The doc for smtp_accept_queue_per_connection says:
This option limits the number of delivery processes that Exim starts
automatically when receiving messages via SMTP, whether via the daemon or
by the use of -bs or -bS. If the value of the option is greater than zero,
and the number of messages received in a single SMTP session exceeds this
number, subsequent messages are placed on the queue, but no delivery
processes are started. This helps to limit the number of Exim processes
when a server restarts after downtime and there is a lot of mail waiting
for it on other systems. On large systems, the default should probably be
increased, and on dial-in client systems it should probably be set to zero
(that is, disabled).
in particular: "...subsequent messages are placed on the queue, but no
delivery processes are started." When does a delivery process get started
for these messages? How can I shorten the time between being queued and
being delivered?