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This study aims (i) to analyze theoretical properties of a recently proposed describing-function (DF) based approach (Li and Ouyang, 2011; Li et al., 2012) for traffic oscillation quantification, (ii) to adapt it for estimating fuel consumption and emission from traffic oscillation and (iii) to explore vehicle control strategies of smoothing traffic with advanced technologies. The DF approach was developed to predict traffic oscillation propagation across a platoon of vehicles following each other by a nonlinear car-following law with only the leading vehicle’s input. We first simplify the DF approach and prove a set of properties (e.g., existence and uniqueness of its solution) that assure its prediction is always consistent with observed traffic oscillation patterns. Then we integrate the DF approach with existing estimation models of fuel consumption and emission to analytically predict environmental impacts (i.e., unit-distance fuel …