A Monte-Carlo code has been developed that can be used to optimally design vapor transport systems for isotope-separator-on-line-based radioactive ion beam facilities in lieu of costly iterative trial and error design methods. The code provides a powerful means for delineating diffusion-release and effusive-flow (molecular-flow) processes, in combination, the delay times of which are principal intensity limiters of short-lived radioactive species at such facilities. The code provides time dependent particle evacuation, average distance traveled per particle, and particle/wall interaction information during particle transit through a given vapor-transport system under molecular-flow conditions, independent of the chemistry between particles of interest and the materials of which the transport system are constructed. In addition, the code provides powerful graphical insight via particle trajectories that serve as strong assets in arriving at a final design by identifying regions within the transport system where hold-up times are problematical. In this article, we compare simulation and experimental measurement results for transport of noble gases through selected vapor-transport systems using both cosine and isotropic particle re-emission distributions about the normal to the surface following adsorption (isotropic re-emission distributions are found to be in close agreement with experimental measurements) and describe a concept vapor-transport system that reduces transport times over those of conventional systems by >two orders of magnitude.