From modified KdV-equation to a second-order cellular automaton for traffic flow

We propose a cellular automaton (CA) model for traffic flow which is second order in time. The model is derived from the modified Korteweg–de Vries (MKdV) equation by use of the ‘ultra-discretization method’ (UDM) proposed by Tokihiro et al. (Phys. Rev. Lett. 76, (1996) 3247). This result can be seen as an analogue of the derivation of nonlinear evolution equations from differential- and differential-difference-equation traffic models. It is the intention of this paper to draw attention to exactly this analogy. We show that the model exhibits a crossover from a freely moving regime to a jammed regime with increasing density.