  We calculate the time taken by a wave packet to tunnel through a series of
complex barrier potentials using stationary phase method to show its saturation
(Hartman-Fletcher effect) with number of barriers in various situations. We
numerically study the effect of the coupling between the elastic and inelastic
channels, width of the individual barrier, separation between the consecutive
barriers on the saturation of tunneling time. Nature of HF effect has further
been investigated for more realistic barriers with random inelasticity and also
for emissive inelastic channels.
