A parsimonious model for the formation of oscillations in car-following models

•Random error in drivers’ acceleration processes may be responsible for traffic instabilities.•This error determines average vehicle speeds at bottlenecks and the period and amplitude of stop-and-go waves.•Driver error increases with roadway grade, therefore upgrades also exacerbate oscillation growth.

This paper shows that the formation and propagation of traffic oscillations in the absence of lane changes can be explained by the stochastic nature of drivers’ acceleration processes. By adding a white noise to drivers’ desired acceleration in free-flow, oscillations are produced that accord well with observation. This theory suggests that driver error is a function of roadway geometry, that it determines the average speed at the bottleneck, as well as oscillation period and amplitude. The model has been implemented with a single additional parameter compared to the kinematic wave model with bounded accelerations.