The influence of multiple scattering in a plasma layer with random irregularities on the propagation time of a totally reflected pulse signal has been considered. Two approaches have been implemented. The first one is based on an analytical solution of the radiative transfer equation. The second one is based on a numerical simulation in the spirit of the Monte Carlo technique. The general conclusion is that, subject to relative position of a transmitter and a receiver and the irregularity shape, one can observe both a decrease and an increase of the propagation time in comparison with the reflection from the same layer deprived of random irregularities. The numerical estimates made in this paper regard the case of radio sounding of the ionospheric plasma. It has been shown that the magnitude of the considered effect is of the order of the characteristic pulse length applied in the ionosphere vertical sounding.