In some quantum text books , the tunneling transmission formula depends only on the density of states of 2 regions (DOS) involved in tunneling. ($T(E) = C \times DOS_1(E) \times DOS_2(E)$, where C is constant). However, in Landauer transmission formula (without tunneling) the transmission depends on both DOS and velocity of carriers ($T(E) = C' \times DOS(E) \times v$). So I am wondering if velocity is important too? If yes, which velocity in which region?!
 For example, see "Introduction to Many-body quantum theory in condensed matter physics", Bruus et al.