Abstract
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.
Similar content being viewed by others
References
Anastassopoulos, I. (2000). “Fault Tolerance and Incident Detection Using Fourier Transforms.” M.S. Thesis, Purdue University.
Ashok, K. and M.E. Ben-Akiva. (2000). “Alternative Approaches for Real-time Estimation and Prediction of Time-dependent Origin-Destination Flows.” Transportation Science 34(1), 21–36.
Beckmann, M.J., C.B. McGuire, and C.B. Winston. (1956). Studies in the Economics of Transportation. Connecticut: Yale University Press.
Ben-Akiva, M.E., Bierlaire, M., Bottom, J., Koutsopoulos, H.N. and Mishalani, R. (1997a). “Development of a Route Guidance Generation System for Real-Time Application.” Proceedings of the 8 th International Federation of Automatic Control Symposium on Transportation Systems, Chania, Greece, pp. 433–438.
Ben-Akiva, M.E., Koutsopoulos, H.N., Mishalani, R. and Yang, Q. (1997b). “Simulation Laboratory for Evaluating Dynamic Traffic Management Systems.” ASCE Journal of Transportation Engineering 123(4), 283–289.
Ben-Akiva, M., Bierlaire, M., Koutsopoulos, H.N., and Mishalani, R. (1998). “DynaMIT: A Simulation-based System for Traffic Prediction and Guidance Generation.” Proceedings of the 3 rd Triennial Symposium on Transportation Systems, San Juan, Puerto Rico.
Birge, J.R. and J.K. Ho. (1993). “Optimal Flows in Stochastic Dynamic Networks with Congestion.” Operations Research 41(1), 203–216.
Boyce, D.E., B. Ran, and L.J. LeBlanc. (1995). “Solving an Instantaneous Dynamic User-Optimal Route Choice Model.” Transportation Science 29, 128–142.
Cantarella, G.E. and E. Cascetta. (1995). “Dynamic Processes and Equilibrium in Transportation Networks: Towards a Unifying Theory.” Transportation Science 29, 305–329.
Carey, M. (1986). “A Constraint Qualification for a Dynamic Traffic Assignment Model.” Transportation Science 20, 55–58.
Carey, M. (1987). “Optimal Time Varying Flows On Congested Networks.” Operations Research 35(1), 58–69.
Carey, M. (1992). “Nonconvexity of the Dynamic Assignment Problem.” Transportation Research 26B(2), 127–133.
Carey, M. and E. Subrahmanian. (2000). “An Approach to Modeling Time-Varying Flows on Congested Networks.” Transportation Research 34B(3), 157–183.
Cascetta, E., D. Inaudi, and G. Marquis. (1993). “Dynamic Estimators of Origin-Destination Matrices Using Traffic Counts.” Transportation Science 27, 363–373.
Chang, G.-L. and H.S. Mahmassani. (1988). “Travel Time Prediction and Departure Time Adjustment Behavior Dynamics in A Congested Traffic System.” Transportation Research 22B(3), 217–232.
Chang, G.L. and X.D. Tao. (1999). “An Integrated Model for Estimating Time-Varying Network Origin-Destination Distributions.” Transportation Research 33A(5), 381–399.
Chen, H.-K. (1999). Dynamic Travel Choice Models. Berlin: Springer-Verlag.
Chen, H.-K. and C.F. Hsueh. (1998). “A Model and An Algorithm for the Dynamic User-Optimal Route Choice Problem.” Transportation Research 32B(3), 219–234.
Cremer, M. and H. Keller. (1987). “A New Class of Dynamic Methods for the Identification of Origin-Destination Flows.” Transportation Research 21B(2), 117–132.
Dafermos, S. (1980). “Traffic Equilibrium and Variational Inequalities.” Transportation Science 14, 42–54.
Daganzo, C. (1994). “Cell Transmission Model: A Dynamic Representation of Highway Traffic Consistent with the Hydrodynamic Theory.” Transportation Research 28B(4), 269–287.
De Palma, A., Ben-Akiva, M., Lefevre, C. and Litinas, N. (1983). “Stochastic Equilibrium Model of Peak Period Traffic Congestion.” Transportation Science 17(4), 430–453.
De Palma, A. and F. Marchai. (2000) “Dynamic Traffic Analysis with Static Data”: Some Guidelines from the Application to Paris, TRB Preprint. Transportation Research Record.
