A cell-based simultaneous route and departure time choice model with elastic demand

This paper develops a cell-based formulation for the simultaneous route and departure time choice problem with elastic demands through a variational inequality problem (VIP). This formulation follows the ideal Dynamic User Optimal (DUO) route and departure time choice principle and encapsulates a network version of the cell transmission model to improve the accuracy of dynamic traffic modeling. To solve the formulation, we adopt a descent method developed for co-coercive VIP. Two numerical studies are set up to demonstrate the quality of the solutions. The results show that the formulation correctly determines the DUO solution even in the presence of queue spillback and junction blockage. In the analysis, we prove that the origin-destination (OD) first-in-first-out (FIFO) property is only maintained under certain conditions of the travel time and schedule delay costs. These conditions on the cost parameters are, interestingly, consistent with the empirical results. Thus, the theoretical analyses together with the empirical results indicate that OD FIFO should hold in reality. This finding is a reasonable reflection of our experience, which shows that OD FIFO generally holds subject to overtaking not occurring commonly.