Download or read book Mathematics of Traffic Flow Networks written by Michael Herty and published by Logos Verlag Berlin GmbH. This book was released on 2004 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Traffic Flow on Networks written by Mauro Garavello and published by Debolsillo. This book was released on 2006 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Traffic Flow on Transportation Networks written by Gordon Frank Newell and published by MIT Press (MA). This book was released on 1980 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains in detail the advantages and limitations of network analysis applied to transportation problems.
Download or read book A Mathematical Model of Traffic Flow on a Network of Unidirectional Roads written by Helge Holden and published by . This book was released on 1992 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Flows in Transportation Networks written by Oliver and published by Academic Press. This book was released on 1972-09-29 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: Flows in Transportation Networks
Download or read book Optimization of Traffic Flow Networks written by Claus Kirchner and published by . This book was released on 2007 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematical Theories of Traffic Flow written by Haight and published by Academic Press. This book was released on 1963-01-01 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Theories of Traffic Flow
Download or read book Models for Vehicular Traffic on Networks written by Mauro Garavello and published by . This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Traffic Flow Dynamics written by Martin Treiber and published by Springer Science & Business Media. This book was released on 2012-10-10 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Advanced Engineering Mathematics written by Dennis G. Zill and published by Jones & Bartlett Learning. This book was released on 2006 with total page 1060 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thoroughly Updated, Zill'S Advanced Engineering Mathematics, Third Edition Is A Compendium Of Many Mathematical Topics For Students Planning A Career In Engineering Or The Sciences. A Key Strength Of This Text Is Zill'S Emphasis On Differential Equations As Mathematical Models, Discussing The Constructs And Pitfalls Of Each. The Third Edition Is Comprehensive, Yet Flexible, To Meet The Unique Needs Of Various Course Offerings Ranging From Ordinary Differential Equations To Vector Calculus. Numerous New Projects Contributed By Esteemed Mathematicians Have Been Added. Key Features O The Entire Text Has Been Modernized To Prepare Engineers And Scientists With The Mathematical Skills Required To Meet Current Technological Challenges. O The New Larger Trim Size And 2-Color Design Make The Text A Pleasure To Read And Learn From. O Numerous NEW Engineering And Science Projects Contributed By Top Mathematicians Have Been Added, And Are Tied To Key Mathematical Topics In The Text. O Divided Into Five Major Parts, The Text'S Flexibility Allows Instructors To Customize The Text To Fit Their Needs. The First Eight Chapters Are Ideal For A Complete Short Course In Ordinary Differential Equations. O The Gram-Schmidt Orthogonalization Process Has Been Added In Chapter 7 And Is Used In Subsequent Chapters. O All Figures Now Have Explanatory Captions. Supplements O Complete Instructor'S Solutions: Includes All Solutions To The Exercises Found In The Text. Powerpoint Lecture Slides And Additional Instructor'S Resources Are Available Online. O Student Solutions To Accompany Advanced Engineering Mathematics, Third Edition: This Student Supplement Contains The Answers To Every Third Problem In The Textbook, Allowing Students To Assess Their Progress And Review Key Ideas And Concepts Discussed Throughout The Text. ISBN: 0-7637-4095-0
Download or read book Mathematical Descriptions of Traffic Flow Micro Macro and Kinetic Models written by Gabriella Puppo and published by Springer Nature. This book was released on 2021-03-31 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Traffic Flow Theory written by Daiheng Ni and published by Butterworth-Heinemann. This book was released on 2015-11-09 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Introduction to Network Traffic Flow Theory written by Wen-Long Jin and published by Elsevier. This book was released on 2021-04-13 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Network Traffic Flow Theory: Principles, Concepts, Models, and Methods provides a comprehensive introduction to modern theories for modeling, mathematical analysis and traffic simulations in road networks. The book breaks ground, addressing traffic flow theory in a network setting and providing researchers and transportation professionals with a better understanding of how network traffic flows behave, how congestion builds and dissipates, and how to develop strategies to alleviate network traffic congestion. The book also shows how network traffic flow theory is key to understanding traffic estimation, control, management and planning. Users wills find this to be a great resource on both theory and applications across a wide swath of subjects, including road networks and reduced traffic congestion. Covers the most theoretically and practically relevant network traffic flow theories Provides a systematic introduction to traditional and recently developed models, including cell transmission, link transmission, link queue, point queue, macroscopic and microscopic models, junction models and network stationary states Applies modern network traffic flow theory to real-world applications in modeling, analysis, estimation, control, management and planning
