Traffic Flow On Networks

This book explains in detail the advantages and limitations of network analysis applied to transportation problems.

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.

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.

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

This book describes a coherent approach to the explanation of the movement of individual vehicles or groups of vehicles. To avoid possible misunderstandings, some preliminary remarks are called for. 1. This is intended to be a textbook. It brings together methods and approaches that are widely distributed throughout the literature and that are therefore difficult to assess. Text citations of sources have been avoided; literature references are listed together at the end of the book. 2. The book is intended primarily for students of engineering. It describes the theoretical background necessary for an understanding of the methods by which links in a road network are designed and dimensioned or by which traffic is controlled; the methods themselves are not dealt with. It may also assist those actually working in such sectors to interpret the results of traffic flow measure ments more accurately than has hitherto been the case. 3. The book deals with traffic flow on links between nodes, and not at nodes themselves. Many readers will probably regret this, since nodes are usually the bottlenecks which limit the capacity of the road network. A book dedicated to the node would be the obvious follow-up. A separation of link and node is justified, however, partly because the quantity of material has to be kept within reasonable bounds and partly because the treatment of traffic flow at nodes requires additional mathematical techniques (in particular, those relating to queueing theory).

The problems of urban traffic in the industrially developed countries have been at the top of the priority list for a long time. While making a critical contribution to the economic well being of those countries, transportation systems in general and highway traffic in particular, also have detrimental effects which are evident in excessive congestion, high rates of accidents and severe pollution problems. Scientists from different disciplines have played an important role in the development and refinement of the tools needed for the planning, analysis, and control of urban traffic networks. In the past several years, there were particularly rapid advances in two areas that affect urban traffic: 1. Modeling of traffic flows in urban networks and the prediction of the resulting equilibrium conditions; 2. Technology for communication with the driver and the ability to guide him, by providing him with useful, relevant and updated information, to his desired destination.

Traditionally, networking has had little or no basis in analysis or architectural development, with designers relying on technologies they are most familiar with or being influenced by vendors or consultants. However, the landscape of networking has changed so that network services have now become one of the most important factors to the success of many third generation networks. It has become an important feature of the designer's job to define the problems that exist in his network, choose and analyze several optimization parameters during the analysis process, and then prioritize and evaluate these parameters in the architecture and design of the system. Network Analysis, Architecture, and Design, Third Edition, uses a systems methodology approach to teaching these concepts, which views the network (and the environment it impacts) as part of the larger system, looking at interactions and dependencies between the network and its users, applications, and devices. This approach matches the new business climate where customers drive the development of new services and the book discusses how networks can be architected and designed to provide many different types of services to customers. With a number of examples, analogies, instructor tips, and exercises, this book works through the processes of analysis, architecture, and design step by step, giving designers a solid resource for making good design decisions. With examples, guidelines, and general principles McCabe illuminates how a network begins as a concept, is built with addressing protocol, routing, and management, and harmonizes with the interconnected technology around it. Other topics covered in the book are learning to recognize problems in initial design, analyzing optimization parameters, and then prioritizing these parameters and incorporating them into the architecture and design of the system. This is an essential book for any professional that will be designing or working with a network on a routine basis. Substantially updated design content includes ad hoc networks, GMPLS, IPv6, and mobile networking Written by an expert in the field that has designed several large-scale networks for government agencies, universities, and corporations Incorporates real-life ideas and experiences of many expert designers along with case studies and end-of-chapter exercises