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On Cellular Automata Models of Traffic Flow with Look-Ahead Potential

We study the statistical properties of a cellular automata model of traffic flow with the look-ahead potential. The model defines stochastic rules for the movement of cars on a lattice. We analyze the underlying statistical assumptions needed for the derivation of the coarse-grained model and demonstrate that it is possible to relax some of them to obtain an improved coarse-grained ODE model. We also demonstrate that spatial correlations play a crucial role in the presence of the look-ahead potential and propose a simple empirical correction to account for the spatial dependence between neighboring cells.