I am a bit confused about this. If you're building a distributed application, which in some cases may perform parallel operations (although not necessarily mathematical), should you use ASIO or something like MPI? I take it MPI is a higher level than ASIO, but it's not clear where in the stack one would begin.
I know nothing about ASIO but from a quick Google it looks to me to be a lot lower level than MPI. For me the whole point of MPI is so that I can program against a higher level of abstraction from the messaging than, it seems, ASIO provides. Where you begin depends on your needs. For mine, parallelising scientific codes for high-performance, the obvious answer is MPI. I'm not sure I'd use it, or at least not sure it would be my default choice, if I were writing more general-purpose distributed, as opposed to parallel, applications. Well, actually, it probably would be my default choice to avoid learning another approach (most of which are less portable and less long-lived than MPI) but I'll admit it might not be the best choice if starting from an equal footing.
As far as I know MPI is currently incapable of handling the situation, when the new distributed nodes want to join the already started group. The problems also may occur if one of the nodes goes offline.
MPI does not reveal any network related machinery that is underneath. Thus if you would ever need something on the lower level -- you're in trouble. If you on the other hand do not aticipate such a need, then you'll save yourself a lot of time using MPI.