Transition matrices associated with MCs based on Kronecker products have a rich structure that is nested and recursive. Preprocessing techniques such as reordering, grouping, and lumping can take advantage of this structure to expedite analysis. All iterative analysis methods rely on an efficient vector–Kronecker product multiplication algorithm. Block iterative methods based on splittings, ... [Show full abstract] projection methods preconditioned with block iterative methods, and multilevel iterative methods for steady-state analysis come across as a strong set of solvers that should be integrated to software packages working with Kronecker products. Among these, multilevel methods perform better on a larger number of problems in the literature.