Hello azhar,
I think you are a litte bit wrong about EJB concepts. You are trying to use a Stateful Session Beans as a singleton (you want it to keep the state between calls from different clients). Stateful Session Beans are intended to keep the state between calls from the same client.
Given your scenario, I think
you should use Stateless session beans. You should read about Entity Manager. It is the responsible for keeping synchronized your beans with database so you don't have to worry about that at all...
Hope this helps,
Manuel