Forking is probably the best solution, but, as always, there is more that one way to do it. For a rather exhaustive list of the possibilities i would suggest Network Programming With Perl. The book covers using
- fork()
- Threading (not for production systems)
- IO Multiplexing (complex, but works on non-fork systems)
- Pre-forking/pre-threading
- And a ton more information on style, security, and production ready code.

A quick answer is the fork() solution above. But if you are going to be doing alot of traffic, i suggest giving the book a read.

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may the foo be with you