In this paper, we present a comprehensive model for a CW Raman laser in a silicon-on-insulator (SOI) platform. We validate this model by comparing its output with experimental results from the literature. We then design a 2.232 im Raman laser with an on-chip ring resonator cavity. Numerical analysis of laser characteristics, such as threshold power and output power, are conducted. The optimized values for the cavity length and power coupling ratios are determined taking into account fabrication variations. Finally, by designing a tunable directional coupler (DC) for the laser cavity, a robust design of Raman laser is presented. We show that the reduction of propagation loss down to 0.6 dB/cm for the silicon waveguides and free carriers removal, by the use of a p-i-n junction, will enable a Raman laser with a threshold power of 16 mW and a slope efficiency of 62%.