The Traffic Assignment Problem: Models and Methods (Topics in Transportation Series)
By M. Patriksson
* Publisher: V.S.P. Intl Science
* Number Of Pages: 223
* Publication Date: 1994-10
* ISBN-10 / ASIN: 9067641812
* ISBN-13 / EAN: 9789067641814
Description:
This book is the result of several years of research into the modelling and efficient solution
of problems in transportation planning and related areas.
The aim of this book is to provide a unified account of the development of models and
methods for the problem of estimating equilibrium traffic flows in urban areas, from the
early days of transportation planning heuristics to today's advanced equilibrium models
and methods. Also, the aim is to show the scope and—just as important—the limitations
of present traffic models. The development is described and analyzed using the powerful
instruments of nonlinear optimization and mathematical programming within the field of
operations research. The book includes historical references as well as many recent developments,
and aims to clarify the close relationships between several lines of development
by placing them in a new, unifying framework.
The first part of the book is devoted to mathematical models for the analysis of transportation
network equilibria. Chapter 1 describes the traditional transportation planning
process of which traffic assignment is a central part. The development of traffic assignment
heuristics is described. Chapter 2 analyzes the basic models of traffic assignment,
based on the principles of Wardrop. Existence, uniqueness and stability results are given.
Extensions of the basic models, including non-deterministic travel cost perceptions and
additional flow relationships modelled through the introduction of side constraints, are
discussed. Chapter 3 analyzes traffic equilibrium models for general travel cost functions
such as variational inequality, nonlinear complementarity, and fixed point problems. The
recent development of optimization reformulations of asymmetric variational inequalities
is accounted for in detail.
The second part of the book is devoted to methods for traffic equilibrium problems.
Chapter 4 gives a uniform description of methods for the basic traffic assignment models
and their extensions discussed in Chapter 2. Important concepts, such as partial
linearization, decomposition, and column generation, are described in detail for general
convex programs, and are subsequently used to describe and interrelate traffic assignment
methods. Chapter 5 gives the corresponding treatment of the general traffic equilibrium
models described in Chapter 3, based on the concepts of cost approximation, decomposition,
and column generation. Optimization reformulations of general traffic equilibrium
problems are utilized to derive a new class of traffic equilibrium methods which requires
mild assumptions on the models.
An appendix summarizes the definitions of the concepts most frequently used.
The scope of the material is limited to static models of traffic equilibrium; neither
dynamic nor combined traffic models are dealt with in detail. The results obtained in this
book can, however, be applied to the analysis and solution of such models also.
In order to economize with the space available, the reader is often directed to other
works for more details. The resulting reference list is extensive—it contains more than
1,000 entries—and serves the additional purpose of being a source for anyone interested
in acquiring deeper knowledge in the field.
The book will be of interest to researchers in transportation, operations research, and quantitative economics—and those entering these areas of research—who wish to extend their knowledge
of equilibrium modelling and analysis, and of the foundations of efficient optimization methods
adapted for the solution of large-scale models. The book can also be used in advanced graduate
courses in the areas just mentioned. This book could provide the basic material for a course in
transportation research. A course in structured mathematical programming, with application to
traffic equilibrium problems, is defined by Chapters 2 and 4, or by Chapters 2-5, the latter including
the foundations of variational inequality models and methods. A course in equilibrium modelling is
defined by Chapters 2 and 3.
The text assumes some familiarity with nonlinear programming theory and techniques: it would
therefore be preferable to combine material from this book with that of a modern textbook in
nonlinear programming.
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