You do not even need to save the token and timestamp. What you want is a hash of the user's IP address, a timestamp and some nice long secret salt (preferably generated uniquely for every user):
$token = somehash($ip_address . $timestamp . $secret);
$url = 'http://xxx/' . $token . '/' . $timestamp . '/filename';
Once the user visits the URL you replay the hash with the user's data. If equal and the request didn't expire, yet, serve the video.