A set of exact solutions for a cellular automaton, which is a hybrid of the optimal velocity and the slow-to-start models, is presented. The solutions allow coexistence of free flows and jamming or slow clusters, which is observed in asymptotic behaviors of numerically obtained spatio-temporal patterns. An exact expression of the flow--density relation given by the exact solutions of the model agrees with an empirical formula for numerically obtained flow--density relations.
Categories: nlin.CG math-ph math.MP