Delay-Aware Car-Following Model for Mixed Traffic: Impacts of Automated Vehicles on Traffic Dynamics

Recent studies on the yet-to-be-realized integration of autonomous vehicles (AVs) into conventional traffic, i.e., with human-driven vehicles (HVs), identify heterogeneous temporal responses as a distinguishing characteristic, which can alter traffic stability, safety, and disturbance propagation. The classical car-following model, Intelligent Driver Model (IDM), characterizes traffic based on instantaneous reaction and fixed headways, and perception response delays of drivers. To address this limitation, this study proposes a temporal extension of the IDM that embeds a source term, i.e., effective headway, to model the desired dynamic gap. The proposed extension has been tested on a 1000-m single-lane hypothetical corridor under varying levels of automation (0%, 60%, 100%). Further, a controlled deceleration perturbation was applied to evaluate disturbance propagation, recovery dynamics, and string stability. Results show that HVs traffic exhibits pronounced speed drops, amplified oscillations, and slow return to equilibrium due to long reaction delays. The results demonstrate that incorporating realistic reaction delays and buffer-based spacing yields a more accurate representation of mixed traffic and highlights the stabilizing role of AVs as temporal headways decrease. The proposed framework provides an extensible basis for multi-lane applications, control-policy design, and empirical calibration using AV-HV trajectory datasets.