Foundations of Dynamic Traffic Assignment: The Past, the Present and the Future

Dynamic Traffic Assignment (DTA) has evolved substantially since the pioneering work of Merchant and Nemhauser. Numerous formulations and solutions approaches have been introduced ranging from mathematical programming, to variational inequality, optimal control, and simulation-based. The aim of this special issue is to document the main existing DTA approaches for future reference. This opening paper will summarize the current understanding of DTA, review the existing literature, make the connection to the approaches presented in this special issue, and attempt to hypothesize about the future.

[1]  Mike Smith,et al.  A new dynamic traffic model and the existence and calculation of dynamic user equilibria on congested capacity-constrained road networks , 1993 .

[2]  Lei Rao,et al.  A simultaneous route and departure time choice equilibrium model on dynamic networks , 1999 .

[3]  S. Peeta,et al.  Stability issues for dynamic traffic assignment , 2003, Autom..

[4]  Haris N. Koutsopoulos,et al.  Simulation Laboratory for Evaluating Dynamic Traffic Management Systems , 1997 .

[5]  Hani S. Mahmassani,et al.  Development of Dynasmart-X Software for Real-Time Dynamic Traffic Assignment Technical , 1997 .

[6]  Malachy Carey,et al.  An approach to modelling time-varying flows on congested networks , 2000 .

[7]  Hani S. Mahmassani,et al.  Network performance under system optimal and user equilibrium dynamic assignments: Implications for , 1993 .

[8]  Hani S. Mahmassani,et al.  On-Line Monitoring System for Real-Time Traffic Management Applications , 1999 .

[9]  Mike Smith,et al.  The existence, uniqueness and stability of traffic equilibria , 1979 .

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

[11]  Hani S. Mahmassani,et al.  Time dependent, shortest-path algorithm for real-time intelligent vehicle highway system applications , 1993 .

[12]  Terry L. Friesz,et al.  A Variational Inequality Formulation of the Dynamic Network User Equilibrium Problem , 1993, Oper. Res..

[13]  Malachy Carey Nonconvexity of the dynamic traffic assignment problem , 1992 .

[14]  Bruce N Janson CONVERGENT ALGORITHM FOR DYNAMIC TRAFFIC ASSIGNMENT , 1991 .

[15]  James V. Krogmeier,et al.  Estimation of Dynamic Assignment Matrices and OD Demands Using Adaptive Kalman Filtering , 2001, J. Intell. Transp. Syst..

[16]  Malachy Carey,et al.  A Constraint Qualification for a Dynamic Traffic Assignment Model , 1986, Transp. Sci..

[17]  Srinivas Peeta,et al.  AN INTERNET BASED ON-LINE ARCHITECTURE FOR REAL-TIME TRAFFIC SYSTEMS CONTROL , 2000 .

[18]  Michael J. Smith,et al.  The Stability of a Dynamic Model of Traffic Assignment - An Application of a Method of Lyapunov , 1984, Transp. Sci..

[19]  Hani S. Mahmassani,et al.  System optimal and user equilibrium time-dependent traffic assignment in congested networks , 1995, Ann. Oper. Res..

[20]  Markos Papageorgiou,et al.  Simple Decentralized Feedback Strategies for Route Guidance in Traffic Networks , 1999, Transp. Sci..

[21]  Terry L. Friesz,et al.  A Discrete Time, Nested Cost Operator Approach to the Dynamic Network User Equilibrium Problem , 1995, Transp. Sci..

[22]  Anna Nagurney,et al.  On the local and global stability of a travel route choice adjustment process , 1996 .

[23]  Ta-Hui Yang DEPLOYABLE STABLE TRAFFIC ASSIGNMENT MODELS FOR CONTROL IN DYNAMIC TRAFFIC NETWORKS : A DYNAMICAL SYSTEMS APPROACH , 2001 .

[24]  Hani S. Mahmassani,et al.  DYNASMART-X Real-Time Dynamic Traffic Assignment Systems: Off Line Laboratory Test Results for the DYNASMART-X Real-Time Dynamic Traffic Assignment System , 1998 .

[25]  Hani S. Mahmassani,et al.  Multiple user classes real-time traffic assignment for online operations: A rolling horizon solution framework , 1995 .

[26]  Yosef Sheffi,et al.  Urban Transportation Networks: Equilibrium Analysis With Mathematical Programming Methods , 1985 .

