Cellular automata traffic flow model derived through the ultradiscrete limit of the correlated random walk

In this paper, we show that a generalization of the discrete Burgers equation can be obtained by a kind of discrete Cole--Hopf transformation to the discrete diffusion equation corresponding to the correlated random walk, which is also known as a generalization of the well known random walks. By applying the technique called ultradiscretization, we obtain the generalization of the ultradiscrete diffusion equation, the ultradiscrete Cole--Hopf transformation and the ultradiscrete Burgers equation. Moreover, we show that the resulting ultradiscrete Burgers equation yields cellular automata. The relationship of the ultradiscrete Burgers equation to the traffic flow is also discussed.