Trade-off between safety, mobility and stability in automated vehicle following control: An analytical method

A recent empirical study (Shi and Li, 2021) showed that commercial automated vehicles (AVs) became more unstable as the headway was set to a smaller value, implying possible intrinsic tradeoffs between safety, mobility, and stability aspects in AV following control design. This study aims to analytically explain the underlying vehicle control mechanism that dictates these tradeoffs. To this end, a robust optimization model is formulated based upon a parsimonious linear AV following model to capture the first-order tradeoffs between safety, mobility, and stability. The robust optimization model aims to maintain a sufficient safety buffer to avoid collisions against all possible realistic preceding vehicle trajectories. As opposed to a numerical solution, we managed to solve this model to an analytical solution that captures relationships between the key parameters determining safety, mobility, and stability. The analytical solution reveals that improving AV mobility (or reducing AV following headway) would require overcoming more safety challenges (e.g., enhancing vehicle control to maintain a short safety buffer) while causing more string-instability. The theoretical findings are consistent with the empirical observations in previous studies. Further, they provide a possible explanation for the observed string instability of commercial AV following control (e.g., adaptive cruise control) as a tradeoff for a smaller headway. Overall, this study lays a new methodology foundation for incorporating safety in traffic flow analysis that traditionally focused on only mobility and stability. Further, the findings yield a set of managerial insights into reasonable AV following design and its implications to emerging AV traffic management.