Modeling the Car-Truck Interaction in a System-Optimal Dynamic Traffic Assignment Model

Several transportation problems, such as implementation of truck-only lanes, require understanding the interaction of heterogeneous dynamic traffic flows in order to provide accurate solutions. System-optimal dynamic traffic assignment can be modeled using a network loading procedure based on the cell transmission model, that is, the hydrodynamic wave model, and solved by linear programming. However, this framework cannot handle the asymmetric integration between the flow of trucks and cars. This article presents a novel formulation for network loading in system-optimal dynamic traffic assignment considering car-truck interactions. By using an embedded cell transmission model, this formulation incorporates a set of assumptions related to the kinematic characteristics of the flow of cars, trucks, and their interactions that can be solved using linear programming. We present numerical results supporting our modeling assumptions. Likewise, the observed emergent behavior captures the car-truck interactions accurately and indicates that minimum system-optimal travel time is obtained by encouraging cars to use highways with shorter distances.