Why Java provides two methods to remove element from Queue?

In some situations it's expected that a queue will be empty, and in those cases having a method that doesn't throw an exception is appropriate. In other situations it's an exceptional circumstance that the queue is empty, and an exception is appropriate.

Throwing exceptions incurs a performance penalty, and if it's the case that you expect the queue to be empty from time to time you don't want to have to handle the queue-empty-logic as catching an exception -- it's both costly and difficult to read.

In the opposite case where you don't expect the queue to ever be empty it is a sign of a programming error, or some other exceptional circumstance that it is, and you don't want to write ugly error condition checking code (e.g. checking for null), because in this case that would be less readable than catching an exception (which you can do in another scope).

The abstract class AbstractQueue<E> implements Queue<E> and define the remove method.

You can take a look at source code:

public E remove() {
    E x = poll();
    if (x != null)
        return x;
    else
        throw new NoSuchElementException();
}

So, as you can see, the remove() method use poll() method.

You can use which one you prefer.

Remove() method differs from poll only in that it throws an exception if this queue is empty.

When you know how to react right now and/or expect elements to be absent then use poll.

Otherwise use remove.

Sometimes you want a null value returned for an empty queue and sometimes you want it to treat an empty queue as a exception case.

The two methods are used differently in classic discussions about a Queue structure. I use poll() mostly to retrieve items, and remove() mostly if I need to modify the Queue outside of the normal loop.