A rate equation model is developed to investigate the plasma assisted MBE growth of GaN in the presence of a fractional monolayer of Mg. Four distinct cases were identified and modeled - (i) Ga-limited regime (ii) Low N-limited regime (iii) Medium N-limited regime and (iv) High N-limited regime. In the model, it is assumed that Ga arriving on a Mg site undergoes faster incorporation into the epilayer through an exchange reaction compared to Ga arriving directly on a N surface. Additionally the incorporation rate of Ga was assumed to depend on the size of the Ga cluster. The results of the model are in good agreement with that of experiments. The non-monotonic behavior of growth rate with Ga flux for moderate Mg coverage is explained based on the incorporation rate dependence of Ga on the cluster size.