Semiconductor ring lasers are promising sources in photonic integrated circuits because they do not require cleaved facets or mirrors to form a laser cavity. In this work, we characterize the wavelength switching speed of a tunable semiconductor ring lasers using filtered optical feedback. The filtered optical feedback is realized by employing two arrayed waveguide gratings to split/recombine light into different wavelength channels. Semiconductor optical amplifiers are placed in the feedback loop in order to control the feedback of each wavelength channel independently. The wavelength switching is achieved by changing the currents injected in the semiconductor optical amplifier gates. Experimentally, we observe a wavelength transition time of 5 ns. However, we also noticed a non-negligible delay in the switching process. [ Khoder et al, IEEE Photon. Technol. Lett. 26, 520-523, 2014]. We numerically reproduce the experimental results using rate equations taking into account the effect of spontaneous emission. The simulations further elaborate on the effect of the noise strength on the wavelength transition time and the delay time.