Great idea, but it should be open 24/7 with eight 3-hour windows. One account can only use a single window during the 24-hour period. This will handle the timezone differences.
The better way would be to choose a time slot when you sign up. Then you always socialise within that slot. Allowing you to use any time any day kills the concept.
I think you could also be allowed to modify your “three hour slot” up to 24 hours in advance somehow. That way you can handle travelling and relocation without allowing people to game the system and extend their slot to 6 hours or some other weird thing you didn’t anticipate.