A theoretical model describing the dynamical behavior of dual-frequency solid-state lasers including a buffer reservoir (BR) is presented. It relies on the introduction of two additional coupled rate equations describing the interaction of the two laser modes with the BR. The relative intensity noise is derived by taking into account the fluctuations of both pump intensity and intra-cavity photons. This modelling approach accurately predicts the experimental noise spectra obtained with an Er,Yb:glass dual-frequency laser implemented in different cavity architecture configurations. The mode coupling strength in the BR is shown to rule the reduction efficiency of the excess noise lying at the in-phase and anti-phase frequencies.