postfix smtpd connection hangs with no banner

I ran into an issue the other day where my Postfix mail server would accept an SMTP connection, but then would just hang without ever sending the initial ESMTP welcome banner. I discovered that because of high mail traffic, I had reached the maximum number of smtpd connections, so the new connection was stuck waiting. Since the server load was fairly low, I just raised the smtpd incoming connection limit. You can do this one of two ways

First way: change the process limit just for smtpd in master.cf.
Note the 200 in the "maxproc" field (the default is 100)

smtp      inet  n       -       n       -       200       smtpd 

Second way: change default_process_limit in your main.cf file (the default is 100).
This will affect all postfix processes, so be careful about taxing your server.

default_process_limit=200