I am guessing part of the problem is a lot of students have exams, so with no lessons on students are surfing, gaming and streaming all day long.
We have 2 x 1GB links to the regional broadband but one of those is reserved (as it is paid for from the department) for HPC (High Performance Computing) so we can't divert traffic down that link when we are busy.
Although the graphs don't show us actually hitting our 1GB limit the problems occur because we have two links and two firewalls for load balancing and resilience. The switches look at the IP addresses and send even numbers down one path and odd down the other (if one route failed all traffic would go the same way). Now when you have more even than odd addresses, or vice versa, the link for those can become full. Changing the IP address of those experiencing problems by one will temporarily fix it, but you can imagine having to do that for hundreds of users is not practical.
In the long term it is hoped to get a 10GB link to the region but this is something other institutions are dragging their feet over. For now we are looking at new traffic shaping software that is more effective than what we have got.
As with every educational institution the problem is having to get quotes, putting it out to tender and getting a board to sign off on it. Not a quick fix.