Time-Out User Connections In Wordpress Multi-User

I was talking to our server team today after we experienced a little downtime. Here was the gist - We were told by managed services that we overloaded our server resources.

When I prodded a little further, they said that we have too many open connections (I think "time wait" was what he called it). He said that wordpress is not "timing out users" after idle time and the connections are too great. We expanded the number of connections, but I want this managed better...

Is this traditionally handled on the server level or handled from within Wordpress?

We have a solid server package. Any advice is greatly appreciated.