I heard from Tier 3 vendor support that NFS has some sort of limit (I was told 16) as to the number of concurrent operations that can be executing at the same time.
I apologize that I don't have any more specifics, and some Googling hasn't turned up what I am looking for.
Does this hard limitation of NFS exist, and if so, could someone explain a bit more about it?
You can control the number of instances of nfsd but each instance of nfsd might have multiple operations queued with the kernel. In Linux and Solaris (as far as I remember) the default has been 8 processes for a long time but there are plenty of circumstances where it makes sense to increase this number. I haven't heard of any absolute limit to concurrency in NFS as a protocol, however.
There are no connection limits as such, but there are some practical limits imposed by port selection, as outlined in the man page for NFS:
You're probably thinking of
sunrpc.tcp_slot_table_entries
which needs to be set before mounting a given filesystem.Up to RHEL 6.3, this was a static value of 16 which is often pushed up to 128 to remove a bottleneck. In 6.3, this becomes self tuning and auto-adjusting - see P22 of the following link.