Monitoring Logged-in Users With Sessions: Autologoff

I'm currently relying on logged-in users hitting "logout"
(logoff) before they leave, in order to terminate the session.

With PHP the session filename is in a cookie that lasts for the
current session. The problem is that the server does not know
when the current session expires. (I have quite long timeouts.)

Did anybody attempt a script to automatically call "logout"
when the session expires? It seems quite complicate, as there
are multiple urls that share the same session and the user is
not actually logging out until one of them is open in some
client window.