Dynamic system optimum simultaneous route and departure time choice problems: Intersection-movement-based formulations and comparisons

In this paper, we propose intersection-movement-based models to formulate dynamic system optimum simultaneous route and departure time choice (DSO-SRDTC) problems over general networks and compare the models with the link-based and path-based counterparts. Each of these three types of models has four variants, which are formed by whether to consider first-in-first-out (FIFO) constraints and non-vehicle holding (NVH) constraints. In all three types of DSO-SRDTC models and their variants, the link transmission model (LTM) is incorporated as their traffic flow model. The DSO-SRDTC problems without FIFO constraints are formulated as linear programming (LP) problems, while the DSO-SRDTC problems with FIFO constraints are formulated as non-convex non-linear programming problems. We find that existing link-based NVH constraints cannot completely eliminate vehicle holding (VH) solutions, and propose both intersection-movement-based and path-based NVH constraints, which can completely eliminate VH solutions. We also prove that the link-based, intersection-movement-based, and path-based models of DSO-SRDTC problems without FIFO constraints are equivalent in terms of obtaining the same optimal total system travel cost (TSTC). However, the three types of models for DSO-SRDTC problems with FIFO constraints can obtain different optimal TSTCs. Based on the solution properties of the DSO-SRDTC problems with FIFO constraints, branch-and-bound algorithms are modified to solve the DSO-SRDTC problems with FIFO constraints for global optima. Numerical examples are set up to demonstrate the properties and performance of the proposed models. To the best of our knowledge, we are the pioneers to provide intersection-movement-based formulations for DSO-SRDTC problems and analyze their mathematical properties.