Java EE 7 also comes with a standardized WebSockets client (part of JSR-356), which can be directly used in Java applications like Swing, JavaFX or Unit Tests to access remote WebSockets.
With a little help of Java EE 7, both sides can be implemented in < 9 mins :-):
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See you at Java EE Workshops at Munich Airport, Terminal 2 or Virtual Dedicated Workshops / consulting
NEW MUC Airport Workshop: Migrating Java Client (Swing / Java FX) to Web Standards
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A book about rethinking Java EE Patterns