Dynamic traffic assignment: model classifications and recent advances in travel choice principles

Dynamic Traffic Assignment (DTA) has been studied for more than four decades and numerous reviews of this research area have been conducted. This review focuses on the travel choice principle and the classification of DTA models, and is supplementary to the existing reviews. The implications of the travel choice principle for the existence and uniqueness of DTA solutions are discussed, and the interrelation between the travel choice principle and the traffic flow component is explained using the nonlinear complementarity problem, the variational inequality problem, the mathematical programming problem, and the fixed point problem formulations. This paper also points out that all of the reviewed travel choice principles are extended from those used in static traffic assignment. There are also many classifications of DTA models, in which each classification addresses one aspect of DTA modeling. Finally, some future research directions are identified.

[1]  Joel P. Franklin,et al.  Travel Time Reliability for Stockholm Roadways , 2009 .

[2]  A. Tversky,et al.  Advances in prospect theory: Cumulative representation of uncertainty , 1992 .

[3]  B Ran,et al.  CONSIDERING TRAVELERS' RISK-TAKING BEHAVIOR IN DYNAMIC TRAFFIC ASSIGNMENT , 1998 .

[4]  J. Jucker,et al.  An Empirical Study of Travel Time Variability and Travel Choice Behavior , 1982 .

[5]  William H. K. Lam,et al.  A Reliability-Based Stochastic Traffic Assignment Model for Network with Multiple User Classes under Uncertainty in Demand , 2006 .

[6]  A. Tversky,et al.  The Effect of Myopia and Loss Aversion on Risk Taking: An Experimental Test , 1997 .

[7]  W. Y. Szeto,et al.  Enhanced Lagged Cell-Transmission Model for Dynamic Traffic Assignment , 2008 .

[8]  Byungkyu Park,et al.  Development and Evaluation of a Stochastic Traffic Signal Optimization Method , 2007 .

[9]  Deepak K. Merchant,et al.  A Model and an Algorithm for the Dynamic Traffic Assignment Problems , 1978 .

[10]  Ilsoo Yun,et al.  Stochastic Optimization for Sustainable Traffic Signal Control , 2009 .

[11]  H. Simon,et al.  Models of Man. , 1957 .

[12]  Zhong Zhou,et al.  The [alpha]-reliable Mean-Excess Traffic Equilibrium Model with Stochastic Travel Times , 2010 .

[13]  Hani S. Mahmassani,et al.  Dynamic Traffic Assignment in Design and Evaluation of High-Occupancy Toll Lanes , 2000 .

[14]  A. Tversky,et al.  Prospect Theory : An Analysis of Decision under Risk Author ( s ) : , 2007 .

[15]  Kenneth A. Small,et al.  THE SCHEDULING OF CONSUMER ACTIVITIES: WORK TRIPS , 1982 .

[16]  Jin‐Su Mun,et al.  Traffic Performance Models for Dynamic Traffic Assignment: An Assessment of Existing Models , 2007 .

[17]  Wai Yuen Szeto.  Cooperative game approaches to measuring network reliability considering paradoxes , 2011 .

[18]  W. Y. Szeto,et al.  DYNAMIC TRAFFIC ASSIGNMENT: PROPERTIES AND EXTENSIONS , 2006 .

[19]  Roberto Horowitz,et al.  Optimal freeway ramp metering using the asymmetric cell transmission model , 2006 .

[20]  Zhong Zhou,et al.  A Stochastic α-reliable Mean-excess Traffic Equilibrium Model with Probabilistic Travel Times and Perception Errors , 2009 .

[21]  J. Prashker,et al.  Violations of Expected Utility Theory in Route-Choice Stated Preferences: Certainty Effect and Inflation of Small Probabilities , 2004 .

[22]  Andy H.F. Chow,et al.  Dynamic system optimal traffic assignment – a state-dependent control theoretic approach , 2009 .

[23]  Carlos F. Daganzo,et al.  On Stochastic Models of Traffic Assignment , 1977 .

