Optimization Of Traffic Flow Networks
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Optimization Of Traffic Flow Networks
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Author : Claus Kirchner
language : en
Publisher:
Release Date : 2007
Optimization Of Traffic Flow Networks written by Claus Kirchner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.
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.
Mathematics Of Traffic Flow Networks
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Author : Michael Herty
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2004
Mathematics Of Traffic Flow Networks written by Michael Herty and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
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.
Optimization And Control Of Traffic Flow Networks
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Author : Anita Kumari Singh
language : en
Publisher:
Release Date : 2006
Optimization And Control Of Traffic Flow Networks written by Anita Kumari Singh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.
Modelling And Optimisation Of Flows On Networks
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Author : Luigi Ambrosio
language : en
Publisher: Springer
Release Date : 2012-12-14
Modelling And Optimisation Of Flows On Networks written by Luigi Ambrosio and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-14 with Mathematics categories.
In recent years flows in networks have attracted the interest of many researchers from different areas, e.g. applied mathematicians, engineers, physicists, economists. The main reason for this ubiquity is the wide and diverse range of applications, such as vehicular traffic, supply chains, blood flow, irrigation channels, data networks and others. This book presents an extensive set of notes by world leaders on the main mathematical techniques used to address such problems, together with investigations into specific applications. The main focus is on partial differential equations in networks, but ordinary differential equations and optimal transport are also included. Moreover, the modeling is completed by analysis, numerics, control and optimization of flows in networks. The book will be a valuable resource for every researcher or student interested in the subject.
Simulation And Optimization Of Traffic Flow On Intercity Networks
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Author : Yi-Chin Hu
language : en
Publisher:
Release Date : 1983
Simulation And Optimization Of Traffic Flow On Intercity Networks written by Yi-Chin Hu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Queuing theory categories.
Urban Transport And Hybrid Vehicles
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Author : Seref Soylu
language : en
Publisher: BoD – Books on Demand
Release Date : 2010-08-18
Urban Transport And Hybrid Vehicles written by Seref Soylu and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-18 with Technology & Engineering categories.
This book is the result of valuable contributions from many researchers who work on both technical and nontechnical sides of the field to be remedy for typical road transport problems. Many research results are merged together to make this book a guide for industry, academia and policy makers.
Control Problems For Conservation Laws With Traffic Applications
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Author : Alexandre Bayen
language : en
Publisher: Springer Nature
Release Date : 2022-04-23
Control Problems For Conservation Laws With Traffic Applications written by Alexandre Bayen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-23 with Mathematics categories.
Conservation and balance laws on networks have been the subject of much research interest given their wide range of applications to real-world processes, particularly traffic flow. This open access monograph is the first to investigate different types of control problems for conservation laws that arise in the modeling of vehicular traffic. Four types of control problems are discussed - boundary, decentralized, distributed, and Lagrangian control - corresponding to, respectively, entrance points and tolls, traffic signals at junctions, variable speed limits, and the use of autonomy and communication. Because conservation laws are strictly connected to Hamilton-Jacobi equations, control of the latter is also considered. An appendix reviewing the general theory of initial-boundary value problems for balance laws is included, as well as an appendix illustrating the main concepts in the theory of conservation laws on networks.
A Practical Approach To Advanced Mathematical Modelling In Civil Engineering
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Author : Mohammad Heidarzadeh
language : en
Publisher: Oxford University Press
Release Date : 2025-04-18
A Practical Approach To Advanced Mathematical Modelling In Civil Engineering written by Mohammad Heidarzadeh and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-18 with Technology & Engineering categories.
A Practical Approach to Advanced Mathematical Modelling in Civil Engineering introduces advanced mathematical techniques and modelling concepts through real-world practical applications in key areas of Civil Engineering. It fills a crucial gap in the existing literature by using examples from structural analysis, coastal processes, and soil behaviour. The authors approach to teaching has been developed over years of experience and aims to engage readers by demonstrating the universal utility of mathematical methods in solving engineering challenges. The chapters are designed around engineering subject areas such as structural, transportation, and geotechnical engineering. A focus on engineering rather than mathematical concepts helps students of engineering to concentrate on real-world applications and prescribe available mathematical techniques to each, as well as being useful for expanding the knowledge of already practicing engineers. The appendix backs this learning up with basic engineering mathematics, providing a comprehensive resource for all levels from undergraduate and graduate engineering students. Those already familiar with the basics can turn to the appendix at a later date to revisit their knowledge. The book will also be accompanied by a companion website hosting downloadable ready-to-use computer programs and code addressing real-world engineering problems, designed in the popular programming environment MATLAB. For those who are unfamiliar with the program, Appendix B provides a useful introduction to MATLAB. These codes are referred to throughout the book and are available for readers to download and use themselves.
Traffic Congestion Control By Pde Backstepping
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Author : Huan Yu
language : en
Publisher: Springer Nature
Release Date : 2022-12-16
Traffic Congestion Control By Pde Backstepping written by Huan Yu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-16 with Science categories.
This monograph explores the design of controllers that suppress oscillations and instabilities in congested traffic flow using PDE backstepping methods. The first part of the text is concerned with basic backstepping control of freeway traffic using the Aw-Rascle-Zhang (ARZ) second-order PDE model. It begins by illustrating a basic control problem – suppressing traffic with stop-and-go oscillations downstream of ramp metering – before turning to the more challenging case for traffic upstream of ramp metering. The authors demonstrate how to design state observers for the purpose of stabilization using output-feedback control. Experimental traffic data are then used to calibrate the ARZ model and validate the boundary observer design. Because large uncertainties may arise in traffic models, adaptive control and reinforcement learning methods are also explored in detail. Part II then extends the conventional ARZ model utilized until this point in order to address more complex traffic conditions: multi-lane traffic, multi-class traffic, networks of freeway segments, and driver use of routing apps. The final chapters demonstrate the use of the Lighthill-Whitham-Richards (LWR) first-order PDE model to regulate congestion in traffic flows and to optimize flow through a bottleneck. In order to make the text self-contained, an introduction to the PDE backstepping method for systems of coupled first-order hyperbolic PDEs is included. Traffic Congestion Control by PDE Backstepping is ideal for control theorists working on control of systems modeled by PDEs and for traffic engineers and applied scientists working on unsteady traffic flows. It will also be a valuable resource for researchers interested in boundary control of coupled systems of first-order hyperbolic PDEs.
Theory Numerics And Applications Of Hyperbolic Problems I
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Author : Christian Klingenberg
language : en
Publisher: Springer
Release Date : 2018-06-23
Theory Numerics And Applications Of Hyperbolic Problems I written by Christian Klingenberg and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-23 with Mathematics categories.
The first of two volumes, this edited proceedings book features research presented at the XVI International Conference on Hyperbolic Problems held in Aachen, Germany in summer 2016. It focuses on the theoretical, applied, and computational aspects of hyperbolic partial differential equations (systems of hyperbolic conservation laws, wave equations, etc.) and of related mathematical models (PDEs of mixed type, kinetic equations, nonlocal or/and discrete models) found in the field of applied sciences.