A hybrid of the optimal velocity and the slow-to-start models without overtaking and its ultradiscretization

Abstract

Exploiting the arbitrariness of inverse ultradiscretization, we introduce a hybrid model that combines the optimal velocity (OV) and the slow-to-start (s2s) models while enforcing the no-overtaking constraint as a discrete-time equation. The ultradiscretization of the new model coincides with the us2s–OV model, which also prohibits overtaking. Furthermore, in the continuum limit, the new model reduces to the s2s–OV model multiplied by a step function.