Connections to what?
Do you mean physical connections?
Or is it more like 'how many requests can be processed'?
Physical connection can be configured in the subsystems, depend what you use EJB, http ...
The other thing is related to the application and what the app-code need.
Yes. It is how many requests can be processed at a time. Is it 512 * no. of processors?
As I said, the number of requests depends extreme to the application.
- If the app use intensive the processor you may have less
- If a database is used with hard requests this instances will be the bottleneck and you can process many in parallel as the Threads in JBoss are idle
- heap usage and garbage collecting come also into the play
Sorry but I can't give a simple answer to it, you have to measure it and think about the results.