Is there any reason K-9 doesn’t connect to multiple accounts concurrently to fetch/send email? I usually check 5 IMAP servers on-demand and when one of them is slow to respond, it slows down the whole process. A while back I know another client (Profimail) was dramatically faster fetching/sending email simply because it connected concurrently, so it must be technically possible. It felt even faster because I was kept busy with messages flowing in while the client was trying to connect to a slow server in the background.
You mean with POP3? IMAP Push should be more or less in parallel by principle.
I don’t use IMAP Push. I start IMAP fetches manually. I am not sure what is really happening in the background but when I start a manual fetch accounts seem to be checked in sequence. x messages from account 1 appear all at the same time, then y messages from account 2 etc. If one of the servers takes longer to respond, the rest of the accounts in what looks like a queue apparently have to wait, sometimes for very long. There are other possible explanations for the behaviour I see (eg K-9 processing messages to be displayed in batches by account), but without packet sniffing it’s difficult to tell.
In an earlier K-9 version this was so bad that some of the servers timed out. To avoid this, I had to fetch messages from one account at a time.