A: The Compressed Baryonic Matter (CBM) experiment in the upcoming Facility for Antiproton and Ion Research (FAIR), designed to take data in nuclear collisions at very high interaction rates of up to 10 MHz, will employ a free-streaming data acquisition with self-triggered readout electronics, without any hardware trigger. A simulation framework with a realistic digitization of the detectors in the muon chamber (MuCh) subsystem in CBM has been developed to provide a realistic simulation of the time-stamped data stream. In this article, we describe the implementation of the free-streaming detector simulation and the basic data related effects on the detector with respect to the interaction rate.