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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.
A landmark work that belongs on the bookshelf of every researcher working with networks In this classic book, first published in 1962, L. R. Ford, Jr., and D. R. Fulkerson set the foundation for the study of network flow problems. The models and algorithms introduced in Flows in Networks are used widely today in the fields of transportation systems, manufacturing, inventory planning, image processing, and Internet traffic. The techniques presented by Ford and Fulkerson spurred the development of powerful computational tools for solving and analyzing network flow models, and also furthered the understanding of linear programming. In addition, the book helped illuminate and unify results in combinatorial mathematics while emphasizing proofs based on computationally efficient construction. With an incisive foreword by Robert Bland and James Orlin, Flows in Networks is rich with insights that remain relevant to current research in engineering, management, and other sciences.
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
This book collects selected presentations of the Meeting of the EURO Working Group on Transportation, which took place at the Department of Ma- ematics at Chalmers University of Technology, Göteborg (or, Gothenburg), Sweden, September 9–11, 1998. [The EURO Working Group on Transpor- tion was founded at the end of the 7th EURO Summer Institute on Urban Traffic Management, which took place in Cetraro, Italy, June 21–July, 1991. There were around 30 founding members of the Working Group, a number which now has grown to around 150. Meetings since then include Paris (1993), Barcelona (1994), and Newcastle (1996). ] About 100 participants were present, enjoying healthy rain and a memorable conference dinner in the Feskekôrka. The total number of presentations at the conference was about 60, coming from quite diverse areas within the field of operations research in transportation, and covering all modes of transport: Deterministic traffic equilibrium models (6 papers) Stochastic traffic equilibrium models (5 papers) Combined traffic models (3 papers) Dynamic traffic models (7 papers) Simulation models (4 papers) Origin–destination matrix estimation (2 papers) Urban public transport models (8 papers) Aircraft scheduling (1 paper) Ship routing (2 papers) Railway planning and scheduling (6 papers) Vehicle routing (3 papers) Traffic management (3 papers) Signal control models (3 papers) Transportation systems analysis (5 papers) ix x TRANSPORTATION PLANNING Among these papers, 14 were eventually selected to be included in this volume.
This text provides a comprehensive and concise treatment of the topic of traffic flow theory and includes several topics relevant to today’s highway transportation system. It provides the fundamental principles of traffic flow theory as well as applications of those principles for evaluating specific types of facilities (freeways, intersections, etc.). Newer concepts of Intelligent transportation systems (ITS) and their potential impact on traffic flow are discussed. State-of-the-art in traffic flow research and microscopic traffic analysis and traffic simulation have significantly advanced and are also discussed in this text. Real world examples and useful problem sets complement each chapter. This textbook is meant for use in advanced undergraduate/graduate level courses in traffic flow theory with prerequisites including two semesters of calculus, statistics, and an introductory course in transportation. The text would also be of interest to transportation professionals as a refresher in traffic flow theory, or as a reference. Students and engineers of diverse backgrounds will find this text accessible and applicable to today’s traffic issues.
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.
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