Reactivity controlled compression ignition (RCCI) technology has gained in popularity due to its ability to achieve low level NOx and soot emissions with relatively high brake thermal efficiency. However, control of RCCI combustion is a complex task. Nonetheless, this challenge can be overcome with model-based control design (MBCD). In this work, a linear physics-based time-varying RCCI combustion model was developed and improved with an addition of a start-of-combustion (SOC) model. The model we developed, which is capable of real-time simulations, can predict the combustion phasing, heat-release, and cylinder pressure of an RCCI marine engine. The model showcases the trend-wise, high accuracy estimation of cumulative heat-release and cylinder pressure. Additionally, it is able to predict combustion phasing parameters with an error of less than 1% for control design.