Call Scripts independent of Request

I’m wondering if anybody knows how to, when a user calls a web page, start the server processing other scripts independent of the script that the user requested. So, for example

The user requests “script.php” from my webserver. “script.php” is executed by the server and then the script starts another script running called “independent.php” which runs even after “script.php” has finished.

I’m thinking along the lines of

system("php /file/to/run/independent.php");

How plausible is this? Thanks