Friesz, T.L., Bernstein, D., Mehta, N.J., Tobin, R.L. and Ganjalizadeh, S. (1989). “Dynamic Network Traffic Assignment Considered as a Continuous Time Optimal Control Problem.” Operations Research 37(6) 893–901.
Friesz, T.L., T.L., Bernstein, D., Smith, T.E., Tobin, R.L. and Wie, B.W. (1993). “A Variational Inequality Formulation of the Dynamic Network User Equilibrium Problem.” Operations Research 41(1), 179–191.
Friesz, T.L., Bernstein, D., Mehta, N.J., Tobin, R.L., and Ganjalizadeh, S. (1994). “Day-to-Day Dynamic Network Disequilibrium and Idealized Traveler Information Systems.” Operations Research 42(6), 1120–1136.
Ghali, M.O. and M.J. Smith. (1992a). “A Dynamic Traffic Assignment Model.” Presented at the 71st TRB Annual Meeting, Washington D.C.
Ghali, M.O. and M.J. Smith. (1992b). “Dynamic Road Pricing and Dynamic Traffic Assignment for Congested Large Networks.” Presented at the 39th North American Regional Science Association International Conference, Chicago.
Ghali, M.O. and M.J. Smith. (1992c). “Optimal Dynamic Traffic Assignment of a Congested City Network.” Proceedings of the Second International Capri Seminar on Urban Traffic Networks, Capri, Italy.
Ghali, M.O. and M.J. Smith. (1993). “Traffic Assignment, Traffic Control and Road Pricing.” Proceedings of the Twelfth International Symposium on Transportation and Traffic Theory, Daganzo (ed.), University of California, Berkeley, California, pp. 147–170.
Hawas, Y.E. (1995). “A Decentralized Architecture and Local Search Procedures for Real-Time Route Guidance in Congested Vehicular Traffic Networks.” Ph.D. Dissertation, The University of Texas at Austin.
Hawas, Y.E. and H.S. Mahmassani. (1995). “A Decentralized Scheme for Real-time Route Guidance in Vehicular Traffic Networks.” Proceedings of the Second World Congress on Intelligent Transport Systems, Yokohama, Japan.
Hawas, Y.E. and H.S. Mahmassani. (1997). “Comparative Analysis of Robustness of Centralized and Distributed Network Route Control Systems in Incident Situations.” Transportation Research Record 1537, 83–90.
Hawas, Y.E., Mahmassani, H.S., Chang, G.L., Taylor, R., Peeta, S. and Ziliaskopoulos, A. (1997). “Development of DYNASMART-X Software for Real-Time Dynamic Traffic Assignment.” Technical Report ST067–85-TASK-E, Center for Transportation Research, The University of Texas at Austin.
Hendrickson, C. and G. Kocur. (1981). “Schedule Delay and Departure Time Decisions in a Deterministic Model.” Transportation Science 15, 62–77.
Ho, J.K. (1980). “A Successive Linear Optimization Approach to the Dynamic Traffic Assignment Problem.” Transportation Science 14, 295–305.
Horowitz, J.L. (1984). “The Stability of Stochastic Equilibrium in a Two-link Transportation Network.” Transportation Research 18B, 12–28.
Hu, S.-R., Madant, S. M., Krogmeier, J.V. and Peeta, S. (2001). “Estimation of Dynamic Assignment Matrices and O-D Demands using Adaptive Kalman Filtering”, to appear in the Intelligent Transportation Systems Journal.
Janson, B.N. (1991a). “Convergent Algorithm for Dynamic Traffic Assignment.” Transportation Research Record 1328, 69–80.
Janson, B.N. (1991b). “Dynamic Traffic Assignment for Urban Road Networks.” Transportation Research 25B(2/3), 143–161.
Jayakrishnan, R., H.S. Mahmassani, and T.Y. Hu. (1994). “An Evaluation Tool for Advanced Traffic Information and Management Systems in Urban Networks.” Transportation Research 2C(3), 129–147.
Leonard, D., P. Gower, and N.B. Taylor. (1989). “CONTRAM: Structure of the Model.” TRRL Research Report RR 178, Transport and Road Research Laboratory, Crowthorne, United Kingdom.
Li, Y. (2001). “Development of Dynamic Traffic Assignment Models for Planning Applications.” Ph.D. Dissertation, Northwestern University, Evanston, IL.
Li, I.Y., A.K. Ziliaskopoulos, and S.T. Waller. (1999). “Linear Programming Formulations for System Optimum Dynamic Traffic Assignment with Arrival Time Based and Departure Time Based Demands.” Transportation Research Record 1832, 121–142.
