I know there are similar questions, but not similar enough, and in fact, I don't remember seeing this kind of time travel in fiction.

Before I start, it doesn't matter how the time machine works in this world (could even be many different types), and time travel is allowed to violate matter/energy conservation laws (i.e. time traveler or time machine appears out of thin air).

**Now the rules are as follows:**

* Only time travel to the past is allowed.
* The timeline always changes due to the arrival of the time traveler.
* There's only one real timeline. The "old" timelines are destroyed forever.
* There's a first ever time traveler by the time of arrival.

That last part is important. Clearly, time travel events are countable. So if you go back in the real timeline, you eventually find the earliest arrival. It doesn't really matter when this time traveler departed in their original, destroyed timeline.

I believe this system is internally logically consistent and doesn't allow for any paradoxes. If you travel back and kill your grandfather, you will just have to live your life knowing your double will never be born.

Here's an illustration of multiple time travelers (or time travel events) in this scheme:

[![enter image description here](https://i.stack.imgur.com/9B3Oj.png)](https://i.stack.imgur.com/9B3Oj.png)

As you can see, time travelers are ordered by their arrival time and nothing else. They can bring records, devices and anything else from their own timeline and all of that will exist, even though the timeline itself is lost.

The first ever time traveler doesn't have to be the "original" one either. For example, it could have happened like this:

[![enter image description here](https://i.stack.imgur.com/FilPy.png)](https://i.stack.imgur.com/FilPy.png)

Somebody invented the time machine, tested it out, which created a new timeline, then somebody else got a hold of the same technology and traveled back far enough to become the first arrival.

**So what I'm asking is this:**

* **is this system internally consistent?**

*Edited due to comments*

* how to explain why somebody later who finds out the arrival time of the 1st (2nd, 3rd) time traveler can't travel father back?

I mean, that would make everything inconsistent again. Maybe they can and will simply become the first time traveler themselves? But where does it end? Now I'm confused again. Logically it has to end somewhere so we get a final timeline **with a set and ordered list of time travelers** up to some point.

Maybe Primer idea is not that bad (for those who haven't seen the movie SPOILERS ahead): we can only travel back to the point when the time machine was first turned on. But I don't like this restriction very much.

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Some extra stuff that's not very important:

People often complain that maleable timeline stories don't have high enough stakes because the character can always go back and change something else, or if multiple realities coexist, then nothing even matters. But here's only one eventual reality and nobody will ever be able to recreate their original timeline, especially due to multiple time travel arrivals after their own.

I think there's a good narrative potential here. For example, there could be a whole society (or two competing ones) made of time travelers who are all by definition come from different timelines, quite possibly very very different. With different societies, technologies etc.