Stability analysis of mixed-traffic platoons considering driver heterogeneity and the communication scale of connected vehicles

The car-following behavior of vehicles is influenced by multiple factors, including driver heterogeneity, automation level, and multi-vehicle interactions. Based on the German HighD high-precision aerial traffic trajectory dataset, this study systematically investigates the longitudinal dynamic characteristics and stability mechanisms of mixed traffic platoons composed of human-driven vehicles (HDVs) and connected and automated vehicles (CAVs). Special attention is given to the behavioral differences between heterogeneous human drivers and automated driving control systems. In modeling human-driven vehicles, K-means clustering is applied to classify driver types from empirical trajectory data, explicitly introducing driver heterogeneity into the model. Based on this, an improved Intelligent Driver Model (IDM) is proposed, capable of distinguishing among conservative, normal, and aggressive driving behaviors. The enhanced model significantly improves the fitting accuracy to real-world data, with the average trajectory fitting error reduced by approximately 21.9 % compared with the traditional IDM. This allows for a more accurate depiction of actual driver longitudinal behavior under varying traffic densities and speed conditions. For connected and automated vehicles (CAVs), an improved car-following model is developed that integrates multi-preceding-vehicle information and rearward-looking effects. The model also incorporates a functional degradation mechanism to capture the performance loss of CAVs when following HDVs, due to limited perception and communication capabilities in vehicular networks. Based on this model, linear stability conditions for both CAVs and the automated driving system are derived, and sensitivity analysis is conducted to identify key parameter ranges ensuring system stability. This provides theoretical guidance for the control parameter design of mixed traffic platoons. Building on this foundation, a Markov platoon modeling framework is employed to construct a stability analysis model for heterogeneous traffic flow. The stability criteria of mixed platoons are derived, and numerical simulations are conducted to systematically examine the impacts of platoon size, CAV penetration rate, and platoon cohesion on traffic flow stability. The results show that multi-vehicle information interaction significantly expands the stability region, with the most pronounced improvement observed when information from two preceding vehicles is available. As the CAV penetration rate increases, the amplitude of speed fluctuations gradually decreases each 20 % increase in penetration reduces speed disturbance amplitude by approximately 1.4 times. Moreover, the influence of platoon cohesion on stability is penetration-dependent: under high penetration conditions, stronger cooperation enhances stability markedly; however, under low penetration conditions, excessively strong cohesion may amplify oscillatory disturbances. The optimal platoon cohesion strength is found to be −0.2.