On dynamic fundamental diagrams: Implications for automated vehicles

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.