ScheduledExecutorService multiple threads in parallel

I'm interested in using ScheduledExecutorService to spawn multiple threads for tasks if task before did not yet finish. For example I need to process a file every 0.5s. First task starts processing file, after 0.5s if first thread is not finished second thread is spawned and starts processing second file and so on. This can be done with something like this:

    ScheduledExecutorService executor = Executors.newScheduledThreadPool(4)
    while (!executor.isShutdown()) {  
        executor.execute(task);
        try {
            Thread.sleep(500);
        } catch (InterruptedException e) {
            // handle
        }
    }

Now my question: Why I can't do it with executor.scheduleAtFixedRate?

What I get is if the first task takes longer, the second task is started as soon as first finished, but no new thread is started even if executor has pool of threads. executor.scheduleWithFixedDelay is clear - it executes tasks with same time span between them and it doesn't matter how long it takes to complete the task. So probably I misunderstood ScheduledExecutorService purpose.

Maybe I should look at another kind of executor? Or just use code which I posted here? Any thoughts?