Not sure, maybe?

 

What my client wants is to have a number of moderators (about 4) and users can login to a waiting room where no posts can be made, then a moderator can invite the longest waiting user into some form of private room/chat and the user can then chat with that moderator. But the moderator needs to know how long each user has been waiting so they can pick a user to chat with.

I guess it needent be a waiting room, it could just be a live chat support app as long as all the operators can pick from a global pool of waiting users by longest waiting user.