Event(pop-up) on the client

I have a bit weird requirement - the scenario is as follows :

1. Many users will be logged into a web application which is a legacy JSP-Servlets app. with client code written in pure JS and some DWR. The app. server is IBM WAS 7.x. There is a load balancer and two web servers in between. The application supports only IE
2. The app. will have a new web service which will be called by some third party app. quite frequently
3. Whenever this ws is called, the web app receives and stores some data. When this happens, a pop-up must appear in the RELEVANT user's browser(session) notifying him about the new data received via the ws By RELEVANT I mean suppose 10 users(10 sessions) from diff. locations are logged in but the new data is relevant only to 4 users(4 sessions), only those 4 users must receive the pop-up.
4. I want to avoid the awful 'polling js' code :(

I read about the web sockets but I'm not sure if EE 5 supports that and given the set-up(point 1), web sockets will work. How shall I proceed ?