modal verbs - I'll call you when I get there

“I’ll call you when I get there.”

This could be said to a person who comes to see me off in a terminal, I think. But this ‘will’ seems to be somewhat awkward, in that ‘will’ denotes strong willingness that has an implicature of actualization (CGEL, p.212). We can see that this farewell saying is just stereotyped one and not rarely they forget about the ‘willingness’. So there seems to be a contradiction to use ‘will’ in the situation.
However, “I’ll going to call you when I get there” seems to be stranger than ‘will’. For although ‘be going’ is an intention not volition, it has an implicature of arrangement. It would be funny to arrange to call the person who comes to see me off.
Can the ‘will’ be okay in the situation?

Answer

But this 'will' seems to be somewhat awkward, in that ‘will’ denotes strong willingness that has an implicature of actualization

(Note: Given that you are asking about "I'll", you may or may not know that "implicature" is an esoteric technical term. It would not be used in ordinary writing, unless you are a linguist. So "strong willingness that has an implicature of actualization" => "strong willingness that implies actualization"..., at least for the audience of this site!)

When someone says they "will do" something, it does mean they intend to do it. But it is a casual way of saying it, in no way stronger than saying they "shall do" it.

You can put spoken emphasis on the "will" when speaking, or bold in writing, if someone doubts and you want to invoke a stronger sense that you really, really mean it:

I will call you when I get there!

But it has no great or unique commitment in it by default. It's just an ordinary word for expressing something you intend to do. To raise the stakes and be "strong" you really would have to add more words, with patterns like:

I promise I'll call you when I get there.

or

I vow to call you when I get there.

or

By Grabthar's hammer, by the suns of Warvan, you shall be called!

:-)