How can I limit the number of active local sessions

I wasn't really sure which forum to post this under, but my concern is based on the limited resources available to PCs so I put it here; anyway ....

I'm interning/working at a college, and right now we're talking about the issue of students walking away from the PCs without logging off. While everyone is in agreement that a lockout policy of, say, 30 minutes can mitigate the risks associated with this behaviour, I'm concerned with the PCs slowing down with too many of these locked sessions.

Our PCs are configured to reboot once every week, so if two students walk away from the PC each day without logging off (which I think is a conservative estimate), leaving all their programs open, there could be 10+ active, but disconnected, sessions end of day friday, slowing the PC down for any students who have a night class and logon to that PC.

So is there a way we can put a limit on how many active, local sessions there can be a computer? I'm hoping for something that goes along the lines of

Code:

IF new user logging on AND current active sessions >= 3
   force logoff oldest session
ELSE
   continue as normal

Any existing programs/built-in windows tools or help with making a script for this would be cool

Edit: I should mention we don't want to logoff idle users since some classes are 3+ hours, and if a student stops working for a bit during a lecture we wouldn't want to close their work on them and have them lose everything

This is old (2005) but I wonder if it still applies?

How can I limit the number of allowed concurrent sessions per user in an Active Directory (AD) domain?