Skip to main content
SpringerLink
Log in
Book cover

Dynamic Optimization and Differential Games pp 411–456Cite as

Dynamic User Equilibrium

  • Chapter
  • First Online:

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

Abstract

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.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   189.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

List of References Cited and Additional Reading

  • 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 

  • 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 

  • 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 

  • 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.

    Article  Google Scholar 

  • Carey, M. (1986). A constraint qualification for a dynamic traffic assignment problem. Transportation Science 20(1), 55–58.

    Article  Google Scholar 

  • Carey, M. (1987). Optimal time-varying flows on congested networks. Operations Research 35(1), 58–69.

    Article  Google Scholar 

  • Carey, M. (1992). Nonconvexity of the dynamic traffic assignment problem. Transportation Research 26B(2), 127–132.

    Google Scholar 

  • 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 

  • Daganzo, C. (1994). The cell transmission model. Part I: A simple dynamic representation of highway traffic. Transportation Research B 28(4), 269–287.

    Article  Google Scholar 

  • Daganzo, C. (1995). The cell transmission model. Part II: Network traffic. Transportation Research Part B 29(2), 79–93.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Halmos, P. (1974). Measure Theory. New York: Springer-Verlag.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Merchant, D. and G. Nemhauser (1978a). A model and an algorithm for the dynamic traffic assignment problems. Transportation Science 12(3), 183–199.

    Article  Google Scholar 

  • Merchant, D. and G. Nemhauser (1978b). Optimality conditions for a dynamic traffic assignment model. Transportation Science 12(3), 200–207.

    Article  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • Ran, B. and D. Boyce (1996). Modeling Dynamic Transportation Networks: An Intelligent Transportation System Oriented Approach. New York: Springer-Verlag.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Tobin, R. (1993). Notes on flow propagation constraints. Working Paper 93-10, Network Analysis Laboratory, George Mason University.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Zhu, D. L. and P. Marcotte (2000). On the existence of solutions to the dynamic user equilibrium problem. Transportation Science 34(4), 402–414.

    Article  Google Scholar 

  • Ziliaskopoulos, A. K. (2000). A linear programming model for the single destination system optimum dynamic traffic assignment problem. Transportation Science 34(1), 1–12.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. Industrial & Manufacturing Engineering, Pennsylvania State University, 305 Leonhard Building, University Park, Pennsylvania, 16802, USA

    Terry L. Friesz

Authors
  1. Terry L. Friesz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Terry L. Friesz .

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Friesz, T.L. (2010). Dynamic User Equilibrium. In: Dynamic Optimization and Differential Games. International Series in Operations Research & Management Science, vol 135. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-72778-3_9

Download citation

Publish with us

Policies and ethics

Search

Navigation