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

[28]  Bin Ran,et al.  Dynamic Urban Transportation Network Models , 1994 .

[29]  John R. Birge,et al.  Optimal Flows in Stochastic Dynamic Networks with Congestion , 1993, Oper. Res..

[30]  Ennio Cascetta,et al.  Dynamic Estimators of Origin-Destination Matrices Using Traffic Counts , 1993, Transp. Sci..

[31]  Jorge Ramos,et al.  Content of Variable Message Signs and On-Line Driver Behavior , 2000 .

[32]  S. Travis Waller,et al.  An Internet-based geographic information system that integrates data, models and users for transportation applications , 2000 .

[33]  David Bernstein,et al.  An alternative formulation of the simultaneous route and departure-time choice equilibrium problem , 1996 .

[34]  Yue Li,et al.  Linear Programming Formulations for System Optimum Dynamic Traffic Assignment with Arrival Time-Based and Departure Time-Based Demands , 1999 .

[35]  George L. Nemhauser,et al.  Optimality Conditions for a Dynamic Traffic Assignment Model , 1978 .

[36]  A. Nagurney,et al.  Projected Dynamical Systems and Variational Inequalities with Applications , 1995 .

[37]  Hani S. Mahmassani,et al.  A note on least time path computation considering delays and prohibitions for intersection movements , 1996 .

[38]  Hani S. Mahmassani,et al.  An evaluation tool for advanced traffic information and management systems in urban networks , 1994 .

[39]  Antoine G. Hobeika,et al.  Parameter optimization methods for estimating dynamic origin-destination trip-tables , 1997 .

[40]  A. Nagurney,et al.  On the stability of projected dynamical systems , 1995 .

[41]  Che-Fu Hsueh,et al.  A model and an algorithm for the dynamic user-optimal route choice problem , 1998 .

[42]  Bruce N Janson,et al.  DYNAMIC TRAFFIC ASSIGNMENT WITH ARRIVAL TIME COSTS. , 1993 .

[43]  Athanasios K. Ziliaskopoulos,et al.  A Linear Programming Model for the Single Destination System Optimum Dynamic Traffic Assignment Problem , 2000, Transp. Sci..

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

[45]  Haris N. Koutsopoulos,et al.  DEVELOPMENT OF A ROUTE GUIDANCE GENERATION SYSTEM FOR REAL-TIME APPLICATION , 1997 .

[46]  J. Ho A Successive Linear Optimization Approach to the Dynamic Traffic Assignment Problem , 1980 .

[47]  Chris Hendrickson,et al.  Schedule Delay and Departure Time Decisions in a Deterministic Model , 1981 .

[48]  Peeta Srinivas,et al.  System optimal dynamic traffic assignment in congested networks with advanced information systems. , 1996 .

[49]  Hani S. Mahmassani,et al.  DYNAMIC ASPECTS OF DEPARTURE-TIME CHOICE BEHAVIOR IN A COMMUTING SYSTEM: THEORETICAL FRAMEWORK AND EXPERIMENTAL ANALYSIS , 1985 .

[50]  Hani S. Mahmassani,et al.  Comparative analysis of robustness of centralized and distributed network route control systems in incident situations , 1996 .

[51]  Bin Ran,et al.  A New Class of Instantaneous Dynamic User-Optimal Traffic Assignment Models , 1993, Oper. Res..

[52]  Bin Ran,et al.  A link-based variational inequality model for dynamic departure time/route choice , 1996 .

[53]  Hani S. Mahmassani,et al.  A DECENTRALIZED SCHEME FOR REAL-TIME ROUTE GUIDANCE IN VEHICULAR TRAFFIC NETWORKS , 1995 .

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

[55]  Stella Dafermos,et al.  Traffic Equilibrium and Variational Inequalities , 1980 .

[56]  Sungjoon Lee,et al.  A cell transmission based assignment-simulation model for integrated freeway/surface street systems , 1996 .

[57]  C. Daganzo THE CELL TRANSMISSION MODEL.. , 1994 .

[58]  N B Taylor CONTRAM 5: AN ENHANCED TRAFFIC ASSIGNMENT MODEL , 1990 .

[59]  Giulio Erberto Cantarella,et al.  Dynamic Processes and Equilibrium in Transportation Networks: Towards a Unifying Theory , 1995, Transp. Sci..

