A Multiclass Link Transmission Model for a Class-Varying Capacity and Congested Wave Speed

Varying implementations and availability of vehicle automation result in vehicles using significantly different driving behaviors. Adaptive cruise control implementations vary by manufacturer and also differ from human driving. Due to the prevalence of partial automation on new vehicles, researchers and practitioners interested in forecasting future traffic conditions are considering mixed or multiclass flow scenarios. Prior work on automated vehicles proposed a multiclass kinematic wave theory where the flow-density relationship changes in space and time in response to local variations in class proportions, They solved this theory using a Godunov approximation (cell transmission model). Capacity and congested wave speed are assumed to vary with respect to class proportions, and a triangular flow-density relationship is used. This problem is challenging because the flow-density relationship varies endogenously with the movement of vehicles, resulting in two unknowns that must be solved together: vehicle movements (cumulative counts) and boundaries defining changes in the flow-density relationship. This paper derives a multiclass link transmission model to solve the multiclass kinematic wave theory for any finite number of classes. In the process, we derive a multiclass Newell's method to find exact solutions as a linear program. A simplified iterative algorithm is obtained to more quickly solve the multiclass link transmission model to be useful for large networks.