Thin-body self-aligned InGaAs MOSFETs are fabricated on a III-V-On-Insulator structure on a silicon active substrate (III-V-OIAS). The p-type Si active substrate acts as a back gate that can modulate the threshold voltage and other electrical characteristics of the device. This paper explores the physics behind this effect through 2-D simulations and comparison with experiments. In the off-state, we find that the application of a positive body-to-source (Vbs) voltage increases the subthreshold swing but reduces drain-induced barrier lowering. The first effect is related to the electron profile and the location of the centroid of electron charge in the channel while the second is closely associated with the modulation of a depletion region in the silicon substrate. In the on-state, the series resistance is observed to improve under positive Vbs due to the increased accumulation of electrons in the extrinsic portion of the device. In addition, the channel mobility exhibits a two-branch behavior in its dependence on the average vertical electric field in the channel. This is explained by the different interfacial scattering that takes place at the front and back channel surfaces. This paper highlights the tradeoffs involved in attempting to exploit the body bias in the operation of QW-MOSFETs in III-V-On-Insulator with active substrate.