Spring Integration and ThreadPoolTaskExecutor

I'm working on a Spring Integration Project with annotation based configuration.
We inherited this project from another team and are trying to figure out if the ThreadPoolTaskExecutors are being used correctly. Below is a configuration of TaskExecutors:

@Bean
public TaskExecutor businessTaskExecutor() {
	ThreadPoolTaskExecutor pool = new ThreadPoolTaskExecutor();
	pool.setCorePoolSize(30);
	pool.setMaxPoolSize(Integer.MAX_VALUE);
	pool.setQueueCapacity(Integer.MAX_VALUE);
	return pool;
}

@Bean
public TaskExecutor eventTaskExecutor() {
	ThreadPoolTaskExecutor pool = new ThreadPoolTaskExecutor();
	pool.setCorePoolSize(30);
	pool.setMaxPoolSize(Integer.MAX_VALUE);
	pool.setQueueCapacity(Integer.MAX_VALUE);
	return pool;
}

There are 5 TaskExecutor defined as indicate above. I'm not an expert but I know for sure they should be configured differently. These executors are used as follows:

@Bean
public MessageChannel inputChannel() {
	return new PublishSubscribeChannel(businessTaskExecutor());
}

@Bean
public MessageChannel outputChannel() {
	PublishSubscribeChannel outputChannel = new PublishSubscribeChannel(
			businessTaskExecutor());
	outputChannel
			.addInterceptor(new WireTap(eventTrackerChannel()));
	return outputChannel;
}

@Bean
public MessageChannel eventTrackerChannel() {
	return new ExecutorChannel(eventTaskExecutor());
}

The input and output channels are used in some ServiceActivator. The eventTrackerChannel is used to split the Spring Integration flow and write some events on DB. These are just examples to understand how the project is structured.

Now the question is, are taskexecutors used correctly? If we eliminate the ThreadPoolTaskExecutors and they are not provided for the channels, should Spring manage the threads? Could there be problems in proceeding with this second approach?

I would like to learn Spring Integration as best I can and the answers to these questions would help a lot. I thank in advance who will help me understand this behavior.

ThreadPool is a helper for us to not hold the main thread while some process that not depend of order is running. But it's not mandatory to use theses pools, but I am afraid that you may lose performance or increase the chance of failure without them, since these mechanisms normally has some kind of control besides pooling, like queuing events when the pool is full or reusing threads. Of course each case needs to be checked to see what fits better, but I believe if you don't need these events happening in a specifically order, I suggest you let this how it's.

What I've found different is how big your pools were set. But I don't know your requirements, so I can't conclude anything about this. What I normally see is the PoolSize something like 5 and maxSize like 10. Another thing is maybe you don't need each pool for each thing, one for all maybe it's suitable. But as I said, I can't say what's right or wrong, since each system has its own requirements.

The last detail that could be better is not hardcoding this setup, put in your application.properties these information like maxThreadPoolSize=10 or threadPoolSize=5 and then access it in the moment you setup the bean.