  In this article we construct a tiny graviton matrix model for type IIB string
theory on a plane-wave background with null dilaton. For the linear null
dilaton case, we analyze its vacuum and the excitation spectrum around the
vacuum, and discuss the time-dependent fuzzy three-sphere solutions and their
evolution. It turns out that at very late time the non-Abelian fuzzy degrees of
freedom disappear, which indicates the appearance of perturbative strings.
