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The traffic assignment problem : models and methods

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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.
• (source: Nielsen Book Data)

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The Traffic Assignment Problem: Models and Methods PDF

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....

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 Assignments to Transportation Networks

• First Online: 01 January 2014

Cite this chapter

• Dietmar P. F. Möller 3  

Part of the book series: Simulation Foundations, Methods and Applications ((SFMA))

1880 Accesses

This chapter begins with a brief overview of traffic assignment in transportation systems. Section 3.1 introduces the assignment problem in transportation as the distribution of traffic in a network considering the demand between locations and the transport supply of the network. Four trip assignment models relevant to transportation are presented and characterized. Section 3.2 covers traffic assignment to uncongested networks based on the assumption that cost does not depend on traffic flow. Section 3.3 introduces the topic of traffic assignment and congested models based on assumptions from traffic flow modeling, e.g., each vehicle is traveling at the legal velocity, v , and each vehicle driver is following the preceding vehicle at a legal safe velocity. Section 3.4 covers the important topic of equilibrium assignment which can be expressed by the so-called fixed-point models where origin to destination (O-D) demands are fixed, representing systems of nonlinear equations or variational inequalities. Equilibrium models are also used to predict traffic patterns in transportation networks that are subject to congestion phenomena. Section 3.5 presents the topic of multiclass assignment, which is based on the assumption that travel demand can be allocated as a number of distinct classes which share behavioral characteristics. In Sect. 3.6, dynamic traffic assignment is introduced which allows the simultaneous determination of a traveler’s choice of departure time and path. With this approach, phenomenon such as peak spreading in response to congestion dynamics or time-varying tolls can be directly analyzed. In Sect. 3.7, transportation network synthesis is introduced which focuses on the modification of a transportation road network to fit a required demand. Section 3.8 covers a case study involving a diverging diamond interchange (DDI), an interchange in which the two directions of traffic on a nonfreeway road cross to the opposite side on both sides of a freeway overpass. The DDI requires traffic on the freeway overpass (or underpass) to briefly drive on the opposite side of the road. Section 3.9 contains comprehensive questions from the transportation system area. A final section includes references and suggestions for further reading.

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References and Further Readings

Bando M, Hasebe K, Nakayama A, Shibata A, Sugiyama Y (1995) Dynamic model of traffic congestion and numerical simulation. Phys Rev E 51(2):1035–1042

Article   Google Scholar  

Bliemer MCJ (2001) Analytical dynamic traffic assignment with interacting user-classes: theoretical advances and applications using a variational inequality approach. PhD thesis, Delft University of Technology, The Netherlands

Google Scholar  

Bliemer MCJ, Castenmiller RJ, Bovy PHL (2002) Analytical multiclass dynamic traffic assignment using a dynamic network loading procedure. In: Proceedings of the 9th meeting EURO Working Group on Transportation. Tayler & Francis Publication, pp 473–477

Cascetta E (2009) Transportation systems analysis: models and application. Springer Science + Business Media, LLV, New York

Book   Google Scholar  

Chiu YC, Bottom J, Mahut M, Paz A, Balakrishna R, Waller T, Hicks J (2011) Dynamic Traffic Assignment, A Primer for the Transportation Network Modeling Committee, Transportation Research Circular, Number E-C153, June 2011

Chlewicki G (2003) New interchange and intersection designs: the synchronized split-phasing intersection and the diverging diamond interchange. In: Proceedings of the 2nd urban street symposium, Anaheim

Correa ER, Stier-Moses NE (2010) Wardrop equilibria. In: Cochran JJ (ed) Encyclopedia of operations research and management science. Wiley, Hoboken

Dafermos SC, Sparrow FT (1969) The traffic assignment problem for a general network. J Res US Nat Bur Stand 73B:91–118

Article   MathSciNet   Google Scholar  

Dubois D, Bel G, Llibre M (1979) A set of methods in transportation network synthesis and analysis. J Opl Res Soc 30(9):797–808

Florian M (1999) Untangling traffic congestion: application of network equilibrium models in transportation planning. OR/MS Today 26(2):52–57

MathSciNet   Google Scholar  

Florian M, Hearn DW (2008) Traffic assignment: equilibrium models. In: Optimization and its applications, vol 17. Springer Publ., pp 571–592

Hughes W, Jagannathan R (2010) Double crossover diamond interchange. TECHBRIEF FHWA-HRT-09-054, U.S. Department of Transportation, Federal Highway Administration, Washington, DC, FHWA contact: J. Bared, 202-493-3314

Inman V, Williams J, Cartwright R, Wallick B, Chou P, Baumgartner M (2010) Drivers’ evaluation of the diverging diamond interchange. TECHBRIEF FHWA-HRT-07-048, U.S. Department of Transportation, Federal Highway Administration, Washington, DC. FHWA contact: J. Bared, 202-493-3314

Knight FH (1924) Some fallacies in the interpretation of social cost. Q J Econ 38:582–606

Larsson T, Patriksson M (1999) Side constrained traffic equilibrium models—analysis, computation and applications. Transport Res 33B:233–264

Lozovanu D, Solomon J (1995) The problem of the synthesis of a transport network with a single source and the algorithm for its solution. Comput Sci J Moldova 3(2(8)):161–167

MathSciNet   MATH   Google Scholar  

ProcessModel (1999) Users Manual, ProcessModel Corporation, Provo, UT

Rodrigus J-P (2013) The geography of transportation systems. Taylor & Francis, Routledge

Steinmetz K (2011) How it works, traffic gem, diverging-diamond interchanges can save time and lives. Time Magazine, pp. 54–55, 7 Feb 2011

Wardrop JG (1952) Some theoretical aspects of road traffic research. In: Proceedings of the institute of civil engineers, Part II, vol 1, ICE Virtual Library, Thomas Telford Limited, pp 325–378

Wilson AG (1967) A statistical theory of spatial distribution models. Transport Res 1:253–269

Yang H, Huang H-J (2004) The multi-class multi-criteria traffic network equilibrium and systems optimum problem. Transport Res Part B 38:1–15

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Dietmar P. F. Möller

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Möller, D.P.F. (2014). Traffic Assignments to Transportation Networks. In: Introduction to Transportation Analysis, Modeling and Simulation. Simulation Foundations, Methods and Applications. Springer, London. https://doi.org/10.1007/978-1-4471-5637-6_3

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Published : 12 August 2014

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