Me di cuenta de mi ThreadPoolExecutor con PriorityBlockingQueue como en este ejemplo:https://stackoverflow.com/a/12722648/2206775

y escribió una prueba:

PriorityExecutor executorService = (PriorityExecutor)  PriorityExecutor.newFixedThreadPool(16);
    executorService.submit(new Runnable() {
        @Override
        public void run() {
            try {
                Thread.sleep(1000);
                Thread.sleep(1000);
                System.out.println("1");
            } catch (InterruptedException e) {
                e.printStackTrace();
            }
        }
    }, 1);

    executorService.submit(new Runnable() {
        @Override
        public void run() {
            try {
                Thread.sleep(1000);
                Thread.sleep(1000);
                System.out.println("3");
            } catch (InterruptedException e) {
                e.printStackTrace();
            }
        }
    }, 3);

    executorService.submit(new Runnable() {
        @Override
        public void run() {
            try {
                Thread.sleep(1000);
                Thread.sleep(1000);
                System.out.println("2");
            } catch (InterruptedException e) {
                e.printStackTrace();
            }
        }
    }, 2);

    executorService.submit(new Runnable() {
        @Override
        public void run() {
            try {
                Thread.sleep(1000);
                Thread.sleep(1000);
                System.out.println("5");
            } catch (InterruptedException e) {
                e.printStackTrace();
            }
        }
    }, 5);

    executorService.submit(new Runnable() {
        @Override
        public void run() {
            try {
                Thread.sleep(1000);
                Thread.sleep(1000);
                System.out.println("4");
            } catch (InterruptedException e) {
                e.printStackTrace();
            }
        }
    }, 4);

    executorService.shutdown();
    try {
        executorService.awaitTermination(30, TimeUnit.MINUTES);
    } catch (InterruptedException e) {
        e.printStackTrace();
    }

Pero al final, no obtengo 1 2 3 4 5, obtengo un orden aleatorio de esos números. ¿Hay algún problema con la prueba, o algo más? Y si es primero, ¿cómo puede ser probado correctamente?