[24]  Colin Camerer,et al.  Violations of the betweenness axiom and nonlinearity in probability , 1994 .

[25]  Satish V. Ukkusuri,et al.  Linear Programming Models for the User and System Optimal Dynamic Network Design Problem: Formulations, Comparisons and Extensions , 2008 .

[26]  Giulio Erberto Cantarella,et al.  Modelling dynamics in transportation networks: State of the art and future developments , 1993, Simul. Pract. Theory.

[27]  W. Y. Szeto,et al.  Modeling advanced traveler information services: static versus dynamic paradigms , 2004 .

[28]  Shing Chung Josh Wong,et al.  Collection, spillback, and dissipation in pedestrian evacuation: A network-based method , 2011 .

[29]  W. Y. Szeto,et al.  Road Pricing Modeling for Hyper-Congestion , 2005 .

[30]  Hong Kam Lo,et al.  Dynamic Traffic Assignment: Review and Future Research Directions , 2005 .

[31]  Shing Chung Josh Wong,et al.  An efficient discontinuous Galerkin method on triangular meshes for a pedestrian flow model , 2008 .

[32]  H. Simon,et al.  A Behavioral Model of Rational Choice , 1955 .

[33]  Qiang Meng,et al.  A Pareto-optimization approach for a fair ramp metering , 2010 .

[34]  H. Simon,et al.  Models of Bounded Rationality: Empirically Grounded Economic Reason , 1997 .

[35]  H. Pietrantonio.  URBAN TRAVEL DEMAND MODELING: FROM INDIVIDUAL CHOICES TO GENERAL EQUILIBRIUM , 1997 .

[36]  W. Y. Szeto,et al.  Stochastic cell transmission model (SCTM): A stochastic dynamic traffic model for traffic state surveillance and assignment , 2011 .

[37]  Andy H.F. Chow.  Properties of system optimal traffic assignment with departure time choice and its solution method , 2009 .

[38]  Moshe Ben-Akiva,et al.  Dynamic network models and driver information systems , 1991 .

[39]  P C Vythoulkas.  TWO MODELS FOR PREDICTING DYNAMIC STOCHASTIC EQUILIBRIA IN URBAN TRANSPORTATION NETWORKS , 1990 .

[40]  Fernando Ordóñez,et al.  Wardrop Equilibria with Risk-Averse Users , 2010, Transp. Sci..

[41]  J. Wardrop.  ROAD PAPER. SOME THEORETICAL ASPECTS OF ROAD TRAFFIC RESEARCH. , 1952 .

[42]  Terry L. Friesz,et al.  Dynamic Network Traffic Assignment Considered as a Continuous Time Optimal Control Problem , 1989, Oper. Res..

[43]  Samuel Yagar.  Dynamic traffic assignment by individual path minimization and queuing , 1971 .

[44]  W. Y. Szeto,et al.  Risk-Averse Traffic Assignment with Elastic Demands: NCP Formulation and Solution Method for Assessing Performance Reliability , 2006 .

[45]  P. Kline.  Models of man , 1986, Nature.

[46]  Masao Kuwahara,et al.  Decomposition of the reactive dynamic assignments with queues for a many-to-many origin-destination pattern , 1997 .

[47]  Jason D. Lemp,et al.  The continuous cross-nested logit model: Formulation and application for departure time choice , 2010 .

[48]  Malachy Carey,et al.  Congested network flows: Time-varying demands and start-time policies , 1988 .

[49]  A. Sumalee,et al.  Dynamic marginal cost, access control, and pollution charge: a comparison of bottleneck and whole link models , 2012 .

[50]  Wai Yuen Szeto,et al.  Measuring Network Reliability by considering Paradoxes , 2009 .

[51]  Malachy Carey,et al.  Optimal Time-Varying Flows on Congested Networks , 1987, Oper. Res..

[52]  Athanasios K. Ziliaskopoulos,et al.  Foundations of Dynamic Traffic Assignment: The Past, the Present and the Future , 2001 .