Lighthill, M.J. and J.B. Whitham. (1955). “On Kinematic Waves, I: Flow Modeling in Long Rivers; II: A Theory of Traffic Flow on Long Crowded Roads.” Proceedings of Royal Society A229, 281–345.
Mahmassani, H.S. and G.L. Chang. (1985). “Dynamic Aspects of Departure-Time Choice Behavior in A Commuting System: Theoretical Framework and Experience Analysis.” Transportation Research Record 1037, 88–101.
Mahmassani, H.S. and R. Herman. (1984). “Dynamic User Equilibrium Departure Time and Route Choice on Idealized Traffic Arterials.” Transportation Science 18(4), 362–384.
Mahmassani, H.S. and S. Peeta. (1992). “System Optimal Dynamic Assignment for Electronic Route Guidance in a Congested Traffic Network.” Proceedings of the Second International Capri Seminar on Urban Traffic Networks, Capri, Italy, 1992.
Mahmassani, H.S. and S. Peeta. (1993). “Network Performance Under System Optimal and User Equilibrium Dynamic Assignments: Implications for ATIS.” Transportation Research Record 1408, 83–93.
Mahmassani, H.S. and S. Peeta. (1995). “System Optimal Dynamic Assignment for Electronic Route Guidance in a Congested Traffic Network.” In Gartner and Improta (eds.), Urban Traffic Networks: Dynamic Flow Modeling and Control, Berlin: Springer-Verlag, pp. 2–27.
Mahmassani, Peeta, S., Hu, T., and Ziliaskopoulos, A. (1993). “Algorithm for Dynamic Route Guidance in Congested Networks with Multiple User Information Availability Groups.” Proceedings of the 26 th International Symposium on Automotive Technology and Automation, Aachen, Germany, pp. 273–280.
Mahmassani, H.S., Hawas, Y.E., Abdelghany, K., Abdelfatah, A., Chiu, Y.-C., Kang, Y., Chang, G.L., Peeta, S., Taylor, R. and Ziliaskopoulos, A. (1998a). “DYNASMART-X; Volume II: Analytical and Algorithmic Aspects.” Technical Report ST067–85-Volume II, Center for Transportation Research, The University of Texas at Austin.
Mahmassani, H.S., Chiu, Y.-C., Chang, G.L., Peeta, S. and Ziliaskopoulos, A. (1998b). “Off-line Laboratory Test Results for the Dynasmart-X Real-Time Dynamic Traffic Assignment System.” Technical Report ST067–85-TASK-G, Center for Transportation Research, The University of Texas at Austin.
Merchant, D.K. and G.L. Nemhauser. (1978a). “A Model and an Algorithm for the Dynamic Traffic Assignment Problems.” Transportation Science 12(3), August 1978, 183–199.
Merchant, D.K. and G.L. Nemhauser. (1978b). “Optimality Conditions for a Dynamic Traffic Assignment Model.” Transportation Science 12(3), August 1978, 200–207.
Negurney, A. (1998). Network Economics: A Variational Inequality Approach. Boston: Kluwer Academic Publishers.
Nagurney, A. and D. Zhang. (1996). Projected Dynamical Systems and Variational Inequalities with Applications. Boston: Kluwer Academic Publishers.
Nagurney, A. and D. Zhang. (1997). “Projected Dynamical Systems in the Formulation, Stability Analysis, and Computation of Fixed-demand Traffic Network Equilibria.” Transportation Science 31, 147–158.
Patriksson, M. (1994). The Traffic Assignment Problem: Models and Methods. Utrecht, The Netherlands: VSP.
Pavlis, Y. and M. Papageorgiou. (1999). “Simple Decentralized Feedback Strategies for Route Guidance in Traffic Networks.” Transportation Science 33, 264–278.
Peeta, S. (1994). “System Optimal Dynamic Traffic Assignment in Congested Networks with Advanced Information Systems.” Ph.D. Dissertation, The University of Texas at Austin.
Peeta, S. and S. Bulusu. (1999). “A Generalized Singular Value Decomposition Approach for Consistent Online Dynamic Traffic Assignment.” Transportation Research Record 1667, 77–87.
Peeta, S. and H.S. Mahmassani. (1995a). “System Optimal and User Equilibrium Time-Dependent Traffic Assignment in Congested Networks.” Annals of Operations Research 60, 81–113.
