Mathematics Of Traffic Flow Networks
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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.
Traffic Flow On Networks
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Author : Mauro Garavello
language : en
Publisher: Debolsillo
Release Date : 2006
Traffic Flow On Networks written by Mauro Garavello and has been published by Debolsillo this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Conservation laws (Mathematics) categories.
A Mathematical Model Of Traffic Flow On A Network Of Unidirectional Roads
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Author : Helge Holden
language : en
Publisher:
Release Date : 1992
A Mathematical Model Of Traffic Flow On A Network Of Unidirectional Roads written by Helge Holden and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with categories.
Introduction To Network Traffic Flow Theory
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Author : Wen-Long Jin
language : en
Publisher: Elsevier
Release Date : 2021-04-13
Introduction To Network Traffic Flow Theory written by Wen-Long Jin and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-13 with Transportation categories.
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
Advanced Engineering Mathematics
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Author : Dennis G. Zill
language : en
Publisher: Jones & Bartlett Learning
Release Date : 2006
Advanced Engineering Mathematics written by Dennis G. Zill and has been published by Jones & Bartlett Learning this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
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
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.
The Mathematics Of Networks
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Author : Stefan Andrus Burr
language : en
Publisher: American Mathematical Soc.
Release Date : 1982
The Mathematics Of Networks written by Stefan Andrus Burr and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Mathematics categories.
The theory of networks is a very lively one, both in terms of developments in the theory itself and of the variety of its applications. This book, based on the 1981 AMS Short Course on the Mathematics of Networks, introduces most of the basic ideas of network theory and develops some of these ideas considerably.
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.
Advances In Dynamic Network Modeling In Complex Transportation Systems
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Author : Satish V. Ukkusuri
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-21
Advances In Dynamic Network Modeling In Complex Transportation Systems written by Satish V. Ukkusuri and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-21 with Business & Economics categories.
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.
Decision Policies For Production Networks
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Author : Dieter Armbruster
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-03-05
Decision Policies For Production Networks written by Dieter Armbruster and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-05 with Business & Economics categories.
The financial results of any manufacturing company can be dramatically impacted by the repetitive decisions required to control a complex production network be it a network of machines in a factory; a network of factories in a company; or a network of companies in a supply chain. Decision Policies for Production Networks presents recent convergent research on developing policies for operating production networks including details of practical control and decision techniques which can be applied to improve the effectiveness and economic efficiency of production networks worldwide. Researchers and practitioners come together to explore a wide variety of approaches to a range of topics including: WIP and equipment management policies, Material release policies, Machine, factory, and supply chain network policies for delivery in the face of supply and demand variability, and Conflicts between complex production network models and their controlling policies. Case studies and relevant mathematical techniques are included to support and explain techniques such as heuristics, global and hierarchical optimization, control theory and filtering approaches related to complex systems or traffic flows. Decision Policies for Production Networks acts as handbook for researchers and practitioners alike, providing findings and information which can be applied to develop methods and advance further research across production networks.