[53]  Xiaojun Chen,et al.  Robust Wardrop’s user equilibrium assignment under stochastic demand and supply: Expected residual minimization approach , 2011 .

[54]  A. Tversky,et al.  Prospect theory: an analysis of decision under risk — Source link , 2007 .

[55]  B. Ran,et al.  A LINK-BASED VARIATIONAL INEQUALITY FORMULATION OF IDEAL DYNAMIC USER-OPTIMAL ROUTE CHOICE PROBLEM , 1996 .

[56]  Hai-Jun Huang,et al.  Dynamic user optimal traffic assignment model for many to one travel demand , 1995 .

[57]  Serge P. Hoogendoorn,et al.  Pedestrian route-choice and activity scheduling theory and models , 2004 .

[58]  Hong Kam Lo,et al.  Properties of Dynamic Traffic Assignment with Physical Queues , 2005 .

[59]  Yanqun Jiang,et al.  A dynamic traffic assignment model for a continuum transportation system , 2011 .

[60]  Chih-Cheng Chen,et al.  Dynamic commuter departure time choice under uncertainty , 2008 .

[61]  Sze Chun Wong,et al.  High-Order Computational Scheme for a Dynamic Continuum Model for Bi-Directional Pedestrian Flows , 2011, Comput. Aided Civ. Infrastructure Eng..

[62]  Hong Kam Lo,et al.  Multiclass Dynamic Traffic Assignment Model: Formulation and Computational Experiences , 1996 .

[63]  Chi-Wang Shu,et al.  A REACTIVE DYNAMIC CONTINUUM USER EQUILIBRIUM MODEL FOR BI-DIRECTIONAL PEDESTRIAN FLOWS ∗ , 2009 .

[64]  W. Y. Szeto,et al.  A cell-based dynamic traffic assignment model: Formulation and properties , 2002 .

[65]  W. Y. Szeto,et al.  A CELL-BASED SIMULTANEOUS ROUTE AND DEPARTURE TIME CHOICE MODEL WITH ELASTIC DEMAND , 2004 .

[66]  Erel Avineri,et al.  The Effect of Reference Point on Stochastic Network Equilibrium , 2006, Transp. Sci..

[67]  Yu Jiang,et al.  Reliability-Based Transit Assignment for Congested Stochastic Transit Networks , 2011, Comput. Aided Civ. Infrastructure Eng..

[68]  Roger L. Hughes,et al.  A continuum theory for the flow of pedestrians , 2002 .

[69]  J. Horowitz.  The stability of stochastic equilibrium in a two-link transportation network , 1984 .

[70]  Hani S. Mahmassani,et al.  Dynamic Aspects of Commuter Decisions Under Advanced Traveler Information Systems: Modeling Framework and Experimental Results , 1998 .

[71]  Hani S. Mahmassani,et al.  Travel time prediction and departure time adjustment behavior dynamics in a congested traffic system , 1988 .

[72]  A. Nagurney.  Network Economics: A Variational Inequality Approach , 1992 .

[73]  Bin Ran,et al.  MODELING DYNAMIC TRANSPORTATION NETWORKS , 1996 .

[74]  Fernando Ordóñez,et al.  Robust Wardrop Equilibrium , 2007, NET-COOP.

[75]  Hani S. Mahmassani,et al.  Dynamic User Equilibrium Departure Time and Route Choice on Idealized Traffic Arterials , 1984, Transp. Sci..

[76]  J. G. Wardrop,et al.  Some Theoretical Aspects of Road Traffic Research , 1952 .

[77]  Hong Kam Lo,et al.  Degradable transport network: Travel time budget of travelers with heterogeneous risk aversion , 2006 .

[78]  W. Y. Szeto,et al.  Discretised link travel time models based on cumulative flows: Formulations and properties , 2011 .

[79]  AvineriErel.  The Effect of Reference Point on Stochastic Network Equilibrium , 2006 .

[80]  E. Cascetta.  A stochastic process approach to the analysis of temporal dynamics in transportation networks , 1989 .

