There's been suggestions to skip battles on arena if you're fighting bots, but I think a lot of time related problems would be solved if you could select playing a game with 60 second turns or one with 30 second turns. A round of Arena is currently about half an hour and for me, too long to not be bored but not long enough to do anything else simultaneously. If it was cut to thirty seconds I'd be a lot happier.
That or, at least, ability to hit done on a turn and if all human players hit done you can skip to the next turn. Arena really needs some tweaking with time.