I just moved Adstaq over to Puma this weekend because I want to experiment with a multithreaded server as a way to keep our web serving costs down and our efficiency high. We're already doing this with Sidekiq for our worker code, to great effect, and philosophically I much prefer plain old Ruby threads over other Ruby concurrency solutions. Dave Copeland gave a GREAT talk at RubyConf last year called Don't Fear the Threads which I highly recommend for further inspiration.
It took some trial and error to get Rails talking to Puma and to get everything running on Heroku, so I put the needed code into a gist, embedded below.
I'm monitoring the change on New Relic but so far have not noticed any memory savings vs. Unicorn. But we're also not drowning in traffic right now. Nonetheless I'm glad we're getting some Rails multithreading experience before that happens.
Update: Watsi posted some great instructions for adjusting ActiveRecord's connection pool size.