[60]  Michel Bierlaire,et al.  DynaMIT: a simulation-based system for traffic prediction and guidance generation , 1998 .

[61]  Steven Travis Waller,et al.  OPTIMIZATION AND CONTROL OF STOCHASTIC DYNAMIC TRANSPORTATION SYSTEMS : FORMULATIONS, SOLUTION METHODOLOGIES, AND COMPUTATIONAL EXPERIENCE , 2000 .

[62]  Hani S. Mahmassani,et al.  Design and implementation of parallel time-dependent least time path algorithms for Intelligent Transportation Systems applications , 1997 .

[63]  M. Ben-Akiva,et al.  STOCHASTIC EQUILIBRIUM MODEL OF PEAK PERIOD TRAFFIC CONGESTION , 1983 .

[64]  P Gower,et al.  CONTRAM, STRUCTURE OF THE MODEL , 1989 .

[65]  Yue Li Development of dynamic traffic assignment models for planning applications , 2000 .

[66]  M O Ghali,et al.  TRAFFIC ASSIGNMENT, TRAFFIC CONTROL AND ROAD PRICING. , 1993 .

[67]  M. Cremer,et al.  A new class of dynamic methods for the identification of origin-destination flows , 1987 .

[68]  Anna Nagurney,et al.  Projected Dynamical Systems in the Formulation, Stability Analysis, and Computation of Fixed-Demand Traffic Network Equilibria , 1997, Transp. Sci..

[69]  T Shimazaki,et al.  A GENERAL MODEL AND ALGORITHM FOR THE DYNAMIC TRAFFIC ASSIGNMENT PROBLEMS , 1989 .

[70]  Gang-Len Chang,et al.  An integrated model for estimating time-varying network origin–destination distributions , 1999 .

[71]  T. Koopmans,et al.  Studies in the Economics of Transportation. , 1956 .

[72]  Moshe E. Ben-Akiva,et al.  Alternative Approaches for Real-Time Estimation and Prediction of Time-Dependent Origin-Destination Flows , 2000, Transp. Sci..

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

[74]  Bin Ran,et al.  Solving an Instantaneous Dynamic User-Optimal Route Choice Model , 1995, Transp. Sci..

[75]  Bruce N Janson,et al.  Dynamic traffic assignment for urban road networks , 1991 .

[76]  Athanasios K. Ziliaskopoulos,et al.  An intermodal optimum path algorithm for multimodal networks with dynamic arc travel times and switching delays , 2000, Eur. J. Oper. Res..

[77]  Gang-Len Chang,et al.  Estimation of time-varying origin-destination distributions with dynamic screenline flows , 1996 .

[78]  Srinivas Peeta,et al.  ROBUSTNESS OF THE OFF-LINE A PRIORI STOCHASTIC DYNAMIC TRAFFIC ASSIGNMENT SOLUTION FOR ON-LINE OPERATIONS , 1999 .

[79]  Byung-Wook Wie,et al.  DYNAMIC ANALYSIS OF USER-OPTIMIZED NETWORK FLOWS WITH ELASTIC TRAVEL DEMAND , 1991 .

[80]  Terry L. Friesz,et al.  Day-To-Day Dynamic Network Disequilibria and Idealized Traveler Information Systems , 1994, Oper. Res..

[81]  Hani S. Mahmassani,et al.  System Optimal Dynamic Assignment for Electronic Route Guidance in a Congested Traffic Network: Dynamic Flow Modelling and Control , 1995 .

[82]  M J Lighthill,et al.  On kinematic waves II. A theory of traffic flow on long crowded roads , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[83]  D. Watling STABILITY OF THE STOCHASTIC EQUILIBRIUM ASSIGNMENT PROBLEM: A DYNAMICAL SYSTEMS APPROACH , 1999 .

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

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

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

[87]  Srinivas Peeta,et al.  Generalized Singular Value Decomposition Approach for Consistent On-Line Dynamic Traffic Assignment , 1999 .

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

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

[90]  Hani S. Mahmassani ALGORITHM FOR DYNAMIC ROUTE GUIDANCE IN CONGESTED NETWORKS WITH MULTIPLE USER INFORMATION AVAILABILITY GROUPS , 1993 .

[91]  Huey-Kuo Chen,et al.  Dynamic Travel Choice Models , 1999 .