Finite-state machine-based scenario-aware dataflow (FSM-SADF) is a dynamic non-deterministic dataflow model of computation that combines streaming data and finite-state control. However, FSM-SADF in its current state cannot be used in applications involving modeling and analysis of systems whose behavior depends on explicit values of timestamp of events. In this work we propose a compositional semantics for FSM-SADF that enables FSM-SADF to be used in modeling and analysis of such systems. We base the semantics of the composition on standard composition of processes with conditional rendezvous communication at the control level and the compositions of SDF graphs at the dataflow level. We evaluate the approach on a case study from the multim...