The Traffic Assignment Problem

Models and Methods
 
 
Dover Publications (Verlag)
  • erschienen am 19. Januar 2015
  • |
  • 240 Seiten
 
E-Book | ePUB mit Adobe DRM | Systemvoraussetzungen
978-0-486-80227-5 (ISBN)
 
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.
weitere Ausgaben werden ermittelt
Michael Patriksson
  • Title Page
  • Copyright Page
  • Table of Contents
  • Preface
  • Some notations
  • I Models
  • 1 Urban traffic planning
  • 1.1 Introduction
  • 1.2 The transportation planning process
  • 1.3 Organization and goal definition
  • 1.4 Base year inventory
  • 1.5 Model analysis
  • 1.5.1 Trip generation
  • 1.5.2 Trip distribution
  • 1.5.3 Modal split
  • 1.5.4 Traffic assignment
  • 1.6 Travel forecast
  • 1.7 Network evaluation
  • 1.8 Discussion
  • 2 The basic equilibrium model and extensions
  • 2.1 The Wardrop conditions
  • 2.1.1 The fixed demand case
  • 2.1.2 The variable demand case
  • 2.1.3 Discussion
  • 2.2 The mathematical program for user equilibrium
  • 2.2.1 The fixed demand case
  • 2.2.2 Network representations
  • 2.2.3 The elastic demand case
  • 2.2.4 Equivalent fixed demand reformulations
  • 2.2.5 Discussion
  • 2.3 Properties of equilibrium solutions
  • 2.3.1 Existence of equilibrium solutions
  • 2.3.2 Uniqueness of equilibrium solutions
  • 2.3.3 Further properties of equilibrium solutions
  • 2.3.4 Stability and sensitivity of equilibrium solutions
  • 2.4 User equilibrium versus system optimum
  • 2.5 Nonseparable costs and multiclass-user transportation networks
  • 2.6 Related network problem
  • 2.6.1 Traffic equilibria and network games
  • 2.6.2 Discrete traffic equilibrium models
  • 2.6.3 Traffic equilibria and electrical networks
  • 2.6.4 Spatial price equilibria
  • 2.6.5 Optimal message routing in computer communication networks
  • 2.7 Discussion
  • 2.8 Some extension
  • 2.8.1 Stochastic assignment models
  • 2.8.2 Side constrained assignment models
  • 3 General traffic equilibrium models
  • 3.1 Introduction
  • 3.1.1 Alternative definitions of equilibria
  • 3.1.2 Variational inequality problems
  • 3.1.3 Nonlinear complementarity problems
  • 3.1.4 Fixed point problems
  • 3.1.5 Mathematical programming reformulations
  • 3.2 Traffic equilibrium models
  • 3.2.1 Variational inequality models
  • 3.2.2 Nonlinear complementarity models
  • 3.2.3 Fixed point models
  • 3.3 Properties of equilibrium solutions
  • 3.3.1 Existence of equilibrium solutions
  • 3.3.2 Uniqueness of equilibrium solutions
  • 3.3.3 Further properties of equilibrium solutions
  • 3.3.4 Stability and sensitivity of equilibrium solutions
  • II Methods
  • 4 Algorithms for the basic model and its extensions
  • 4.1 The Frank-Wolfe algorithm and its extensions
  • 4.1.1 The Frank-Wolfe algorithm
  • 4.1.2 Termination criteria
  • 4.1.3 The use of the Frank-Wolfe approach for the solution of [TAP] .
  • 4.1.4 Shortest route algorithms
  • 4.1.5 Convergence characteristics of the Frank-Wolfe method
  • 4.1.6 Improvements and extensions
  • 4.2 Algorithm concepts
  • 4.2.1 Partial linearization algorithms
  • 4.2.2 Decomposition algorithms
  • 4.2.3 Column generation algorithms
  • 4.2.4 Discussion
  • 4.2.5 A taxonomy of algorithms for [TAP]
  • 4.3 Algorithms for the basic model
  • 4.3.1 Decomposition algorithms
  • 4.3.2 Sequential decomposition algorithms
  • 4.3.3 Parallel decomposition algorithms
  • 4.3.4 Aggregate simplicial decomposition algorithms
  • 4.3.5 Disaggregate simplicial decomposition algorithms
  • 4.3.6 Comparisons between aggregated and disaggregated representations
  • 4.3.7 Dual algorithms
  • 4.3.8 Network aggregation algorithms
  • 4.3.9 Other algorithms
  • 4.4 Algorithms for elastic demand problems
  • 4.5 Algorithms for stochastic assignment models
  • 4.5.1 Stochastic network loading
  • 4.5.2 Stochastic user equilibrium
  • 4.6 Algorithms for side constrained assignment models
  • 4.6.1 Algorithms for capacity side constrained assignment models
  • 4.7 Discussion
  • 5 Algorithms for general traffic equilibria
  • 5.1 Introduction
  • 5.2 Algorithm concepts
  • 5.2.1 Cost approximation algorithms
  • 5.2.2 Decomposition algorithms
  • 5.2.3 Column generation algorithms
  • 5.2.4 Algorithmic equivalence results
  • 5.2.5 Descent algorithms for variational inequalities
  • 5.3 Algorithms for general traffic equilibria
  • 5.3.1 Linear approximation algorithms
  • 5.3.2 Sequential decomposition algorithms
  • 5.3.3 Parallel decomposition algorithms
  • 5.3.4 Algorithms based on the primal and dual gap functions
  • 5.3.5 Column generation algorithms
  • 5.3.6 Dual algorithms
  • 5.3.7 Other algorithms
  • 5.4 Discussion
  • A Definitions
  • References
  • Index

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