Study on traffic flow dynamics of connected autonomous vehicles on road slopes

In this paper, we propose a car-following model that captures the driving behavior of connected autonomous vehicles (CAVs) on sloped roads. The model considers the ability of CAVs to receive information from multiple preceding vehicles via communication devices, as well as the time delays associated with perception, computation, and actuation. By leveraging the transformation relationship between microscopic and macroscopic traffic variables, we derive a corresponding macroscopic model. For the initial homogeneous equilibrium state, the linear stability condition under small disturbance is obtained by linear stability analysis, and the global stability condition under large disturbance is derived by wave front expansion method. Our findings indicate that increasing the upslope angle enhances traffic flow stability, whereas increasing the downslope angle reduces it. Furthermore, incorporating connected autonomous vehicles mitigates both linear and global instability. For non-uniform traffic flow, we perform a Hopf bifurcation analysis near the equilibrium point. Numerical simulations verify the effects of slope angle and connected autonomous driving on traffic stability. Finally, we present a phase diagram of the Hopf bifurcation and classify its types using MatCont software.