Peeta, S. and H.S. Mahmassani. (1995b). “Multiple user Classes Real-time Traffic Assignment for On-line operations: A Rolling Horizon Solution Framework.” Transportation Research 3C(2), 83–98.
Peeta, S. and T.-H. Yang. (2000a). “Stability Issues for Dynamic Traffic Assignment.” Proceedings of the 9 th International Federation of Automatic Control Symposium on Control in Transportation Systems, Schnieder and Becker (eds.), Braunschweig, Germany, pp. 507–511.
Peeta, S. and T.-H. Yang. (2000b). “Stability of Large-scale Dynamic Traffic Networks under On-line Control Strategies.” Proceedings of the 6 th International Conference on Applications of Advanced Technologies in Transportation Engineering, Singapore.
Peeta, S. and C. Zhou. (1999a). “Robustness of the Off-line A Priori Stochastic Dynamic Traffic Assignment Solution for On-Line Operations.” Transportation Research 7C, 281–303.
Peeta, S. and C. Zhou. (1999b). “On-line Dynamic Update Heuristics for Robust Route Guidance.” In Adamski, Rudnicki and Zak (eds.), Proceedings of the International Conference on Modeling and Management in Transportation, Cracow, Poland, 2, 119–126.
Peeta, S., J.L. Ramos, and R. Pasupathy. (2000a). “Content of Variable Message Signs and On-line Driver Behavior.” Transportation Research Record 1725, 102–108.
Peeta, S., R. Pasupathy, and S. Gedela. (2000b). “An Internet Based On-line Architecture for Real-Time Traffic Systems Control.” Proceedings of the 9 th International Federation of Automatic Control Symposium on Control in Transportation Systems, Schnieder and Becker (eds.), Braunschweig, Germany, 314–319.
Ran, B. and D. Boyce. (1994). Dynamic Urban Transportation Network Models, Lecture Notes in Economics and Mathematical Systems 417. Berlin: Springer-Verlag.
Ran, B. and D. Boyce. (1996a). Modeling Dynamic Transportation Networks. Berlin: Springer-Verlag.
Ran, B. and D.E. Boyce. (1996b). “A Link-based Variational Inequality Formulation of Ideal Dynamic User-Optimal Route Choice Problem.” Transportation Research 4C(1), 1–12.
Ran, B. and T. Shimazaki. (1989a). “A General Model and Algorithm for the Dynamic Traffic Assignment Problems.” Proceedings of the Fifth World Conference on Transport Research, Yokohoma, Japan.
Ran, B. and T. Shimazaki. (1989b). “Dynamic User Equilibrium Traffic Assignment for Congested Transportation Networks.” Presented at the Fifth World Conference on Transport Research, Yokohoma, Japan.
Ran, B., D.E. Boyce, and L.J. LeBlanc. (1993). “A New Class of Instantaneous Dynamic User-Optimal Traffic Assignment Models.” Operations Research 41(1), 1993.
Ran, B., R.W. Hall, and D.E. Boyce. (1996). “A Link-based Variational Inequality Model for Dynamic Departure Time/Route Choice.” Transportation Research 30B(1), 31–46.
Richards, P.I. (1956). “Shockwaves on the Highway.” Operations Research 4, 42–51.
Sheffi, Y. (1985). Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods. NJ: Prentice-Hall.
Sherali, H.D., N. Arora, and A.G. Hobeika. (1997). “Parameter Optimization Methods for Estimating Dynamic Origin-Destination Trip-Tables.” Transportation Research 31B(2), 141–157.
Smith, M.J. (1979). “Existence, Uniqueness, and Stability of Traffic Equilibria.” Transportation Research 13B, 295–304.
Smith, M.J. (1984). “The Stability of a Dynamic Model of Traffic Assignment — An Application of a Method of Lyapunov.” Transportation Science 18, 245–252.
Smith, M.J. (1994). “A New Dynamic Traffic Model and the Existence and Calculation of Dynamic User Equilibria on Congested Capacity-constrained Road Networks.” Transportation Research 27B, 49–63.
Taylor, N.B. (1990). “CONTRAM 5: An Enhanced Traffic Assignment Model.” TRRL Research Report RR 249, Transport and Road Research Laboratory, Crowthorne, United Kingdom.
Taylor, N.B. (1996). “CONTRAM Modeling in the Real-time Context — A Review and Prognosis.” TRRL Project Report PR/TT/088/96, Transport and Road Research Laboratory, Crowthorne, United Kingdom.
