages : en
Pages : 0
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Book Description
We apply both cellular automaton (CA) and kinematic wave (KW) models to simulating vehicle traffic. We investigate three different CA models and show how each choice affects the fundamental diagram, which is a plot of the traffic flux versus density. Based on these CA simulations as well as empirical observations in the literature, we propose that the fundamental diagram can be approximated by a piecewise linear function having a discontinuity at a single point. We then construct a KW model that consists of a hyperbolic conservation law for the traffic density with this this discontinuous, non-convex function as the traffic flux function. We then derive the exact solution of the corresponding Riemann problem analytically for general piecewise constant initial data, which requires use of a mollifier to smooth out the discontinuity in the flux function. Another necessary component of the analytical solution is the construction of a convex hull for the mollified problem, which is then considered in the limit as the support of the mollifier goes to zero. Finally, the Riemann solution is used to construct a high resolution finite volume scheme for the KW model, which we use to simulate various traffic scenarios and draw comparisons with not only the CA model but also the analytical solution of the KW problem.
Author: Carlos Daganzo
Publisher:
ISBN:
Category : Cellular automata
Languages : en
Pages : 28
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Book Description
This paper proves that the vehicle trajectories predicted by (i) a simple linear carfollowing model, CF(L), (ii) the kinematic wave model with a triangular fundamental diagram, KW(T), and (iii) two cellular automata models CA(L) and CA(M) match everywhere to within a tolerance comparable with a single "jam spacing". Thus, CF(L) = KW(T) = CA(L,M).
Author: Martin Treiber
Publisher: Springer Science & Business Media
ISBN: 3642324606
Category : Science
Languages : en
Pages : 505
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Book Description
This textbook provides a comprehensive and instructive coverage of vehicular traffic flow dynamics and modeling. It makes this fascinating interdisciplinary topic, which to date was only documented in parts by specialized monographs, accessible to a broad readership. Numerous figures and problems with solutions help the reader to quickly understand and practice the presented concepts. This book is targeted at students of physics and traffic engineering and, more generally, also at students and professionals in computer science, mathematics, and interdisciplinary topics. It also offers material for project work in programming and simulation at college and university level. The main part, after presenting different categories of traffic data, is devoted to a mathematical description of the dynamics of traffic flow, covering macroscopic models which describe traffic in terms of density, as well as microscopic many-particle models in which each particle corresponds to a vehicle and its driver. Focus chapters on traffic instabilities and model calibration/validation present these topics in a novel and systematic way. Finally, the theoretical framework is shown at work in selected applications such as traffic-state and travel-time estimation, intelligent transportation systems, traffic operations management, and a detailed physics-based model for fuel consumption and emissions.
Author: Wenlong Jin
Publisher:
ISBN:
Category :
Languages : en
Pages : 444
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Book Description
Author: Serge P. Hoogendoorn
Publisher: Springer Science & Business Media
ISBN: 354028091X
Category : Mathematics
Languages : en
Pages : 593
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Book Description
These proceedings are the fifth in the series Traffic and Granular Flow, and we hope they will be as useful a reference as their predecessors. Both the realistic modelling of granular media and traffic flow present important challenges at the borderline between physics and engineering, and enormous progress has been made since 1995, when this series started. Still the research on these topics is thriving, so that this book again contains many new results. Some highlights addressed at this conference were the influence of long range electric and magnetic forces and ambient fluids on granular media, new precise traffic measurements, and experiments on the complex decision making of drivers. No doubt the “hot topics” addressed in granular matter research have diverged from those in traffic since the days when the obvious analogies between traffic jams on highways and dissipative clustering in granular flow intrigued both c- munities alike. However, now just this diversity became a stimulating feature of the conference. Many of us feel that our joint interest in complex systems, where many simple agents, be it vehicles or particles, give rise to surprising and fascin- ing phenomena, is ample justification for bringing these communities together: Traffic and Granular Flow has fostered cooperation and friendship across the scientific disciplines.
Author: National Research Council (U.S.). Transportation Research Board
Publisher:
ISBN:
Category : Traffic estimation
Languages : en
Pages : 176
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Book Description
Author: Gabriella Puppo
Publisher: Springer Nature
ISBN: 3030665607
Category : Mathematics
Languages : en
Pages : 102
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Book Description
The book originates from the mini-symposium "Mathematical descriptions of traffic flow: micro, macro and kinetic models" organised by the editors within the ICIAM 2019 Congress held in Valencia, Spain, in July 2019. The book is composed of five chapters, which address new research lines in the mathematical modelling of vehicular traffic, at the cutting edge of contemporary research, including traffic automation by means of autonomous vehicles. The contributions span the three most representative scales of mathematical modelling: the microscopic scale of particles, the mesoscopic scale of statistical kinetic description and the macroscopic scale of partial differential equations.The work is addressed to researchers in the field.
Author: Femke Kessels
Publisher: Springer
ISBN: 3319786954
Category : Business & Economics
Languages : en
Pages : 139
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Book Description
This book introduces readers to the main traffic flow modelling approaches and discusses their features and applications. It provides a comprehensive and cutting-edge review of traffic flow models, from their roots in the 1930s to the latest developments in the field. In addition, it presents problem sets that offer readers further insights into the models and hands-on experience with simulation approaches. The simulations used in the exercises can be built upon for readers’ own research or other applications. The models discussed in this book are applied to describe, predict and control traffic flows on roads with the aid of rapid and accurate estimations of current and future states. The book shows how these models are developed, what their chief characteristics are, and how they can be effectively employed.
Author: Dietrich E Wolf
Publisher: World Scientific
ISBN: 9814547948
Category :
Languages : en
Pages : 394
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Book Description
Prediction of traffic (like weather forecast), its planning and control are counted among the great scientific and technological challenges. Similarly, flow of granular material like tablets or powders is of immense importance for industrial processing of solids. Both fields have intriguing conceptual analogies.From 9-11 October, 1995, the German Supercomputing Center HLRZ (Höchstleitungsrechenzentrum) at the research center Jülich (KFA) organized an international workshop 'Traffic and Granular Flow'. The purpose of this workshop was to promote the interaction between these two scientific fields, to which supercomputing is making essential contributions, and to stimulate the transfer between basic and applied research.
Author: Alejandro Salcido
Publisher: BoD – Books on Demand
ISBN: 953307230X
Category : Computers
Languages : en
Pages : 584
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Book Description
Cellular automata make up a class of completely discrete dynamical systems, which have became a core subject in the sciences of complexity due to their conceptual simplicity, easiness of implementation for computer simulation, and their ability to exhibit a wide variety of amazingly complex behavior. The feature of simplicity behind complexity of cellular automata has attracted the researchers' attention from a wide range of divergent fields of study of science, which extend from the exact disciplines of mathematical physics up to the social ones, and beyond. Numerous complex systems containing many discrete elements with local interactions have been and are being conveniently modelled as cellular automata. In this book, the versatility of cellular automata as models for a wide diversity of complex systems is underlined through the study of a number of outstanding problems using these innovative techniques for modelling and simulation.
