Optical pump powers required for Raman amplification were significantly higher than that for Erbium doped fiber amplifier (EDFA), and the pump laser technology could not reliably deliver the required powers. However, with the improvement of pump laser technology Raman amplification is now an important means of expanding span transmission reach and capacity. In the present paper, we have deeply investigated the proposed model for optical distributed fiber Raman amplifiers in the transmission signal power and pump power within Raman amplification technique in co-pumped, counter-pumped, and bi-directional pumping direction configurations through different types of fiber cable media. The validity of this model was confirmed by using experimental data and numerical simulations.