@GET
@Produces("text/plain")
public void execute(@Suspended AsyncResponse response){
    System.out.println("Initially invoked on thread - "+ Thread.currentThread.getName() + ". This will free up soon !");
    new Thread(){
        @Override
        public void run(){
            response.resume("executed asynchronously on thread - "+ Thread.currentThread.getName());
        }
    }.start();
}

//JDK 8 version - passing a Runnable (in form of a Lambda Expression) to a thread

@GET
@Produces("text/plain")
public void execute(@Suspended AsyncResponse response){
    System.out.println("Initially invoked on thread - "+ Thread.currentThread.getName() + ". This will free up soon !");
    new Thread(() -> response.resume("executed asynchronously on thread - "+ Thread.currentThread().getName())).start();
}

Behind the scenes ??

The underlying I/O connection b/w the server and the client continues to remain open. But there are scenarios where you would want not want the client to wait for a response forever. In such a case, you can allocate a time out (threshold)

The default behavior in case of a time out is a HTTP 503 response. In case you want to override this behavior, you can implement a TimeoutHandler and register it with your AsyncResponse. In case you are using Java 8, you need not bother with a separate implementation class or even an anonymous inner class – you can just provide a Lambda Expression since the TimeoutHandler is a Functional Interface with a Single Abstract Method

@GET
@Produces("text/plain")
public void execute(@Suspended AsyncResponse response){
    System.out.println("Initially invoked on thread - "+ Thread.currentThread.getName() + ". This will free up soon !");
    //just having this would result in HTTP 503 after 10 seconds
    response.setTimeout(10, TimeUnit.SECONDS); 
    //client will recieve a HTTP 408 (timeout error) after 10 seconds
    response.setTimeoutHandler((asyncResp) -> asyncResp.resume(Response.status(Response.Status.REQUEST_TIMEOUT)).build());
    new Thread(() -> {
                try {
                    Thread.sleep(11000);
                } catch (InterruptedException ex) {
                   //ignoring
                }
            }).start();
}