Evaluation of Mixed Traffic Modeling: Comparing Microscopic and Macroscopic Components

As more and more Connected and Automated Vehicles enter public roads, Lagrangian traffic control strategies that leverage their presence to improve traffic flow are being proposed. As a result, the disparity in driving behaviours between different classes of vehicles is likely to continue increasing. Although numerous multi-class traffic models have been proposed, few adequately capture the complex interactions between vehicles with significantly different driving behaviour. In this work we study the simplest case of two-class traffic, with vehicle classes differentiated only by their desired speeds. The dynamics of this model are analysed in detail through solving the state discontinuity problems, where class traffic densities change, and interface discontinuity problems, where the reference speed of one class changes. The resulting traffic density profiles are compared with those arising from a corresponding microscopic model, incorporating both the car-following and lane-changing behaviour of vehicles of different classes. We show that the studied macroscopic model is congruent with an appropriately calibrated microscopic model.