Yanfeng Ouyang University of Illinois at Urbana-Champaign Unlike linear car-following models, nonlinear models generally can produce more realistic traffic oscillation phenomenon (i.e., stop-and-go traffic), but nonlinearity makes analytical quantification of oscillation characteristics (e.g., periodicity and amplitude) significantly more difficult. In this talk, we present a mathematical framework that builds upon the describing function technique from nonlinear control theory to accurately quantify oscillation characteristics for a general class of nonlinear car-following laws. We also propose a set of new measures on steady-state traffic properties and oscillation characteristics and systematically apply them to calibrate car-following laws and to validate the describing function approach based on field vehicle trajectory data.