As noted, although the most desireable outcome of a time travel event is an N-jump, it is not the most probable. It is more likely that the past will be changed in a critical way that restores the original history, and thereafter oscillates between two iterations. The classic grandfather paradox is the obvious example: what happens if you kill your own grandfather before he has children? The obvious answer is that you are never born; if you are not born that breaks the causal chain, because you cannot travel to the past and kill your grandfather, and thus you are born, and you do, and history is trapped repeating two alternate versions forever: an infinity loop.
Killing your progenitor seems extreme, but infinity loops are a common probable outcome: any time a traveler successfully intentionally changes the past, he likely undoes his reason for doing so and restores the original history and his reason. Kill Hitler and he will never rise to power; however, without his atrocities no one will know about him, and you will have no reason to kill him, and so he will live and become the man you choose to kill.
It is possible, within very narrow parameters, to change the past and preserve the change. It requires preventing the time traveler from knowing that the change has been made, and thus only works for short trips with isolated time travel teams. The television series 7 Days has some potential as a model, although it requires some modifications. In general, an effort to change the past either succeeds and creates an infinity loop, or fails with the possibility of a stable N-jump.