Phase transition of multi-source information-integrated macroscopic continuum model under heterogeneous vehicles environment

In recent years, overtaking behavior has become a major cause of traffic accidents, not only leading to unstable traffic flow but also affecting transportation efficiency and driving safety. With the rapid development of connected autonomous vehicles (CAVs), the heterogeneous traffic flow model composed of CAVs and human-driven vehicles (HDVs) has gradually become the mainstream traffic configuration. To mitigate the instability caused by overtaking in heterogeneous traffic flows, we in this study establish a novel heterogeneous macro continuum model, focusing on analyzing the impact of multi-source integrated information including overtaking, lateral clearance, electronic throttle angle, and CAVs penetration rate on system stability. Through theoretical analysis using linear stability methods and nonlinear perturbation techniques, the neutral stability conditions and KdV-Burgers equation for this new heterogeneous continuum model are derived. Moreover, numerical simulations reveal the quantitative impacts of key parameters: Firstly, by increasing the overtaking coefficient φ from 0 to 0.15, the density wave amplitude is significantly amplified from 0.0574 veh/m to 0.0967 veh/m with a 68.5 % increase, which shows that the overtaking highlights its strong destabilizing effect. Secondly, density fluctuations are effectively suppressed from approximately 0.0597 veh/m to 0.0477 veh/m with a 20.1 % decrease due to increasing the lateral gap coefficient k from 0.1 to 0.3. Simultaneously, the density wave amplitude decreases from 0.0618 veh/m to 0.0508 veh/m with a 17.8 % reduction owing to enhancing the ETAD coefficient γ from 0 to 0.6, which improves system damping and slows disturbance propagation. Finally, the density wave amplitude is reduced from 0.0631 veh/m to 0.0511 veh/m with a 19.0 % decrease by increasing the CAVs penetration rate p from 0.2 to 0.8, effectively suppressing the development of stop-and-go waves and shrinking the phase trajectory limit cycle area. Above results demonstrate that the comprehensive application of multi-source information, particularly maintaining appropriate lateral gap, increasing the coefficient of ETAD and CAVs penetration rates, can significantly enhance the stability of mixed traffic flows, alleviate congestion, and improve road capacity and overall traffic efficiency although overtaking inherently tends to destabilize.