Let me clarify the question.
See the digram
Is such connection possible with all the four sockets running simultaneously!
ServerSocket is the ServerSocket from java.net API normal Socket is Socket from java.net Api
And yes by ServerSocket I mean the socket returned from ServerSocket.accept after connection is established
Have you tried it?
Yes, it is possible as one communication end is defined by ip address and port together. As both servers will have different ip addresses there will be no problem.
Also thought about the internet? Nearly all web servers are running on port 80 and it works just fine.