This book is focused on the discussion of the traffic assignment problem, the mathematical and practical meaning of variables, functions and basic principles. This work gives information about new approaches, methods and algorithms based on original methodological technique, developed by authors in their publications for the past several years, as well as corresponding prospective implementations. The book may be of interest to a wide range of readers, such as civil engineering students, traffic engineers, developers of traffic assignment algorithms etc. The obtained results here are to be used in both practice and theory. This book is devoted to the traffic assignment problem, formulated in a form of nonlinear optimization program. The most efficient solution algorithms related to the problem are based on its structural features and practical meaning rather than on standard nonlinear optimization techniques or approaches. The authors have carefully considered the meaning of the traffic assignment problem for efficient algorithms development.

This comprehensive work examines important recent developments and modern applications in the fields of optimization, control, game theory and equilibrium programming. In particular, the concepts of equilibrium and optimality are of immense practical importance affecting decision-making problems regarding policy and strategies, and in understanding and predicting systems in different application domains, ranging from economics and engineering to military applications. The book consists of 29 survey chapters written by distinguished researchers in the above areas.

The interest in the mathematical modeling of transportation systems stems from the need to predict how people might make use of new or improved transport infrastruc ture in order to evaluate the benefit of the required investments. To this end it is necessary to build models of the demand for transportation and models that de termine the way in which people who travel use the transportation network. If such models may be constructed and their validity reasonably assured, then the predic tion of the traffic flows on future and present transportation links may be carried out by simulating future situations and then evaluating the potential benefits of alternative improvement projects. In the attempts that were made to construct mathematical models of transportation networks, the notion of equilibrium plays a central role. Suppose that the demand for transportation, that is, the number of trips that occur between the - rious origins and destinations is known. Then it is necessary to determine how these trips are attracted to the alternative routes available between origins and destinations. Knight (1924), gave a simple and intuitively clear description of the behaviour of road traffic under conditions of congestion.

This monograph provides both a unified account of the development of models and methods for the problem of estimating equilibrium traffic flows in urban areas and a survey of the scope and limitations of present traffic models. The development is described and analyzed by the use of the powerful instruments of nonlinear optimization and mathematical programming within the field of operations research. The first part is devoted to mathematical models for the analysis of transportation network equilibria; the second deals with methods for traffic equilibrium problems. This title will interest readers wishing to extend their knowledge of equilibrium modeling and analysis and of the foundations of efficient optimization methods adapted for the solution of large-scale models. In addition to its value to researchers, the treatment is suitable for advanced graduate courses in transportation, operations research, and quantitative economics.

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.

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.