The Traffic Assignment Problem: Models and Methods PDF
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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....
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Chapter List (116 chapters):
- Chapter 1: Cover
- Chapter 2: Title Page
- Chapter 3: Copyright Page
- Chapter 4: Table of Contents
- Chapter 5: Preface
- Chapter 6: Some notations
- Chapter 7: I Models
- Chapter 8: 1 Urban traffic planning
- Chapter 9: 1.1 Introduction
- Chapter 10: 1.2 The transportation planning process
- Chapter 11: 1.3 Organization and goal definition
- Chapter 12: 1.4 Base year inventory
- Chapter 13: 1.5 Model analysis
- Chapter 14: 1.5.1 Trip generation
- Chapter 15: 1.5.2 Trip distribution
- Chapter 16: 1.5.3 Modal split
- Chapter 17: 1.5.4 Traffic assignment
- Chapter 18: 1.6 Travel forecast
- Chapter 19: 1.7 Network evaluation
- Chapter 20: 1.8 Discussion
- Chapter 21: 2 The basic equilibrium model and extensions
- Chapter 22: 2.1 The Wardrop conditions
- Chapter 23: 2.1.1 The fixed demand case
- Chapter 24: 2.1.2 The variable demand case
- Chapter 25: 2.1.3 Discussion
- Chapter 26: 2.2 The mathematical program for user equilibrium
- Chapter 27: 2.2.1 The fixed demand case
- Chapter 28: 2.2.2 Network representations
- Chapter 29: 2.2.3 The elastic demand case
- Chapter 30: 2.2.4 Equivalent fixed demand reformulations
- Chapter 31: 2.2.5 Discussion
- Chapter 32: 2.3 Properties of equilibrium solutions
- Chapter 33: 2.3.1 Existence of equilibrium solutions
- Chapter 34: 2.3.2 Uniqueness of equilibrium solutions
- Chapter 35: 2.3.3 Further properties of equilibrium solutions
- Chapter 36: 2.3.4 Stability and sensitivity of equilibrium solutions
- Chapter 37: 2.4 User equilibrium versus system optimum
- Chapter 38: 2.5 Nonseparable costs and multiclass-user transportation networks
- Chapter 39: 2.6 Related network problem
- Chapter 40: 2.6.1 Traffic equilibria and network games
- Chapter 41: 2.6.2 Discrete traffic equilibrium models
- Chapter 42: 2.6.3 Traffic equilibria and electrical networks
- Chapter 43: 2.6.4 Spatial price equilibria
- Chapter 44: 2.6.5 Optimal message routing in computer communication networks
- Chapter 45: 2.7 Discussion
- Chapter 46: 2.8 Some extension
- Chapter 47: 2.8.1 Stochastic assignment models
- Chapter 48: 2.8.2 Side constrained assignment models
- Chapter 49: 3 General traffic equilibrium models
- Chapter 50: 3.1 Introduction
- Chapter 51: 3.1.1 Alternative definitions of equilibria
- Chapter 52: 3.1.2 Variational inequality problems
- Chapter 53: 3.1.3 Nonlinear complementarity problems
- Chapter 54: 3.1.4 Fixed point problems
- Chapter 55: 3.1.5 Mathematical programming reformulations
- Chapter 56: 3.2 Traffic equilibrium models
- Chapter 57: 3.2.1 Variational inequality models
- Chapter 58: 3.2.2 Nonlinear complementarity models
- Chapter 59: 3.2.3 Fixed point models
- Chapter 60: 3.3 Properties of equilibrium solutions
- Chapter 61: 3.3.1 Existence of equilibrium solutions
- Chapter 62: 3.3.2 Uniqueness of equilibrium solutions
- Chapter 63: 3.3.3 Further properties of equilibrium solutions
- Chapter 64: 3.3.4 Stability and sensitivity of equilibrium solutions
- Chapter 65: II Methods
- Chapter 66: 4 Algorithms for the basic model and its extensions
- Chapter 67: 4.1 The Frank-Wolfe algorithm and its extensions
- Chapter 68: 4.1.1 The Frank-Wolfe algorithm
- Chapter 69: 4.1.2 Termination criteria
- Chapter 70: 4.1.3 The use of the Frank-Wolfe approach for the solution of [TAP] .
