In traffic flow, cellular automata = kinematic waves

This paper proves that the vehicle trajectories predicted by (i) a simple linear car-following model, CF(L), (ii) the kinematic wave model with a triangular fundamental diagram, KW(T), and (iii) two cellular automata models CA(L) and CA(M) match everywhere to within a tolerance comparable with a single “jam spacing”. Thus, CF(L) = KW(T) = CA(L, M).