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×DOS1(E)×DOS2(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′×DOS(E)×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.