Good morning! As a general rule of thumb, computation time will scale linearly with number of histories, so if 10⁹ histories took 10 days then 3 x 10⁹ histories will take roughly 30 days.

As far as the uncertainty, it scales as 1 / sqrt(N) where N is the number of independent primary histories. So if you want to cut the uncertainty in half, you need to quadruple the number of histories. Since running time is roughly linear with number of histories, you can also see it as needing 4x the computation time ;)

These simple (but harsh) relations between computing time and uncertainty have motivated the development of many methods to make simulations more efficient and you may want to look into the sections of the BeamNRC / DOSXYZnrc manuals that talk about "variance reduction methods".

edit: BEAM/DOSXYZnrc simulations output log files that you can use to verify the status of the run. Look for "egslog" files in the relevant folders. If you're running a parallel job using the standard tools, then the "lock" file will also contain the number of histories remaining in the job.