Download or read book Breakdown in Traffic Networks written by Boris S. Kerner and published by Springer. This book was released on 2017-05-26 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a detailed investigation of breakdowns in traffic and transportation networks. It shows empirically that transitions from free flow to so-called synchronized flow, initiated by local disturbances at network bottlenecks, display a nucleation-type behavior: while small disturbances in free flow decay, larger ones grow further and lead to breakdowns at the bottlenecks. Further, it discusses in detail the significance of this nucleation effect for traffic and transportation theories, and the consequences this has for future automatic driving, traffic control, dynamic traffic assignment, and optimization in traffic and transportation networks. Starting from a large volume of field traffic data collected from various sources obtained solely through measurements in real world traffic, the author develops his insights, with an emphasis less on reviewing existing methodologies, models and theories, and more on providing a detailed analysis of empirical traffic data and drawing consequences regarding the minimum requirements for any traffic and transportation theories to be valid. The book - proves the empirical nucleation nature of traffic breakdown in networks - discusses the origin of the failure of classical traffic and transportation theories - shows that the three-phase theory is incommensurable with the classical traffic theories, and - explains why current state-of-the art dynamic traffic assignments tend to provoke heavy traffic congestion, making it a valuable reference resource for a wide audience of scientists and postgraduate students interested in the fundamental understanding of empirical traffic phenomena and related data-driven phenomenology, as well as for practitioners working in the fields of traffic and transportation engineering.
Download or read book Advances in Dynamic Network Modeling in Complex Transportation Systems written by Satish V. Ukkusuri and published by Springer Science & Business Media. This book was released on 2013-03-21 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited book focuses on recent developments in Dynamic Network Modeling, including aspects of route guidance and traffic control as they relate to transportation systems and other complex infrastructure networks. Dynamic Network Modeling is generally understood to be the mathematical modeling of time-varying vehicular flows on networks in a fashion that is consistent with established traffic flow theory and travel demand theory. Dynamic Network Modeling as a field has grown over the last thirty years, with contributions from various scholars all over the field. The basic problem which many scholars in this area have focused on is related to the analysis and prediction of traffic flows satisfying notions of equilibrium when flows are changing over time. In addition, recent research has also focused on integrating dynamic equilibrium with traffic control and other mechanism designs such as congestion pricing and network design. Recently, advances in sensor deployment, availability of GPS-enabled vehicular data and social media data have rapidly contributed to better understanding and estimating the traffic network states and have contributed to new research problems which advance previous models in dynamic modeling. A recent National Science Foundation workshop on “Dynamic Route Guidance and Traffic Control” was organized in June 2010 at Rutgers University by Prof. Kaan Ozbay, Prof. Satish Ukkusuri , Prof. Hani Nassif, and Professor Pushkin Kachroo. This workshop brought together experts in this area from universities, industry and federal/state agencies to present recent findings in this area. Various topics were presented at the workshop including dynamic traffic assignment, traffic flow modeling, network control, complex systems, mobile sensor deployment, intelligent traffic systems and data collection issues. This book is motivated by the research presented at this workshop and the discussions that followed.
Download or read book Flows in Networks written by Lester Randolph Ford and published by . This book was released on 2016-04-19 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents simple, elegant methods for dealing, both in theory and in application, with a variety of problems that have formulations in terms of flows in capacity-constrained networks. Since the theoretical considerations lead in all cases to computationally efficient solution procedures, the hook provides a common meeting ground for persons interested in operations research, industrial and communications engineering, or combinatorial mathematics. Originally published in 1962. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Download or read book Traffic and Granular Flow 01 written by Minoru Fukui and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last decade physicists, engineers and computer scientists have joined in an enormously fruitful dialogue about traffic and granular flow. Cars and sand grains have in common, that they interact irreversibly, which is the reason for similar jamming phenomena. The main difference is that car drivers choose their destination and route individually, while grains follow external driving forces. This book gives an overview about the progress in modelling, computer simulation, experiments and field observations, which was reached within the last two years. The contributions are based on the International Workshop Traffic and Granular Flow '01, which took place in Nagoya, 15 - 17 October 2001. Topics include a critical classification of models for highway traffic, new technological applications, friction and arching phenomena in pedestrian traffic, scale free networks and internet traffic, instabilities and fluctuations in avalanches and granular pipe flow.
