What is the parameter "max_q_size" used for in "model.fit_generator"?

This simply defines the maximum size of the internal training queue which is used to "precache" your samples from generator. It is used during generation of the the queues

def generator_queue(generator, max_q_size=10,
                    wait_time=0.05, nb_worker=1):
    '''Builds a threading queue out of a data generator.
    Used in `fit_generator`, `evaluate_generator`, `predict_generator`.
    '''
    q = queue.Queue()
    _stop = threading.Event()

    def data_generator_task():
        while not _stop.is_set():
            try:
                if q.qsize() < max_q_size:
                    try:
                        generator_output = next(generator)
                    except ValueError:
                        continue
                    q.put(generator_output)
                else:
                    time.sleep(wait_time)
            except Exception:
                _stop.set()
                raise

    generator_threads = [threading.Thread(target=data_generator_task)
                         for _ in range(nb_worker)]

    for thread in generator_threads:
        thread.daemon = True
        thread.start()

    return q, _stop

In other words you have a thread filling the queue up to given, maximum capacity directly from your generator, while (for example) training routine consumes its elements (and sometimes waits for the completion)

 while samples_seen < samples_per_epoch:
     generator_output = None
     while not _stop.is_set():
         if not data_gen_queue.empty():
             generator_output = data_gen_queue.get()
             break
         else:
             time.sleep(wait_time)

and why default of 10? No particular reason, like most of the defaults - it simply makes sense, but you could use different values too.

Construction like this suggests, that authors thought about expensive data generators, which might take time to execture. For example consider downloading data over a network in generator call - then it makes sense to precache some next batches, and download next ones in parallel for the sake of efficiency and to be robust to network errors etc.

You might want to pay attention of using max_q_size in combination with fit_generator. In fact, the batch size you declare and use in the generator function will be considered as one single input, which is not the case.

So a batch size of 1000 images and a max_q_size of 2000 will result into a real max_q_size of 2000x1000 = 2,000,000 images, which is not healthy for your memory.

This is the reason why sometimes the Keras model never stop getting increased in the memory until the training process crashes