Around 12000 messages. The queue went from ~3000 to over 12000 in about 30 minutes and then took 3 hours to grind through all of them.
I am still trying to determine if this was an accident or not. The source claims it was not intentionally malicious. Some postconf values: default_destination_concurrency_failed_cohort_limit = 1 default_destination_concurrency_limit = 20 default_process_limit = 100 I did not see anything at http://www.postfix.org/TUNING_README.html that looked like it would help, but then we are operating on a skeleton crew, and I do not have the luxury to spend time digging into the details. Any helpful suggestions would be appreciated.