The kinematic wave model with finite decelerations: A social force car-following model approximation

•We propose a finite deceleration, five-parameter, car-following model.•The model is parsimonious and analytically tractable.•It amplifies small perturbations, to the point of reproducing stop-and-go waves.•In equilibrium, the model behaves as the kinematic wave model.•Model’s parameters are computed from macroscopic traffic features, no calibration needed.

This paper derives a five-parameter social force car-following model that converges to the kinematic wave model with triangular fundamental diagram. Analytical solutions for vehicle trajectories are found for the lead-vehicle problem, which exhibit clockwise and counter-clockwise hysteresis depending on the model’s parameters and the lead vehicle trajectory. When coupled with a stochastic vehicle dynamics module, the model is able to reproduce periods and amplitudes of stop-and-go waves, as reported in the field. The model’s stability conditions are analysed and its trajectories are compared to real data.