In this paper we propose the so-called composite actor model for specifying composed entities such as the Internet. This model extends the actor model of concurrent computation so that it follows the "Reflective Russian Dolls" pattern and supports an arbitrary hierarchical composition of entities. To enable statistical model checking we introduce a new scheduling approach for composite actor models which guarantees the absence of unquantified nondeterminism. The underlying executable specification formalism we use is the rewriting logic-based semantic framework Maude, its probabilistic extension PMaude, and the statistical model checker PVESTA. We formalize a model transformation which - given certain formal requirements - generates a scheduled specification. We prove the correctness of the scheduling approach and the soundness of the transformation by introducing the notions of strong zero-time rule confluence and time-passing bisimulation and by showing that the transformation is a time-passing bisimulation for strongly zero-time rule confluent composite actor specifications.