Characterization of Traffic Oscillation Propagation under Nonlinear Car-Following Laws

Unlike linear car-following models, nonlinear models generally can generate more realistic traffic oscillation phenomenon, but nonlinearity makes analytical quantification of oscillation characteristics (e.g, periodicity and amplitude) significantly more difficult. This paper proposes a novel mathematical framework that accurately quantifies oscillation characteristics for a general class of nonlinear car-following laws. This framework builds on the describing function technique from nonlinear control theory and is comprised of three modules: expression of car-following models in terms of oscillation components, analyses of local and asymptotic stabilities, and quantification of oscillation propagation characteristics. Numerical experiments with a range of well-known nonlinear car-following laws show that the proposed approach is capable of accurately predicting oscillation characteristics under realistic physical constraints and complex driving behaviors. This framework not only helps further understand the root causes of the traffic oscillation phenomenon but also paves a solid foundation for the design and calibration of realistic nonlinear car-following models that can reproduce empirical oscillation characteristics.