Your example of '3' connections is a bit limiting as opening any given
web page, most browsers will pull 12 to 15 connections even without
using any kind of accelerators or optimized enhancements just simply
getting the graphics and supporting files for the page.
This given though, there is a very nice module for Apache available
that will briefly block visitors who make too many requests in a
given amount of time (fully customizable) and reset the blocking
clock if they make any additional requests while being blocked which
is extremely useful against flood attacks.
The module is called mod_evasive from Nuclear Elephant
You can see the author's page and
download mod_evasive here