Dynamic Network User Equilibrium

This book presents advanced research in a relatively new field of scholarly inquiry that is usually referred to as dynamic network user equilibrium, now almost universally abbreviated as DUE. It provides the first synthesis of results obtained over the last decade from applying the differential variational inequality (DVI) formalism to study the DUE problem. In particular, it explores the intimately related problem of dynamic network loading, which determines the arc flows and effective travel delays (or generalized travel costs) arising from the expression of departure rates at the origins of commuter trips between the workplace and home. In particular, the authors show that dynamic network loading with spillback of queues into upstream arcs may be formulated as a differential algebraic equation system. They demonstrate how the dynamic network loading problem and the dynamic traffic user equilibrium problem may be solved simultaneously rather than sequentially, as well as how the first-in-first-out queue discipline may be maintained for each when Lighthill-Whitham-Richardson traffic flow theory is used. A number of recent and new extensions of the DVI-based theory of DUE and corresponding examples are presented and discussed. Relevant mathematical background material is provided to make the book as accessible as possible.

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.

"This book provides a rigorous and comprehensive coverage of transportation models and planning methods and is a must-have to anyone in the transportation community, including students, teachers, and practitioners." Moshe Ben-Akiva, Massachusetts Institute of Technology.

'Since the extraordinary impact of networks is self-evident today both in the field of telecommunications and transportation as well as in the field of economic and financial equilibria, the scientific work carried out by Patrizia Daniele appears as an outstanding resource. The author employs with uncommon competence mathematical topics that are at the forefront of the science, while at the same time enabling the reader to understand the matter treated without any difficulty. Moreover the reader is fascinated by the clarity, depth and soundness with which the evolutionary equilibria problems are studied and by the original efficient computational procedures which allow for the solving of many significant examples and concrete problems. Without any doubt the book represents a shining light and a necessary tool for scholars of pure and applied mathematics, for economists and engineers as well as for practitioners, general managers and managing directors.' - Antonino Maugeri, Università di Catania, Italy This book offers a comprehensive analysis of dynamic networks and evolutionary variational inequalities, a topic of growing prominence in the study of networks. The extraordinary importance of networks in finance, mathematics, computer science and other areas is well known but the relatively new concept of 'dynamic' networks is less well understood. They become dynamic when the constitutive elements of the phenomena associated with the fixed geometry of networks are considered to be evolving over time. Patrizia Daniele offers many numerical examples to illustrate the issues discussed and provides a broad appendix to enrich this challenging but deeply informative book.

This book has been written to address the increasing number of Operations Research and Management Science problems (that is, applications) that involve the explicit consideration of time and of gaming among multiple agents. It is a book that will be used both as a textbook and as a reference and guide by those whose work involves the theoretical aspects of dynamic optimization and differential games.

From driverless cars to vehicular networks, recent technological advances are being employed to increase road safety and improve driver satisfaction. As with any newly developed technology, researchers must take care to address all concerns, limitations, and dangers before widespread public adoption. Transportation Systems and Engineering: Concepts, Methodologies, Tools, and Applications addresses current trends in transportation technologies, such as smart cars, green technologies, and infrastructure development. This multivolume book is a critical reference source for engineers, computer scientists, transportation authorities, students, and practitioners in the field of transportation systems management.

'the editors have done an excellent job in bringing together a comprehensive collection of cutting edge research findings on network theory. . .' - Sierdjan Koster, European Spatial Research and Policy

MICHEL GENDREAU AND PATRICE MARCOTTE As an academic, Michael Florian has always stood at the forefront of transportation research. This is reflected in the miscellaneous contributions that make the chapters of this book, which are related in some way or another to Michael's interests in both the theoretical and practical aspects of his field. These interests span the areas of Traffic Assignment, Network Equilibrium, Shortest Paths, Railroad problems, De mand models, Variational Inequalities, Intelligent Transportation Systems, etc. The contributions are briefly outlined below. BASSANINI, LA BELLA AND NASTASI determine a track pricing policy for railroad companies through the solution of a generalized Nash game. BEN-AKIVA, BIER LAIRE, KOUTSOPOULOS AND MISHALANI discuss simulation-based estimators of the interactions between supply and demand within a real-time transportation system. BOYCE, BALASUBRAMANIAM AND TIAN analyze the impact of marginal cost pricing on urban traffic in the Chicago region. BROTCORNE, DE WOLF, GENDREAU AND LABBE present a discrete model of dynamic traffic assignment where flow departure is endogenous and the First-In-First-Out condition is strictly enforced. CASCETTA AND IMP ROTA give a rigorous treatment of the problem of estimating travel demand from observed data, both in the static and dynamic cases. CRAINIC, DUFOUR, FLo RIAN AND LARIN show how to obtain path information that is consistent with the link information provided by a nonlinear multimodal model. ERLANDER derives the logit model from an efficiency principle rather than from the classical random utility approach.