A detailed theoretical investigation of an integration of a semiconductor optical amplifier (SOA) and distributed Bragg reflector (DBR) laser is presented. The dependence of the device performance on those key design parameters such as the lasing wavelength, light injection direction (co- and contra-propagation), lasing power of the DBR laser, and the biasing condition of the SOA is examined systematically by means of a comprehensive time-domain traveling-wave model. As this integrated structure is particularly designed for high saturation power and fast gain dynamics, these characteristics are simulated and compared with the results from the conventional structures. Depending on different requirements, superior performance on either saturation power or noise figure without compromise on the optical gain can be achieved by different integration configurations (i.e., by different light injection directions). For the structure with the light injection from the output end of the SOA (namely, the integrated SOA-laser structure), the fast gain dynamics is found through simulation, which helps to reduce the large-signal waveform distortion in the amplification of narrow pulses.