A cell-based variational inequality formulation of the dynamic user optimal assignment problem

This paper developed a cell-based dynamic traffic assignment formulation that follows the ideal dynamic user optimal (DUO) principle through a variational inequality approach. To improve the accuracy of dynamic traffic modeling, this formulation encapsulates a network version of the Cell Transmission Model (CTM). Moreover, this formulation satisfies the first-in-first-out (FIFO) conditions through the CTM. For solutions, we employed an alternating direction method developed for co-coercive variational inequality problems. We set up two scenarios to evaluate the properties of this formulation, in the areas of traffic dynamics and the ideal DUO principle. The results showed that the formulation was capable of capturing dynamic phenomena, such as shockwaves, queue formation and dissipation. Moreover, the results demonstrated that this cell-based formulation produced solutions that precisely followed the ideal DUO principle.