We study the behavior of single atoms on an infinite vicinal surface assuming certain degree of step permeability. Assuming complete lack of re-evaporation and ruling out nucleation the atoms will inevitably join kink sites at the steps but will do many attempts before that. Increasing the probability for step permeability or the kink spacing lead to increase of the number of steps crossed before incorporation of the atoms into kink sites. The asymmetry of the attachment-detachment kinetics (Ehrlich-Schwoebel effect) suppresses the step permeability and completely eliminates it in the extreme case of the infinite Ehrlich-Schwoebel barrier. A negligibly small drift of the adatoms in a direction perpendicular to the steps leads to a significant asymmetry of the distribution of the permeability events, the atoms thus visiting more distant steps in the direction of the drift. The curves are fitted with an exponential function containing a constant which can be considered as a length scale of the effect of the drift. Some conclusions concerning the stability of the vicinals are drawn.