These are my thoughts on your problem. Somebody who is a system administrator in a large organization might be able to give you a better answer.
You could use crontab to set the timing. Crontab is a facility to run certain commands at set times daily, weekly, monthly, or even on specific dates like December 25. See:
man crontab
man cron
Then at the specified times you can throw off the users whose time has expired with the killall command (I think. I have never had to throw a user off my computer so I am guessing that killall is the command to use.) At the same time you change the password for the expired user to something unknown by that user. When a user's new time slot comes around you use cron again to change the user's password back to the one he/she knows. See:
man passwd
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