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The existence and calculation of traffic equilibria

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  • Smith, M. J.

Abstract

The paper considers the assignment problem when there are junction interactions. We give an objective function which measures the extent to which a traffic distribution departs from equilibrium, and an algorithm which (under certain conditions) calculates equilibria by steadily reducing the objective function to zero. It is shown that the algorithm certainly works if the network cost-flow function is monotone and continuously differentiable, and a boundary condition is satisfied.

Suggested Citation

  • Smith, M. J., 1983. "The existence and calculation of traffic equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 17(4), pages 291-303, August.
  • Handle: RePEc:eee:transb:v:17:y:1983:i:4:p:291-303
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    Citations

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    Cited by:

    1. Terry E. Daniel & Eyran J. Gisches & Amnon Rapoport, 2009. "Departure Times in Y-Shaped Traffic Networks with Multiple Bottlenecks," American Economic Review, American Economic Association, vol. 99(5), pages 2149-2176, December.
    2. Wen-yi Zhang & Wei Guan & Ji-hui Ma & Jun-fang Tian, 2015. "A Nonlinear Pairwise Swapping Dynamics to Model the Selfish Rerouting Evolutionary Game," Networks and Spatial Economics, Springer, vol. 15(4), pages 1075-1092, December.
    3. repec:eee:transb:v:104:y:2017:i:c:p:1-16 is not listed on IDEAS
    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. David Levinson & Ajay Kumar, 1994. "Integrating Feedback into the Transportation Planning Mode," Working Papers 199404, University of Minnesota: Nexus Research Group.
    6. Xiao, Feng & Shen, Wei & Michael Zhang, H., 2012. "The morning commute under flat toll and tactical waiting," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1346-1359.
    7. Lo, Hong K. & Chen, Anthony, 2000. "Traffic equilibrium problem with route-specific costs: formulation and algorithms," Transportation Research Part B: Methodological, Elsevier, vol. 34(6), pages 493-513, August.
    8. Guo, Ren-Yong & Yang, Hai & Huang, Hai-Jun & Tan, Zhijia, 2015. "Link-based day-to-day network traffic dynamics and equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 248-260.
    9. Dulce Rosas & Jordi Castro & LĂ­dia Montero, 2009. "Using ACCPM in a simplicial decomposition algorithm for the traffic assignment problem," Computational Optimization and Applications, Springer, vol. 44(2), pages 289-313, November.
    10. Peeta, Srinivas, 2016. "A marginal utility day-to-day traffic evolution model based on one-step strategic thinkingAuthor-Name: He, Xiaozheng," Transportation Research Part B: Methodological, Elsevier, vol. 84(C), pages 237-255.
    11. Arnott, Richard & Kraus, Marvin, 1993. "The Ramsey problem for congestible facilities," Journal of Public Economics, Elsevier, vol. 50(3), pages 371-396, March.
    12. Kumar, Amit & Peeta, Srinivas, 2015. "A day-to-day dynamical model for the evolution of path flows under disequilibrium of traffic networks with fixed demand," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 235-256.
    13. He, Xiaozheng & Guo, Xiaolei & Liu, Henry X., 2010. "A link-based day-to-day traffic assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 44(4), pages 597-608, May.
    14. Farokhi, Farhad & Johansson, Karl H., 2015. "A piecewise-constant congestion taxing policy for repeated routing games," Transportation Research Part B: Methodological, Elsevier, vol. 78(C), pages 123-143.
    15. Yang, Fan & Zhang, Ding, 2009. "Day-to-day stationary link flow pattern," Transportation Research Part B: Methodological, Elsevier, vol. 43(1), pages 119-126, January.
    16. 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.
    17. Lo, Hong K. & Szeto, W. Y., 2002. "A methodology for sustainable traveler information services," Transportation Research Part B: Methodological, Elsevier, vol. 36(2), pages 113-130, February.
    18. Otsubo, Hironori & Rapoport, Amnon, 2008. "Vickrey's model of traffic congestion discretized," Transportation Research Part B: Methodological, Elsevier, vol. 42(10), pages 873-889, December.

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