  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.
