I'm not sure if this is exactly what you're asking, but you're system should be programmed in such a way that every time a unique visitor accesses a page, there should only ever be one distinct connection to the database (not multiple connections for the same visitor). If you're opening a connection three times for a single page view, there's something wrong - a hundred visitors, a hundred connections, there's no avoiding that, and your server will have to be able to handle the load.
-m