A cell-based dynamic traffic assignment model: Formulation and properties.

*(English)*Zbl 1001.90016Summary: This paper developed a cell-based dynamic traffic assignment formulation that follows the ideal Dynamic User Optimal (DUO) principle. Through defining an appropriate gap function, we transformed a formulation based on the nonlinear complementarity problem to an equivalent mathematical program. To improve the accuracy of dynamic traffic modelling, this formulation encapsulates a network version of the cell transmission model. We set up four scenarios to evaluate the properties of this formulation, in the aspects of traffic dynamics, traffic interactions across multiple links, and the ideal DUO principle. This formulation produced outputs that are in agreement with what the results ought to be. Namely, the formulation is able to capture dynamic traffic phenomena, such as shock-waves, queue formation, and dissipation. Moreover, it is capable of capturing dynamic traffic interactions across multiple links. Both of these characteristics are inherent from the underlying traffic model adopted in this formulation. The results also demonstrate that this cell-based formulation follows the ideal DUO principle.

##### MSC:

90B20 | Traffic problems in operations research |

90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |

##### Keywords:

cell-based dynamic traffic assignment; nonlinear complementarity problem; dynamic traffic modelling; cell transmission model; ideal DUO principle; shock-waves; queue formation; dissipation
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\textit{H. K. Lo} and \textit{W. Y. Szeto}, Math. Comput. Modelling 35, No. 7--8, 849--865 (2002; Zbl 1001.90016)

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