  We introduce a method to test if a given velocity definition corresponds to
an actual physical flow, when the pulse propagation in dispersive medium is
considered. i) We calculate the mean arrival time between two positions in
space, using the Fourier expansion in real-\omega space. ii) We calculate the
mean spatial displacement between two points in time, using the Fourier
expansion in real-k space. We compare the velocities calculated in the two
approaches. If the velocity definition truly corresponds to an actual flow, the
two velocities must be the same. However, we show that the two velocities
differ significantly (4%) in the region of superluminal propagation even for
the successful definition introduced by Peatross et al. [Phys. Rev. Lett. 84,
2370 (2000)].
