Car-following modeling with multi-model driving assistance and stability analysis under heterogeneous time delay

With the increasing number of regular vehicles obtaining real-time traffic information through mobile applications, many are gradually evolving into connected human-driven vehicles (CHVs). Most existing studies focus on modeling the impact of continuous information in driver assistance systems. However, they often overlook advanced event-triggered information, which can strongly influence drivers' decision-making. This limitation significantly restricts the ability of existing models to capture realistic CHV behavior. To address this issue, this study proposes a CHV car-following model framework capable of responding to multiple types of driver assistance information. The framework is built on two sub-models. The first sub-model, developed under the dual-process theory, responds to continuous information and captures drivers' dynamic compliance rate under perceived risk. The second sub-model responds to advanced event-triggered information and describes drivers' behavioral reactions when emergency messages are received from the cloud control platform. Based on this model, linear and nonlinear stability analyses are conducted to investigate the effects of different delay sources on CHV traffic flow stability. The analyses are performed after eliminating the approximation errors arising from delay simplifications in existing methods. The results show that the driver reaction delay remains the dominant factor influencing string stability. When the driver reaction delay stays within the normal range, maintaining the connected vehicle communication delay below a reasonable threshold can significantly enhance traffic flow stability. In addition, the maximum compliance rate, together with the various delay levels, jointly determines the stability boundary of the traffic flow. Based on these findings, several design recommendations for driver assistance systems are proposed to achieve a coordinated balance among efficiency, safety, and cost in connected traffic environments.