Application of gas-kinetic theory to modelling mixed traffic of manual and ACC vehicles

In this article, we propose an extended multiclass gas-kinetic theory applicable to mixed traffic flow of manual and adaptive cruise control (ACC) vehicles. In the model, the acceleration/deceleration of ACC vehicles is specified explicitly using microscopic models. The macroscopic multiclass traffic equations are obtained from the proposed gas-kinetic model using the well-known method of moments. The influencing conditions to traffic flow stability with respect to a small perturbation are derived by the linear stability method. The analytical results show that ACC vehicles contribute to the improved stabilisation of traffic flow. The numerical simulations of our developed multiclass macroscopic model on a circular freeway support our analytical findings and indicate that increasing the penetration of ACC vehicles results in more stable traffic flow. Simulations of merging flows at an on-ramp in an open freeway are carried out to describe the effects of the penetration of ACC vehicles on the bottleneck capacity. It is found that around 30% ACC vehicles in traffic flow leads to significantly increased capacity and reduced travel time. We argue that, together with other microscopic models, our model provides a wider picture of the effects of ACC vehicles on traffic flow characteristics.