Java: How to wake thread on demand?

I think a combination of a BlockingQueue and a ThreadPoolExecutor will do what you need.

Or, if you deploy on a Java EE app server, you could use JMS and a message-driven bean.

I would use an ExecutorService like

private final ExecutorService executor = Executors.newSingleThreadExecutor();

public void task(final int arg) {
    executor.execute(new Runnable() {
        @Override
        public void run() {
            // perform task using `arg`
        }
    });
}

This has a built in thread which wakes when a tasks is added and sleeps when there is no tasks left, a Blocking Queue for queue tasks.

You can use some BlockingQueue.

When you read from the queue (in the thread), you either get the next item, or if it is empty - wait until one is received.

This you are not actually sleeping the thread, but using the queue's blocking property. For example:

private BlockingQueue queue;
@Override
public void run() {
    while(true) {
        handle(queue.poll());
    }
}

The above code is in a Runnable - you can use an ExecutorService to start a runnable, or the old-fashioned way with a Thread

The queue of course is set externally, and is filled (again externally) with the incoming items.