If someone is traveling, should they say good bye to the people they know or the people should tell him/her goodbye ?

I think the person who is traveling should speak first because it is a signal that "Hey, I am really leaving right now." And also, the person leaving is the one causing the separation, so that person is the one who should make the most effort to ensure a nice parting. But, if I am the one left behind and for some reason the one leaving does not speak, I'd probably go ahead and speak first rather than have a silent parting with someone I care about.