There are modules that would give you much tighter control, but since you have an aversion to using them.....

Check out time(). It returns epoch time, which is number of seconds elapsed since January 1, 1970. Something like the following (untested) code should get you going:

$current_time = time();

# 900 seconds = 15 minutes
expire() if (($time_last_visited + 900) > $current_time);

sub expire {
...
}
[download]

If things get any worse, I'll have to ask you to stop helping me.