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A bi-level programming approach for trip matrix estimation and traffic control problems with stochastic user equilibrium link flows

  • Maher, Michael J.
  • Zhang, Xiaoyan
  • Vliet, Dirck Van
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    This paper deals with two mathematically similar problems in transport network analysis: trip matrix estimation and traffic signal optimisation on congested road networks. These two problems are formulated as bi-level programming problems with stochastic user equilibrium assignment as the second-level programming problem. We differentiate two types of solutions in the combined matrix estimation and stochastic user equilibrium assignment problem (or the combined signal optimisation and stochastic user equilibrium assignment problem): one is the solution to the bi-level programming problem and the other the mutually consistent solution where the two sub-problems in the combined problem are solved simultaneously. In this paper, we shall concentrate on the bi-level programming approach, although we shall also consider mutually consistent solutions so as to contrast the two types of solutions. The purpose of the paper is to present a solution algorithm for the two bi-level programming problems and to test the algorithm on several networks.

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    Article provided by Elsevier in its journal Transportation Research Part B: Methodological.

    Volume (Year): 35 (2001)
    Issue (Month): 1 (January)
    Pages: 23-40

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    Handle: RePEc:eee:transb:v:35:y:2001:i:1:p:23-40
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    1. Cascetta, Ennio, 1984. "Estimation of trip matrices from traffic counts and survey data: A generalized least squares estimator," Transportation Research Part B: Methodological, Elsevier, vol. 18(4-5), pages 289-299.
    2. Yang, Hai & Sasaki, Tsuna & Iida, Yasunori & Asakura, Yasuo, 1992. "Estimation of origin-destination matrices from link traffic counts on congested networks," Transportation Research Part B: Methodological, Elsevier, vol. 26(6), pages 417-434, December.
    3. Maher, Mike, 1998. "Algorithms for logit-based stochastic user equilibrium assignment," Transportation Research Part B: Methodological, Elsevier, vol. 32(8), pages 539-549, November.
    4. Cascetta, Ennio & Nguyen, Sang, 1988. "A unified framework for estimating or updating origin/destination matrices from traffic counts," Transportation Research Part B: Methodological, Elsevier, vol. 22(6), pages 437-455, December.
    5. Leurent, Fabien M., 1997. "Curbing the computational difficulty of the logit equilibrium assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 31(4), pages 315-326, August.
    6. Yang, Hai, 1995. "Heuristic algorithms for the bilevel origin-destination matrix estimation problem," Transportation Research Part B: Methodological, Elsevier, vol. 29(4), pages 231-242, August.
    7. Davis, Gary A., 1994. "Exact local solution of the continuous network design problem via stochastic user equilibrium assignment," Transportation Research Part B: Methodological, Elsevier, vol. 28(1), pages 61-75, February.
    8. Yang, Hai & Yagar, Sam, 1995. "Traffic assignment and signal control in saturated road networks," Transportation Research Part A: Policy and Practice, Elsevier, vol. 29(2), pages 125-139, March.
    9. Maher, M. J. & Hughes, P. C., 1997. "A probit-based stochastic user equilibrium assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 31(4), pages 341-355, August.
    10. Fisk, C. S., 1984. "Game theory and transportation systems modelling," Transportation Research Part B: Methodological, Elsevier, vol. 18(4-5), pages 301-313.
    11. Fisk, C. S., 1988. "On combining maximum entropy trip matrix estimation with user optimal assignment," Transportation Research Part B: Methodological, Elsevier, vol. 22(1), pages 69-73, February.
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