TCP Connections, Am I Running Out?

["Daniel Parker" <dmparker usa net>]

OK,

Here's the deal:

I'm running RedHat 5.0 as a sendmail server.  I've got almost 9000 users on
it (pretty close anyway), lately in the evenings I have been running into a
problem where users can't connect to the POP3 service to pick up their
messages.  It's intermittent and the problem usually doesn't last more than
a few seconds.  sendmail is never affected by this (at least not that I can
see), just popper.

Like I said, this only happens during peak hours and a quick peek at the
system reveals that it isn't processor, disk or memory bound, however
running netstat reveals a *lot* of TCP connections, mostly sendmail and
popper.  (values of 'a *lot*' > 50 and that's not when the problem is
occurring, just right afterwards)

I believe I am running out of TCP connections, is this believable?  I have
several solutions in mind (including separating the SMTP and POP functions
to different machines). But that isn't so easily done (ever tried to educate
9000 users about a significant change like that??)

So, my questions are:

1)  Can I run out of TCP connections when I get 50-60 of them going?

2)  If so, is there some kernel tuning parameter I can change to increase
the number connections? (I already looked in /proc/sys/net/ipv4 and all that
is there is 9 empty files that I have no clue what to do with, and none of
them seem to apply to this problem)