HR has a duty to investigate the complaint in a timely manner, but there is no hard and fast rule what that means. At the outset of the case, ask what the timeline for investigation is, what the process is, and when the case should be finally resolved (substantiated or unsubstantiated). Make sure you also have contact information for the investigator and don't be afraid to periodically check-in to ask how the investigation is going. Ask for updates on when the matter should be resolved. If you're a complainant, it's okay to check in every week or two. Keep on them. Persons complained about may want to check in every couple of weeks just to see if they can clear their name; mention the stress it's causing you to have an open investigation hanging over your head. Witnesses have no right to know necessarily.