The Grandfather paradox

The grandfather paradox is generally used to prove that time traveling to past is impossible. It is one of the most confusing and famous paradoxes.
The paradox is: if a person travels back in time and kills his/her grandfather before he met the person’s grandmother then the person never would have been conceived implying that he/she never traveled back in time and killed his/her grandfather. There are many theories regarding the solution of this paradox. The most logical theory (in my opinion) is:

If we look at time as a river stream then, if we create a barricade large enough in the stream pathway the river will split into two. So when we make simple changes in the history, time will automatically adjust them, but when we make big changes such as killing one’s grandfather then two timelines will be created both interdependent on each other. One timeline (or universe) in which the person and the grandfather are alive and in another, both of them dead. Of course parallel universe concept is just a theory. Both of these universes will be in different position of the space-time dimension.