Cell Transmission Model for Mixed Traffic Flow with Connected and Autonomous Vehicles

The cell transmission model (CTM) is important for solving macroscopic traffic problems. Although some studies have been conducted for multiclass CTM, a simplified CTM for traffic flow mixed with connected and autonomous vehicles (CAVs) is still needed. This paper extends the homogenous CTM to form a mixed CTM under different CAV market penetration rates. To deal with this, the mixed triangular fundamental diagram is derived with different proportions of various vehicle types. The maximum capacity and backward wave speed of the mixed traffic flow are described by vehicle class proportions. Based on the mixed triangular fundamental diagram, the mixed CTM is proposed for different CAV penetration rates. An example application to validate the usefulness of the proposed mixed CTM is carried out. The mixed traffic flow in the application consists of cooperative adaptive cruise control (CACC), adaptive cruise control (ACC), and human vehicles with random vehicle orders. It is defined that CAVs travel under ACC when following a human vehicle without vehicle-to-vehicle (V2V) communication. Otherwise, the CACC function applies. The expected proportions of the CACC, ACC, and human vehicles in the random mixed traffic flow are described by the CAV penetration rate. Mixed CTM numerical experiments are conducted to evaluate the impacts of traffic accidents under different CAV penetration rates. Moreover, car-following simulations are performed to show consistency between macroscopic CTM numerical experiments and microscopic car-following simulations. The example application reveals that the proposed mixed CTM is simple and practical as applied to solve the traffic problem under different CAV penetration rates.