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Author: Michael Herty Publisher: Logos Verlag Berlin GmbH ISBN: Category : Mathematics Languages : en Pages : 150
Book Description
Traffic flow has been a continuous source of challenging mathematical problems. The following work is dedicated to recent questions in modeling, simulation and optimization of traffic flow networks. Mathematics can help to solve traffic problems in different ways. Modelling provides fundamental understanding of traffic dynamics and behaviour. Optimization yields solutions for complex situations and helps to organize traffic flow. During the last decade there has been intensive research in different fields of and related to traffic flow. One of the primary research activities focus on the development of new and more realistic models for traffic flow on a single road. Our work's primary focus is on models for networks. We provide new ideas on modelling flow in networks and solve different optimization problems analytically and numerically. The main result is the derivation of a hierarchy of models treating different situations with suitable traffic flow models. To each level of modeling we consider the optimal control problems and present techniques to address those problems. Furthermore, we derive an adjoint calculus for scalar hyperbolic equations with nonlinear boundary controls. The derived concepts fit for general network problems as well as they do for traffic flow issues. The principles of modeling and simplification can be applied to all kinds of network flows, like fluid flow in open channels or gas networks.
Author: Michael Herty Publisher: Logos Verlag Berlin GmbH ISBN: Category : Mathematics Languages : en Pages : 150
Book Description
Traffic flow has been a continuous source of challenging mathematical problems. The following work is dedicated to recent questions in modeling, simulation and optimization of traffic flow networks. Mathematics can help to solve traffic problems in different ways. Modelling provides fundamental understanding of traffic dynamics and behaviour. Optimization yields solutions for complex situations and helps to organize traffic flow. During the last decade there has been intensive research in different fields of and related to traffic flow. One of the primary research activities focus on the development of new and more realistic models for traffic flow on a single road. Our work's primary focus is on models for networks. We provide new ideas on modelling flow in networks and solve different optimization problems analytically and numerically. The main result is the derivation of a hierarchy of models treating different situations with suitable traffic flow models. To each level of modeling we consider the optimal control problems and present techniques to address those problems. Furthermore, we derive an adjoint calculus for scalar hyperbolic equations with nonlinear boundary controls. The derived concepts fit for general network problems as well as they do for traffic flow issues. The principles of modeling and simplification can be applied to all kinds of network flows, like fluid flow in open channels or gas networks.
Author: Claus Kirchner Publisher: ISBN: 9783832516789 Category : Languages : en Pages : 0
Book Description
The focus of the thesis is placed on macroscopic traffic flow models on networks and corresponding optimal control problems. We present a multi-class traffic model on traffic flow networks that respects driver's destination preferences, i.e., everyone arrives at their desired destination. The result is based on and extends ideas and models devised in publications by Coclite, Garavello and Piccoli in 2005. In particular, we modify their coupling conditions at junctions and show with selected examples how to use the formulas and how they relate to existing road network models. Furthermore, we discuss the solution structure of the new multi-class model in detail and show that we can always construct a weak solution. For the special case of two classes we conduct a more detailed analysis of how to solve Riemann-problems for junctions of a particular type. Numerical simulations are carried out as well. The second aspect treated in the thesis concerns optimization. We review a general framework for PDE-constrained optimization and use it as a basis for the formal derivation of first order necessary optimality conditions for a traffic and a supply network. However, our presented formulas are not mathematically rigorous since we did not prove that all the appearing operators are well-defined in our setup. Nonetheless, the numerical results indicate that the derived equations are correct. The proposed optimization algorithm, essentially a projected gradient method, works reliably. In order to speed up the optimization process, we also investigate an instantaneous control approach in the context of traffic flow networks. Another key result is the derivation of the well-known Aw-Rascle model from a simplified kinetic model on a single road. The derivation implies that kinetic traffic flow models can contain more information than macroscopic ones. Therefore, it is worth studying them in their own right. Additionally, it might we worthwile to investigate kinetic models in a network setup.
Author: Martin Treiber Publisher: Springer Science & Business Media ISBN: 3642324592 Category : Science Languages : en Pages : 505
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: Daiheng Ni Publisher: Butterworth-Heinemann ISBN: 0128041471 Category : Technology & Engineering Languages : en Pages : 414
Book Description
Creating Traffic Models is a challenging task because some of their interactions and system components are difficult to adequately express in a mathematical form. Traffic Flow Theory: Characteristics, Experimental Methods, and Numerical Techniques provide traffic engineers with the necessary methods and techniques for mathematically representing traffic flow. The book begins with a rigorous but easy to understand exposition of traffic flow characteristics including Intelligent Transportation Systems (ITS) and traffic sensing technologies. Includes worked out examples and cases to illustrate concepts, models, and theories Provides modeling and analytical procedures for supporting different aspects of traffic analyses for supporting different flow models Carefully explains the dynamics of traffic flow over time and space
Author: Michael Herty
Author: Michael Herty
Author: Mauro Garavello
Author: Helge Holden
Author: Gordon Frank Newell
Author: Claus Kirchner
Author: Oliver
Author: Haight
Author: Mauro Garavello
Author: Martin Treiber
Author: Daiheng Ni