How do I synchronize state between PHP sessions?

[Couture]

I'm building a webapp. HTML+AJAX <--> PHP <--> MySQL; very traditional. What I need to do is have some state that all sessions can read from, and something that drives state changes even when there are no users looking at the site. A simple example would be a counter. We start the counter running from zero, and then whenever any user connects to the website, they see the current value of the counter. Even if nobody is looking at the website, the counter still increases. Everyone looking at the website sees the same value at the same time.What's the best way to implement this? It seems like I should be able to do this without resorting to storing values in the database and having everyone query the database for state. But I don't know how to have PHP running when nobody is connected. Do I need a fourth component? I don't have my own webserver, this stuff is all hosted at some off the shelf place that setup the environment for me, but they seem to have most up-to-date and reasonable stuff one would expect in this sort of stack.Clearly this isn't my area of expertise, so any nudges in the right direction are appreciated.