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The traffic fundamental diagram (FD) describes the relationships among fundamental traffic variables of flow, density, and speed. FD represents fundamental properties of traffic streams, giving insights into traffic performance. This paper presents a theoretical investigation of dynamic FD properties, derived directly from vehicle car-following (control) models to model traffic hysteresis. Analytical derivation of dynamic FD is enabled by (i) frequency-domain representation of vehicle kinematics (acceleration, speed, and position) to derive vehicle trajectories based on transfer function and (ii) continuum approximation of density and flow, measured along the derived trajectories using Edie’s generalized definitions. The formulation is generic: the derivation of dynamic FD is possible with any analytical car-following (control) laws for human-driven vehicles or automated vehicles (AVs). Numerical experiments shed light on the effects of the density-flow measurement region and car-following parameters on the dynamic FD properties for an AV platoon. 

This paper presents a data-driven framework to quantitatively analyze the disturbance amplification behavior of automated vehicles in car-following (CF). The data-driven framework can be applied to unknown CF controllers based on the concept of empirical frequency response function (FRF). Specifically, a well-known signal processing method, Welch’s method, together with a short time Fourier transformation is developed to extract the empirical transfer functions from vehicle trajectories. The method is first developed assuming a generic linear controller with time-invariant CF control features (e.g., control gains) and later extended to capture time-variant features. The proposed methods are evaluated for estimation consistencies via synthetic data-based simulations. The evaluation includes the performances of the linear approximation accuracy for a linear time-invariant controller, a nonlinear controller, and a linear time-variant controller. Results indicate that our framework can provide reasonably consistent results as theoretical ones in terms of disturbance amplification. Further it can perform better than a linear theoretical analysis of disturbance amplification, particularly when nonlinearity in CF behavior is present. The methods are applied to existing field data collected from vehicles with adaptive cruise control (ACC) on the market. Findings reveal that all tested vehicles tend to amplify disturbances, particularly in low frequency (< 0.5 Hz). Further, the results demonstrate that these ACC vehicles exhibit time-varying features in terms of disturbance amplification ratio depending on the leading vehicle trajectories.