In mid-2010, Heroku redesigned its routing mesh so that new requests would be routed, not to the first available dyno, but randomly, regardless of whether a request was in progress at the destination.
The unfortunate conclusion being that Heroku is not appropriate for any Rails app that’s more than a toy.
Great analysis of Heroku’s routing.
I love the service that Heroku provides, but I probably wouldn’t put too many of my eggs in their basket.