Mathematical Theories of Traffic Flow

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

The author uses mathematical techniques to give an in-depth look at models for mechanical vibrations, population dynamics, and traffic flow.

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.

The understanding of empirical traf?c congestion occurring on unsignalized mul- lane highways and freeways is a key for effective traf?c management, control, or- nization, and other applications of transportation engineering. However, the traf?c ?ow theories and models that dominate up to now in transportation research journals and teaching programs of most universities cannot explain either traf?c breakdown or most features of the resulting congested patterns. These theories are also the - sis of most dynamic traf?c assignment models and freeway traf?c control methods, which therefore are not consistent with features of real traf?c. For this reason, the author introduced an alternative traf?c ?ow theory called three-phase traf?c theory, which can predict and explain the empirical spatiot- poral features of traf?c breakdown and the resulting traf?c congestion. A previous book “The Physics of Traf?c” (Springer, Berlin, 2004) presented a discussion of the empirical spatiotemporal features of congested traf?c patterns and of three-phase traf?c theory as well as their engineering applications. Rather than a comprehensive analysis of empirical and theoretical results in the ?eld, the present book includes no more empirical and theoretical results than are necessary for the understanding of vehicular traf?c on unsignalized multi-lane roads. The main objectives of the book are to present an “elementary” traf?c ?ow theory and control methods as well as to show links between three-phase traf?c t- ory and earlier traf?c ?ow theories. The need for such a book follows from many commentsofcolleaguesmadeafterpublicationofthebook“ThePhysicsofTraf?c”.

The purpose of this four volume series is to make available for college teachers and students samples of important and realistic applications of mathematics which can be covered in undergraduate programs. The goal is to provide illustrations of how modem mathematics is actually employed to solve relevant contemporary problems. Although these independent chapters were prepared primarily for teachers in the general mathematical sciences, they should prove valuable to students, teachers, and research scientists in many of the fields of application as well. Prerequisites for each chapter and suggestions for the teacher are provided. Several of these chapters have been tested in a variety of classroom settings, and all have undergone extensive peer review and revision. Illustrations and exercises are included in most chapters. Some units can be covered in one class, whereas others provide sufficient material for a few weeks of class time. Volume 1 contains 23 chapters and deals with differential equations and, in the last four chapters, problems leading to partial differential equations. Applications are taken from medicine, biology, traffic systems and several other fields. The 14 chapters in Volume 2 are devoted mostly to problems arising in political science, but they also address questions appearing in sociology and ecology. Topics covered include voting systems, weighted voting, proportional representation, coalitional values, and committees. The 14 chapters in Volume 3 emphasize discrete mathematical methods such as those which arise in graph theory, combinatorics, and networks.

The core of ths book presents a theory developed by the author to combine the recent insight into empirical data with mathematical models in freeway traffic research based on dynamical non-linear processes.

Transportation is generally concerned with the efficient, safe, and sustainable movement of people and goods. Transportation engineers work on various aspects of the five stages essential in the life cycle of a transportation facility: planning, designing, building, operating, and maintaining. In the planning stage, we typically forecast traffic demands for a future year/analysis period, perform a preliminary evaluation of alternative solutions, or identify priorities for system improvements. 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. 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.

This book addresses the reader interested in vehicular traffic phenomena, who have not learned about them before. It presents traffic phenomena like traffic breakdown and the emergence of moving traffic jams by showcasing empirical traffic data measured in real-world traffic. The author explains how these empirical traffic studies have led to the three-phase traffic theory and why this new theory is in conflict with standard traffic theories developed before. Moreover, he presents the reason for the failure of applications of standard traffic theories in real-world traffic and discusses why understanding real traffic has caused a paradigm shift in traffic and transportation science. The book examines why understanding real traffic breakdown is the basis for an explanation for the autonomous driving effects on traffic flow. It shows that understanding real traffic is possible from real-world traffic data without the need of mathematical traffic models. This makes the book intuitive for non-specialists, who can qualitatively understand all the basic features of traffic dynamics. In turn, experienced traffic researchers can grasp concepts and ideas made here easily accessible by the author, one of the leading pioneers in the field of vehicular traffic.

Traffic Theory describes and illustrates the key models of traffic flow and associated traffic phenomena such as conflicts in traffic, traffic generation and assignment, and traffic control. The use of these various models are explored both in terms of how they have improved traffic systems over the years and how better implementation of these models can accelerate the successful deployment of Intelligent Transportation Systems (ITS). Furthermore, the book outlines opportunities for development of additional models needed for continued improvement of ITS. The book is intended as a textbook for a college Transportation Science curriculum, and as a reference book for researchers in Transportation Science. Dr. Gazis has concentrated in the book's presentation on the fundamental concepts and methods in the various areas of traffic theory.