Dynamic User Equilibrium

Part of the International Series in Operations Research & Management Science book series (ISOR, volume 135)


Dynamic traffic assignment (DTA) is the positive (descriptive) modeling of time-varying flows of automobiles on road networks consistent with established traffic flow theory and travel demand theory. Dynamic user equilibrium (DUE) is one type of DTA wherein the effective unit travel delay, including early and late arrival penalties, of travel for the same purpose is identical for all utilized path and departure time pairs. In the context of planning, DUE is usually modelled for the within-day time scale based on demands established on a day-to-day time scale.


Variational Inequality Delay Operator User Equilibrium Transportation Research Part Dynamic Traffic Assignment 


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List of References Cited and Additional Reading

  1. Adamo, V., V. Astarita, M. Florian, M. Mahut, and J. H. Wu (1998). A framework for introducing spillback in link-based dynamic network loading models. presented at tristan iii, san juan, puerto rico, june.Google Scholar
  2. Astarita, V. (1995). Flow propagation description in dynamic network loading models. Y.J Stephanedes, F. Filippi, (Eds). Proceedings of IV international conference of Applications of Advanced Technology in Transportation(AATT), 599–603.Google Scholar
  3. Bernstein, D., T. L. Friesz, R. L. Tobin, and B. W. Wie (1993). A variational control formulation of the simultaneous route and departure-time equilibrium problem. Proceedings of the International Symposium on Transportation and Traffic Theory, 107–126.Google Scholar
  4. Bliemer, M. and P. Bovy (2003). Quasi-variational inequality formulation of the multiclass dynamic traffic assignment problem. Transportation Research Part B 37(6), 501–519.CrossRefGoogle Scholar
  5. Carey, M. (1986). A constraint qualification for a dynamic traffic assignment problem. Transportation Science 20(1), 55–58.CrossRefGoogle Scholar
  6. Carey, M. (1987). Optimal time-varying flows on congested networks. Operations Research 35(1), 58–69.CrossRefGoogle Scholar
  7. Carey, M. (1992). Nonconvexity of the dynamic traffic assignment problem. Transportation Research 26B(2), 127–132.Google Scholar
  8. Carey, M. (1995). Dynamic congestion pricing and the price of fifo. In N. H. Gartner and G. Improta (Eds.), Urban Traffic Networks, pp. 335–350. New York: Springer-Verlag.Google Scholar
  9. Daganzo, C. (1994). The cell transmission model. Part I: A simple dynamic representation of highway traffic. Transportation Research B 28(4), 269–287.CrossRefGoogle Scholar
  10. Daganzo, C. (1995). The cell transmission model. Part II: Network traffic. Transportation Research Part B 29(2), 79–93.CrossRefGoogle Scholar
  11. Friesz, T., D. Bernstein, and R. Stough (1996). Dynamic systems, variational inequalities, and control-theoretic models for predicting time-varying urban network flows. Transportation Science 30(1), 14–31.CrossRefGoogle Scholar
  12. Friesz, T., D. Bernstein, Z. Suo, and R. Tobin (2001). Dynamic network user equilibrium with state-dependent time lags. Networks and Spatial Economics 1(3/4), 319–347.CrossRefGoogle Scholar
  13. Friesz, T., C. Kwon, and D. Bernstein (2007). Analytical dynamic traffic assignment models. In D. A. Hensher and K. J. Button (Eds.), Handbook of Transport Modelling (2nd ed.). New York: Pergamon.Google Scholar
  14. Friesz, T., J. Luque, R. Tobin, and B. Wie (1989). Dynamic network traffic assignment considered as a continuous-time optimal control problem. Operations Research 37(6), 893–901.CrossRefGoogle Scholar
  15. Friesz, T. and R. Mookherjee (2006). Solving the dynamic network user equilibrium problem with state-dependent time shifts. Transportation Research Part B 40, 207–229.CrossRefGoogle Scholar
  16. Friesz, T., R. Tobin, D. Bernstein, and Z. Suo (1995). Proper flow propagation constraints which obviate exit functions in dynamic traffic assignment. INFORMS Spring National Meeting, Los Angeles, April 23 26.Google Scholar
  17. Friesz, T. L., D. Bernstein, T. Smith, R. Tobin, and B. Wie (1993). A variational inequality formulation of the dynamic network user equilibrium problem. Operations Research 41, 80–91.CrossRefGoogle Scholar
  18. Friesz, T. L., P. A. Viton, and R. L. Tobin (1985). Economic and computational aspects of freight network equilibrium: a synthesis. Journal of Regional Science 25, 29–49.CrossRefGoogle Scholar
  19. Halmos, P. (1974). Measure Theory. New York: Springer-Verlag.Google Scholar
  20. Li, Y., S. Waller, and T. Ziliaskopoulos (2003). A decomposition scheme for system optimal dynamic traffic assignment models. Networks and Spatial Economics 3(4), 441–455.CrossRefGoogle Scholar
  21. Lo, H. and W. Szeto (2002). A cell-based variational inequality formulation of the dynamic user optimal assignment problem. Transportation Research Part B 36(5), 421–443.CrossRefGoogle Scholar
  22. Merchant, D. and G. Nemhauser (1978a). A model and an algorithm for the dynamic traffic assignment problems. Transportation Science 12(3), 183–199.CrossRefGoogle Scholar
  23. Merchant, D. and G. Nemhauser (1978b). Optimality conditions for a dynamic traffic assignment model. Transportation Science 12(3), 200–207.CrossRefGoogle Scholar
  24. Nie, Y. and H. M. Zhang (2010). Solving the dynamic user optimal assignment problem considering queue spillback. Networks and Spatial Economics 10(2), 1 – 23.Google Scholar
  25. Peeta, S. and A. Ziliaskopoulos (2001). Foundations of dynamic traffic assignment: the past, the present and the future. Networks and Spatial Economics 1(3), 233–265.CrossRefGoogle Scholar
  26. Ran, B. and D. Boyce (1996). Modeling Dynamic Transportation Networks: An Intelligent Transportation System Oriented Approach. New York: Springer-Verlag.Google Scholar
  27. Ran, B., D. Boyce, and L. LeBlanc (1993). A new class of instantaneous dynamic user optimal traffic assignment models. Operations Research 41(1), 192–202.CrossRefGoogle Scholar
  28. Szeto, W. and H. Lo (2004). A cell-based simultaneous route and departure time choice model with elastic demand. Transportation Research Part B 38(7), 593–612.CrossRefGoogle Scholar
  29. Tobin, R. (1993). Notes on flow propagation constraints. Working Paper 93-10, Network Analysis Laboratory, George Mason University.Google Scholar
  30. Wie, B., R. Tobin, T. 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.CrossRefGoogle Scholar
  31. Wu, J., Y. Chen, and M. Florian (1998). The continuous dynamic network loading problem: a mathematical formulation and solution method. Transportation Research Part B 32(3), 173–187.CrossRefGoogle Scholar
  32. Zhu, D. L. and P. Marcotte (2000). On the existence of solutions to the dynamic user equilibrium problem. Transportation Science 34(4), 402–414.CrossRefGoogle Scholar
  33. Ziliaskopoulos, A. K. (2000). A linear programming model for the single destination system optimum dynamic traffic assignment problem. Transportation Science 34(1), 1–12.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Dept. Industrial & Manufacturing EngineeringPennsylvania State UniversityUniversity ParkUSA

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