If emails are getting delayed, its better to inspect postfix mail queues, coupled with postfix mail log.
Status/Shape of Mail Queue
Postfix maintains different queues for different purpose.
deferred queues are of our interest.
Ideally, we should never have a mail in deferred queue.
qshape command will show shape of active mail queue by default. Ideally it should be as close as to empty since postfix sends email instantly!