Currently, Apple's System Status page is not reporting any iMessage outages, and some users appear to be experiencing no issues at all.
The iMessage issue is not a result of the iOS 8.1.1 update, as users who have yet to update are also reporting problems. The outage is likely to be temporary, with service restored shortly.
Update: Apple has documented the outage, which affected "some" iMessage users, on its System Status page. The outage lasted roughly 90 minutes and was fixed by 11:30 AM Pacific Time.