Approximation to Optimal Dynamic Traffic Assignment of Peak Period Traffic to a Congested City Network

  • M. O. Ghali
  • M. J. Smith
Conference paper
Part of the Transportation Analysis book series (TRANSANALY)


We present a vehicle-by-vehicle deterministic queueing traffic assignment model for minimising total travel delay in a congested road network. The model routes drivers, one at a time, according to the marginal delay of each link. This is regarded as a combination of the delay caused by each driver to others travelling in the whole network, and the travel delay experienced by the driver himself. This yields an approximate system optimal routeing pattern and the corresponding road prices needed to cause the user equilibrium traffic pattern, which would arise from each driver minimising only his own travel delays, to be the approximate system optimal one. A key characteristic of the model presented is that it is applicable to (multi-commodity) networks having many origin-destination pairs and many bottlenecks. The model has evolved as a result of the initial study on this problem in Ghali and Smith [1], and basically extends the model in that paper. Computational results comparing network performance of applying the model of this paper against that of the previous paper as well as against network performance due to the natural user equilibrium networks are provided.


Optimal Route Traffic Assignment Link Bottleneck Single Vehicle Dynamic Traffic Assignment 
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  1. [1]
    M. O. Ghali and M. J. Smith. “A Model for the Dynamic System Optimum Traffic Assignment Problem”. Paper presented at the 71st Annual Meeting of the Transportation Research Board, Washington, 1992, and to appear in Transportation Research-B, 1994.Google Scholar
  2. [2]
    D. K. Merchant and G. L. Nemhauser. “A Model and an Algorithm for the Dynamic Traffic Assignment Problem”. Transportation Science, 12 (3), 183–199, 1978. 269CrossRefGoogle Scholar
  3. [3]
    D. K. Merchant and G. L. Nemhauser. “Optimality conditions for a dynamic traffic assignment model”. Transportation Science, 12 (3), 200–207, 1987.CrossRefGoogle Scholar
  4. [4]
    M. Carey. “A constraint qualification for a dynamic traffic assignment model”. Transportation Science 20 (1), 55–58, 1986.CrossRefGoogle Scholar
  5. [5]
    M. Carey. “Optimal Time-Varying Flows on Congested Networks”. Operations Research, 35 (1), 58–69, 1987.CrossRefGoogle Scholar
  6. [6]
    T. L. Friesz, F. J. Luque, R. L. Tobin and B. W. Wie. “Dynamic Network Traffic Assignment Considered as a Continuous Time Optimal Problem”. Operations Research 35, 58–69, 1989.Google Scholar
  7. [7]
    M. O. Ghali and M. J. Smith. “Traffic Assignment, Traffic Control and Road pricing”. Proceedings of the 12th International Symposium on Transportation and Traffic Theory. Editor: C. Daganzo. Elsevier, New York, 147–170, 1993.Google Scholar
  8. [8]
    M. J. Smith and M. O. Ghali. “The dynamics of traffic assignment and traffic control”. Paper presented at the joint Italian/USA Seminar on Congested Urban Networks: Traffic Control and Dynamic Equilibrium, Capri, April 1989, and is published in Transportation Research, Vol. 24B, pp. 409–422, 1990.Google Scholar
  9. [9]
    M. J. Smith and M. O. Ghali. “Dynamic traffic assignment and dynamic traffic control”. Proceedings of the llth International Symposium on Transportation and Traffic Theory. Editor: M. Koshi. Elsevier, New York, London and Amsterdam, 223–263, 1990.Google Scholar
  10. [10]
    NB Taylor. CONTRAM 5: “An Enhanced Traffic Assignment Model”. Transport Research Laboratory, Crowthorne, United Kingdom, 1990.Google Scholar
  11. [11]
    E. W. Dijkstra. “A Note on Two Problems in Connexion with Graphs”. Numer. Math. 1, 269–271, 1959.CrossRefGoogle Scholar
  12. [12]
    R. Bellman. “On a Routing Problem”. Quart. Appl. Math., Vol 16, 87–90, 1958.Google Scholar
  13. [13]
    D. E. Kaufman and R. L. Smith. “Fastest Paths in Time-Dependent Networks for Intelligent Vehicle-Highway Systems Applications”. IVHS Journal, 1 (1), 1–11, 1993.Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1995

Authors and Affiliations

  • M. O. Ghali
    • 1
  • M. J. Smith
    • 1
  1. 1.Department of MathematicsUniversity of YorkYorkUK

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