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In this study, a new s-shaped three-parameter (S3) traffic flow model is proposed to represent the relationships between three fundamental variables (i.e., flow, speed, and density) in highway traffic. An s-shaped speed-density function is proposed to capture the speed-density relationship under a wide range of possible densities. A consistent car-following model was derived in terms of the proposed s-shaped speed-density function. Both the S3 macroscopic model and the derived microscopic car-following model were calibrated using real-world traffic data.