- Chapter 71: 4.1.4 Shortest route algorithms
- Chapter 72: 4.1.5 Convergence characteristics of the Frank-Wolfe method
- Chapter 73: 4.1.6 Improvements and extensions
- Chapter 74: 4.2 Algorithm concepts
- Chapter 75: 4.2.1 Partial linearization algorithms
- Chapter 76: 4.2.2 Decomposition algorithms
- Chapter 77: 4.2.3 Column generation algorithms
- Chapter 78: 4.2.4 Discussion
- Chapter 79: 4.2.5 A taxonomy of algorithms for [TAP]
- Chapter 80: 4.3 Algorithms for the basic model
- Chapter 81: 4.3.1 Decomposition algorithms
- Chapter 82: 4.3.2 Sequential decomposition algorithms
- Chapter 83: 4.3.3 Parallel decomposition algorithms
- Chapter 84: 4.3.4 Aggregate simplicial decomposition algorithms
- Chapter 85: 4.3.5 Disaggregate simplicial decomposition algorithms
- Chapter 86: 4.3.6 Comparisons between aggregated and disaggregated representations
- Chapter 87: 4.3.7 Dual algorithms
- Chapter 88: 4.3.8 Network aggregation algorithms
- Chapter 89: 4.3.9 Other algorithms
- Chapter 90: 4.4 Algorithms for elastic demand problems
- Chapter 91: 4.5 Algorithms for stochastic assignment models
- Chapter 92: 4.5.1 Stochastic network loading
- Chapter 93: 4.5.2 Stochastic user equilibrium
- Chapter 94: 4.6 Algorithms for side constrained assignment models
- Chapter 95: 4.6.1 Algorithms for capacity side constrained assignment models
- Chapter 96: 4.7 Discussion
- Chapter 97: 5 Algorithms for general traffic equilibria
- Chapter 98: 5.1 Introduction
- Chapter 99: 5.2 Algorithm concepts
- Chapter 100: 5.2.1 Cost approximation algorithms
- Chapter 101: 5.2.2 Decomposition algorithms
- Chapter 102: 5.2.3 Column generation algorithms
- Chapter 103: 5.2.4 Algorithmic equivalence results
- Chapter 104: 5.2.5 Descent algorithms for variational inequalities
- Chapter 105: 5.3 Algorithms for general traffic equilibria
- Chapter 106: 5.3.1 Linear approximation algorithms
- Chapter 107: 5.3.2 Sequential decomposition algorithms
- Chapter 108: 5.3.3 Parallel decomposition algorithms
- Chapter 109: 5.3.4 Algorithms based on the primal and dual gap functions
- Chapter 110: 5.3.5 Column generation algorithms
- Chapter 111: 5.3.6 Dual algorithms
- Chapter 112: 5.3.7 Other algorithms
- Chapter 113: 5.4 Discussion
- Chapter 114: A Definitions
- Chapter 115: References
- Chapter 116: Index
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Traffic Assignment: A Survey of Mathematical Models and Techniques
- First Online: 17 May 2018
Cite this chapter
- Pushkin Kachroo 14 &
- Kaan M. A. Özbay 15
Part of the book series: Advances in Industrial Control ((AIC))
1110 Accesses
2 Citations
This chapter presents the fundamentals of the theory and techniques of traffic assignment problem. It first presents the steady-state traffic assignment problem formulation which is also called static assignment, followed by Dynamic Traffic Assignment (DTA), where the traffic demand on the network is time varying. The static assignment problem is shown in a mathematical programming setting for two different objectives to be satisfied. The first one where all users experience same travel times in alternate used routes is called user-equilibrium and another setting called system optimum in which the assignment attempts to minimize the total travel time. The alternate formulation uses variational inequality method which is also presented. Dynamic travel routing problem is also reviewed in the variational inequality setting. DTA problem is shown in discrete and continuous time in terms of lumped parameters as well as in a macroscopic setting, where partial differential equations are used for the link traffic dynamics. A Hamilton–Jacobi- based travel time dynamics model is also presented for the links and routes, which is integrated with the macroscopic traffic dynamics. Simulation-based DTA method is also very briefly reviewed. This chapter is taken from the following Springer publication and is reproduced here, with permission and with minor changes: Pushkin Kachroo, and Neveen Shlayan, “Dynamic traffic assignment: A survey of mathematical models and technique,” Advances in Dynamic Network Modeling in Complex Transportation Systems (Editor: Satish V. Ukkusuri and Kaan Özbay) Springer New York, 2013. 1-25.
This chapter is taken from the following Springer publication and is reproduced here, with permission and with minor changes: Pushkin Kachroo, and Neveen Shlayan, “Dynamic traffic assignment: A survey of mathematical models and techniques,” Advances in Dynamic Network Modeling in Complex Transportation Systems (Editor: Satish V. Ukkusuri and Kaan Özbay) Springer New York, 2013. 1–25.
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Computing Dynamic User Equilibria on Large-Scale Networks with Software Implementation
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Kachroo, P., Özbay, K.M.A. (2018). Traffic Assignment: A Survey of Mathematical Models and Techniques. In: Feedback Control Theory for Dynamic Traffic Assignment. Advances in Industrial Control. Springer, Cham. https://doi.org/10.1007/978-3-319-69231-9_2
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- Part 1 Models: urban traffic planning - the transportation planning process, organization and goal definition, base-year inventory, model analysis, travel forecast, network evaluation, discussion
- the basic equilibrium model and extensions - the Wardrop conditions, the mathematical program for user equilibrium, properties of equilibrium solutions, user equilibrium versus system optimum, non-separable costs and multiclass-user transportation networks, related network problems, discussion, some extentions
- general traffic equilibrium models - traffic equilibrium models, properties of equilibrium solutions. Part 2 Methods: algorithms for the basic model and its extensions - the Frank-Wolfe algorithm and its extensions, algorithm concepts, algorithms for the basic model, algorithms for elastic demand problems, algorithms for stochastic assignment models, algorithms for side-constrained assignment models, discussion
- algorithms for general traffic equilibria - algorithm concepts, algorithms for general traffic equilibria, discussion.
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The second part deals with methods for traffic equilibrium problems. This title should be of interest to researchers in transportation, operations reserch and quantitative economics, who wish to extend their knowledge of equilibrium modelling and analysis, and of the foundations of efficient optimization methods adapted for the solution of ...
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Read The Traffic Assignment Problem by Michael Patriksson with a free trial. Read millions of eBooks and audiobooks on the web, iPad, iPhone and Android. 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 ...