Jam emergence on a circular track in a car-following model

A discrete car-following model (a linear version of the Optimal Velocity Model) is evaluated for vehicles moving on a circular track. The model imposes physical limits on acceleration and deceleration. Braking is treated using a version of Gipps’ safety condition and incorporates the reaction time of drivers. Simulations with two versions of the model, one with a unique velocity–headway relationship and another with a non-unique relationship, show spontaneous emergence of a jam in agreement with the experiment of Sugiyama et al. [Y. Sugiyama, M. Fukui, M. Kikuchi, K. Hasebe, A. Nakayama, K. Nishinari, S. Tadaki, S. Yukawa, New J. Phys. 10 (2008) 033001].