Most "daily active users" are likely to be logged in more than one hour (especially those using FBs Messenger) and on multiple devices (e.g. cellphone with the app and messenger, and on the desktop the "normal" website), so I'd estimate the simultaneous peak count at something like 200-500m connections.

Also, there's a bazillion requests coming in from every website which has FB Share/Recommend buttons or FB Login active...