Running concurrent PHP scripts

I'm having the following problem with my VPS server.

I have a long-running PHP script that sends big files to the browser. It does something like this:

<?php
header("Content-type: application/octet-stream");
readfile("really-big-file.zip");
exit();
?>

This basically reads the file from the server's file system and sends it to the browser. I can't just use direct links(and let Apache serve the file) because there is business logic in the application that needs to be applied.

The problem is that while such download is running, the site doesn't respond to other requests.