Waller, S.T. (2000). “Optimization and Control of Stochastic Dynamic Transportation Systems: Formulations, Solution Methodologies, and Computational Experience.” Ph.D. Dissertation, Northwestern University, Evanston, IL.
Waller, S.T. and A.K. Ziliaskopoulos. (1998). “A Chance-Constrained Based Stochastic Dynamic Traffic Assignment Model: Analysis, Formulation and a Solution Algorithm.” TRISTAN III Proceedings, San Juan, Puerto Rico.
Wardrop, J.G. (1952). “Some Theoretical Aspects of Road Traffic Research.” Proceedings, Institution of Civil Engineers II(1), 325–378.
Watling, D. (1999). “Stability of the Stochastic Equilibrium Assignment Problem: A Dynamical Systems Approach.” Transportation Research 33B, 281–312.
Wie, B.W. (1990). “Dynamic Analysis of User Optimized Network Flows With Elastic Travel Demand.” Presented at the 70th TRB Annual Meeting, Washington, D.C., 1991.
Wie, B.W., R.L. Tobin, T.L. Friesz, and D. Bernstein. (1995). “A Discrete Time, Nested Cost Operator Approach to the Dynamic Network User Equilibrium Problem.” Transportation Science 29(1), 79–92.
Wu, J.F. and G.L. Chang. (1996). “Estimation of Time-Varying Origin-Destination Distributions with Dynamic Screenline Flows.” Transportation Research 30B(4), 277–290.
Yang, T.-H. (2001). “Deployable Stable Traffic Assignment Models for Control in Dynamic Traffic Networks: A Dynamical Systems Approach.” Ph.D. Dissertation, Purdue University.
Zhang, D. and A. Nagurney. (1995). “On the Stability of Projected Dynamical Systems.” Journal of Optimization Theory and Applications 85, 97–124.
Zhang, D. and A. Nagurney. (1996). “On the Local and Global Stability of a Travel Route Choice Adjustment Process.” Transportation Research 30B, 245–262.
Ziliaskopoulos, A.K. (2000). “A Linear Programming Model for the Single Destination System Optimum Dynamic Traffic Assignment Problem.” Transportation Science 34(1), 37–49.
Ziliaskopoulos, A.K. and S. Lee. (1997). “A Cell Transmission Based Assignment-Simulation Model for Integrated Freeway/Surface Street Systems.” Transportation Research Record 1701, 12–23.
Ziliaskopoulos, A.K. and H.S. Mahmassani. (1993). “A Time-Dependent Shortest Path Algorithm for Real-Time Intelligent Vehicle/Highway Systems.” Transportation Research Record 1408, 94–104.
Ziliaskopoulos, A.K. and H.S. Mahmassani. (1994). Technical Commentary on the Paper Entitled “The Fastest Path in Time-Dependent Networks for Intelligent Vehicle/Highway Systems,” by D.E. Kaufman and R.L. Smith, in IVHS Journal 1, 91–95.
Ziliaskopoulos, A.K. and H.S. Mahmassani. (1996). “On Finding Least Time Paths Considering Delays for Intersection Movements.” Transportation Research 30B(5), 359–367.
Ziliaskopoulos, A.K. and L. Rao. (1999). “A Simultaneous Route and Departure Time Choice Equilibrium Model on Dynamic Networks.” International Transactions of Operational Research 6(1), 21–37.
Ziliaskopoulos, A.K. and S.T. Waller. (2000). “An Internet-based Geographical Information System that Integrates Data, Models and Users for Transportation Applications.” Transportation Research 8C(1), 427–444.
Ziliaskopoulos, A.K. and W.W. Wardell. (2000). “An Intermodal Optimum Path Algorithm for Dynamic Multimodel Networks.” European Journal of Operational Research 125, 486–502.
Ziliaskopoulos, A.K., D. Kotzinos, and H.S. Mahmassani. (1997). “Design and Implementation of Parallel Time-Dependent Shortest Path Algorithms for Real-Time Intelligent Transportation Systems.” Transportation Research 5C(2), 95–107.
Ziliaskopoulos, A.K., D. Doan, and H.S. Mahmassani. (1998). “An On-line Monitoring System for Real-Time Traffic Management Applications.” Transportation Research Record 1678, 142–150.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Peeta, S., Ziliaskopoulos, A.K. Foundations of Dynamic Traffic Assignment: The Past, the Present and the Future. Networks and Spatial Economics 1, 233–265 (2001). https://doi.org/10.1023/A:1012827724856
Issue Date:
DOI: https://doi.org/10.1023/A:1012827724856