The closest thing you can come without creating too messy a solution is to enable ASP sessions. This will create a session on the server for each visitor, who will be identified by a cookie.
After a certain amount of inactivity from the visitor, the session will be closed, and a SessionEnd event will be raised. This you can hook up to in the Global.asax file.
I will not recommend this however, because HTTP is pr. definition a session-less protocol, and using server based sessions violates this fact, and are often problematic. Many solutions that use server based sessions run into problems when the user uses the browser-back button, and resubmits a form. Because the content of the submitted form no longer corresponds the data that exists in the server session.
Also, enabling server based sessions seriously hurts the scalability of the application.