Analysis of linear stability and damping characteristics of car-following model with time delay

Previous studies on driver reaction delay time have primarily focused on its influence on vehicle stability and instability, often neglecting its impact on vehicle damping characteristics, which are crucial for enhancing the disturbance resistance of vehicle platoons. This study aims to explore the dual effects of driver reaction delay time on both vehicle stability and damping characteristics. Specifically, the stability and damping characteristics of a general form of the microscopic car-following model, which incorporates driver reaction delay time, are analyzed to identify the stability conditions and critical damping thresholds for traffic flow. Following this, the effects of single and multiple time delays on the stability and damping properties of the model are discussed in relation to the Intelligent Driver Model (IDM). A detailed analysis under single time delay conditions reveals that an increase in reaction time leads to traffic flow instability, and the maximum value of the safe time headway corresponding to underdamping gradually increases. However, under multiple time delay conditions, increasing the reaction time related to the relative velocity enhances the damping of the IDM, whereas increasing the reaction time associated with space gap reduces the model's damping effect.