Frequency-domain stability analysis of mixed traffic flow considering communication degradation and human driving heterogeneity

Mixed traffic containing connected automated vehicles (CAVs) and human-driven vehicles (HDVs) is sensitive to loss of cooperative information and heterogeneous driver responses. This study develops a probability-weighted full-frequency transfer-function framework to evaluate longitudinal string stability under communication degradation. CAVs are represented by cooperative adaptive cruise control (CACC) when cooperative information is available and by adaptive cruise control (ACC) when such information is unavailable; HDV responses are represented by the intelligent driver model (IDM), optimal velocity model (OVM), and risk-sensitive model (RSM). The framework preserves frequency-dependent disturbance responses and interprets the conventional algebraic condition as a low-frequency approximation. Under the adopted single-lane, small-perturbation assumptions, passive CACC-to-ACC degradation raised the global critical CAV penetration threshold from about 87.3% in an ideal connected-upgrade benchmark to about 96.0% in the degraded baseline. HDV heterogeneity mainly compressed local stable-speed regions rather than changing the global threshold, and this pattern persisted under 100 Latin Hypercube samples with ±10% HDV parameter perturbations. A 5% functional communication-reliability loss increased the critical threshold to about 99.7% and compressed the stable domain; an equivalent response delay reduced the stable-area ratio even when the global threshold changed only slightly at 0.20 s. An NGSIM US101 trajectory replay supported the IDM-based HDV component, with median speed and spacing root mean square errors of 0.8456 m/s and 3.5078 m. These findings indicate that mixed-flow stability depends not only on CAV penetration but also on cooperative-information availability and HDV response heterogeneity, while the full speed-penetration stability map remains a model-based prediction.