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The dynamics of traffic assignment and traffic control: A theoretical study

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  • Smith, M. J.
  • Ghali, M.

Abstract

The paper considers traffic assignment, with traffic controls, in an increasingly dynamic way. First, a natural way of introducing the responsive policy, Po, into steady state traffic assignment is presented. Then it is shown that natural stability results follow within a dynamical version of this static equilibrium model (still with a constant demand). We are able to obtain similar stability results when queues are explicitly allowed for, provided demand is constant. Finally we allow demand to vary with time; we consider the dynamic assignment problem with signal-settings now fixed. Here we assume that vehicles are very short and that deterministic queueing theory applies, and show that the time-dependent queueing delay at the bottleneck at the end of a link is a monotone function of the time-dependent input profile to the bottleneck. We have been unable to obtain results when dynamic demand and responsive signal control are combined.

Suggested Citation

  • Smith, M. J. & Ghali, M., 1990. "The dynamics of traffic assignment and traffic control: A theoretical study," Transportation Research Part B: Methodological, Elsevier, vol. 24(6), pages 409-422, December.
  • Handle: RePEc:eee:transb:v:24:y:1990:i:6:p:409-422
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    References listed on IDEAS

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    1. S. Selvanathan, 1987. "Do OECD Consumers Obey Demand Theory?," Economics Discussion / Working Papers 87-04, The University of Western Australia, Department of Economics.
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    Cited by:

    1. Huang, Hai-Jun & Lam, William H. K., 2002. "Modeling and solving the dynamic user equilibrium route and departure time choice problem in network with queues," Transportation Research Part B: Methodological, Elsevier, vol. 36(3), pages 253-273, March.
    2. repec:eee:transb:v:105:y:2017:i:c:p:1-18 is not listed on IDEAS
    3. Yang, Baiyu & Miller-Hooks, Elise, 2004. "Adaptive routing considering delays due to signal operations," Transportation Research Part B: Methodological, Elsevier, vol. 38(5), pages 385-413, June.
    4. Meneguzzer, Claudio, 1995. "An equilibrium route choice model with explicit treatment of the effect of intersections," Transportation Research Part B: Methodological, Elsevier, vol. 29(5), pages 329-356, October.
    5. Iryo, Takamasa, 2011. "Multiple equilibria in a dynamic traffic network," Transportation Research Part B: Methodological, Elsevier, vol. 45(6), pages 867-879, July.
    6. William Lam & Hai-jun Huang, 2002. "A combined activity/travel choice model for congested road networks with queues," Transportation, Springer, vol. 29(1), pages 5-29, February.
    7. Rinaldi, Marco & Tampère, Chris M.J., 2015. "An extended coordinate descent method for distributed anticipatory network traffic control," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 107-131.
    8. David Levinson & Ajay Kumar, 1994. "Integrating Feedback into the Transportation Planning Mode," Working Papers 199404, University of Minnesota: Nexus Research Group.
    9. Smith, M.J. & Liu, R. & Mounce, R., 2015. "Traffic control and route choice: Capacity maximisation and stability," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 863-885.
    10. Jiang, Yi & Li, Shuo & Shamo, Daniel E., 2006. "A platoon-based traffic signal timing algorithm for major-minor intersection types," Transportation Research Part B: Methodological, Elsevier, vol. 40(7), pages 543-562, August.
    11. Mounce, Richard, 2006. "Convergence in a continuous dynamic queueing model for traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 40(9), pages 779-791, November.
    12. Lee, Seunghyeon & Wong, S.C., 2017. "Group-based approach to predictive delay model based on incremental queue accumulations for adaptive traffic control systems," Transportation Research Part B: Methodological, Elsevier, vol. 98(C), pages 1-20.

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