[81]  Chi-Wang Shu,et al.  Dynamic continuum pedestrian flow model with memory effect. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[82]  Qi Yang,et al.  Evaluation of freeway control using a microscopic simulation laboratory , 2003 .

[83]  You-Lian Chu.  Work Departure Time Analysis Using Dogit Ordered Generalized Extreme Value Model , 2009 .

[84]  C Terence,et al.  The Value of Time and Reliability: Measurement from a Value Pricing Experiment , 2003 .

[85]  Yafeng Yin,et al.  Robust congestion pricing under boundedly rational user equilibrium , 2010 .

[86]  Serge P. Hoogendoorn,et al.  Hybrid Route Choice Modeling in Dynamic Traffic Assignment , 2009 .

[87]  Pitu Mirchandani,et al.  Generalized Traffic Equilibrium with Probabilistic Travel Times and Perceptions , 1987, Transp. Sci..

[88]  W. Y. Szeto,et al.  A Cell‐Based Model for Multi‐class Doubly Stochastic Dynamic Traffic Assignment , 2011, Comput. Aided Civ. Infrastructure Eng..

[89]  Bin Ran,et al.  Analytical Models of the Dynamic Traffic Assignment Problem , 2001 .

[90]  W. Y. Szeto,et al.  Multivariate Traffic Forecasting Technique Using Cell Transmission Model and SARIMA Model , 2009 .

[91]  A. Tversky,et al.  Prospect theory: analysis of decision under risk , 1979 .

[92]  W. Y. Szeto,et al.  A cell-based variational inequality formulation of the dynamic user optimal assignment problem , 2002 .

[93]  Serge P. Hoogendoorn,et al.  DYNAMIC USER-OPTIMAL ASSIGNMENT IN CONTINUOUS TIME AND SPACE , 2004 .

[94]  N. Stier-Moses,et al.  Wardrop Equilibria with Risk-Averse Users , 2010 .

[95]  Michael G.H. Bell,et al.  Risk-averse user equilibrium traffic assignment: an application of game theory , 2002 .

[96]  Mansoureh Jeihani,et al.  A Review of Dynamic Traffic Assignment Computer Packages , 2010 .

[97]  Randolph W. Hall,et al.  TRAVEL OUTCOME AND PERFORMANCE: THE EFFECT OF UNCERTAINTY ON ACCESSIBILITY , 1983 .

[98]  Yasunori Iida,et al.  RISK ASSIGNMENT: A NEW TRAFFIC ASSIGNMENT MODEL CONSIDERING THE RISK OF TRAVEL TIME VARIATION. , 1993 .

[99]  Hani S. Mahmassani,et al.  On Boundedly Rational User Equilibrium in Transportation Systems , 1987, Transp. Sci..

[100]  Shing Chung Josh Wong,et al.  A predictive dynamic traffic assignment model in congested capacity-constrained road networks , 2000 .

[101]  Bidisha Ghosh,et al.  Cell-based short-term traffic flow forecasting using time series modelling , 2005 .

[102]  Wai Yuen Szeto,et al.  Generalisation of the Risk-Averse Traffic Assignment , 2007 .

[103]  William H. K. Lam,et al.  IMPACT OF ROAD PRICING ON THE NETWORK RELIABILITY , 2005 .

[104]  Shing Chung Josh Wong,et al.  Dynamic continuum model for bi-directional pedestrian flows , 2009 .

[105]  Kara M. Kockelman,et al.  Empirical Investigation of Continuous Logit for Departure Time Choice with Bayesian Methods , 2010 .

[106]  W. Y. Szeto,et al.  The Impact of Advanced Traveler Information Services on Travel Time and Schedule Delay Costs , 2005, J. Intell. Transp. Syst..

[107]  Chi-Wang Shu,et al.  Revisiting Hughes’ dynamic continuum model for pedestrian flow and the development of an efficient solution algorithm , 2009 .

[108]  W. Vickrey.  Congestion Theory and Transport Investment , 1969 .