We survey various notions of probabilistic automata and
probabilistic bisimulation, accumulating in an expressiveness
hierarchy of probabilistic system types. The aim of this paper is
twofold: On the one hand it provides an overview of existing types
of probabilistic systems and, on the other hand, it explains the
relationship between these models. We overview probabilistic
systems with discrete probabilities only. The expressiveness order
used to built the hierarchy is defined via the existence of
mappings between the corresponding system types that preserve and
reflect bisimilarity. Additionally, we discuss parallel
composition for the presented types of systems, augmenting the map
of probabilistic automata with closedness under this compositional
operator.