Integrated quantum signal sources play a key role in quantum communications in space, where compactness is of utmost importance. InP is an excellent candidate that can provide an on-chip single photon source as a device, where an excitation laser and waveguide for photon generation can be integrated on a single chip, because of its direct bandgap and high nonlinearity. However, one of the significant challenges that remains with InP is the elevated magnitude of the imaginary component of the third-order susceptibility at 1550 nm wavelength. The higher value of leads to two-photon absorption (TPA) and free carrier absorption (FCA) at very low powers, which drastically impacts the photon generation rate. In this paper, HHI and IMOS-based channel waveguides are modelled for the first time as an integrated platform for single photon generation, exploring spontaneous four-wave mixing (SFWM), considering TPA and FCA effects. The IMOS-based waveguide is more dynamic in generating entangled photons over a broader wavelength range, which would benefit photon demultiplexing at later stages. Nonlinear losses become dominant at power levels of 11 mW and 2 mW in HHI and IMOS waveguides, respectively, saturating the generation of single photons. TPA-free photon generation rates at these respective power levels are 4.1 MHz and 4.6 MHz, with generation bandwidths of 12.6 nm and 20.1 nm in the HHI channel and waveguide based on the IMOS platform, respectively. The saturated generation rates obtained are close to 0.15 GHz for both platforms. The on-chip monolithic integration of lasers with the proposed devices will potentially lead to more compact and stable single photon sources without relying on external lasers, in the telecommunications regime.