On a discrete optimal velocity model and its continuous and ultradiscrete relatives

Details On a discrete optimal velocity model and its continuous and ultradiscrete relatives On a discrete optimal velocity model and its continuous and ultradiscrete relatives

2008-09-08

arxiv.org/abs/0809.1265v1

Nonlinear Sciences

Adaptation and Self-Organizing Systems

6pages, 8 figures

Scientific paper

We propose a discrete traffic flow model with discrete time. Continuum limit of this model is equivalent to the optimal velocity model. It has also an ultradiscrete limit and a piecewise-linear type of traffic flow model is obtained. Both models show phase transition from free flow to jam in a fundamental diagram. Moreover, the ultradiscrete model includes the Fukui-Ishibashi model in a special case.

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