Link-based system optimum dynamic traffic assignment problems with environmental objectives

Maintaining air-quality standards has been a priority for transportation planners and policy makers worldwide. However, most existing system optimum dynamic traffic assignment (SO-DTA) models do not accommodate environmental objectives. In this paper, we use the link transmission model (LTM) to develop SO-DTA models that minimize total system emissions (TSE) in single destination networks. We use step functions to approximate cumulative flow curves for individual links, and to decompose link inflow into sub-flows according to time intervals at which they leave the link. The decomposed link inflows are used to estimate link emissions. Dynamic network constraints, non-vehicle holding constraints and link inflow decomposition constraints are considered, and SO-DTA problems with environmental objectives are formulated as mixed integer linear programming (MILP) problems. Any average speed based emission functions can be used for our models. Finally, numerical examples are provided to demonstrate the performance of the proposed models.