Yes, you can do things like that, but that ends up with you having two different sets of stations that are not easy to get between. The normal pattern is express trains that stop a few times with stoppers that "fill-in" between, but there will be different patterns of stopping to try and optimise for different groups of travelers.

Scheduling/timetabling is a wickedly hard problem, especially in a system like a railway, it's the sort of thing people get Maths and CS PhDs in. The contstraints that you have to solve are complex and interconnected and are part of a bigger network, and you are also trying to please a lot of people with very different (often contradictory) needs.

Yeah I've previously worked on some constraint programming tasks and it was fun but mind-boggling.

It was one of my favourite course at uni, I'd love to get back into doing something like that at some point.

I didn't use them in the end, but the Google OR-Tools is a pretty amazing resource for this. I don't have a CS degree, so just seeing the names of the algorithms was helpful ha.

https://developers.google.com/optimization/routing

This is already the case for some of the very low-volume stops on that line. For non-express trains a combination of the following is currently (or at least was pre-covid) in use, with the mix varying throughout the day:

  * stop more or less everywhere
  * stop only at larger stations
  * even/odd stopping at small stations

The scheduling already seems pretty clever, and that's just from observing as a passenger. I suspect behind the scenes there's a whole lot more to it that's not obvious to someone who is just trying to get to work.

Yep, there are whole departments of people who work hard to make the scheduling on railways work as well as possible. People always like to complain, but they always ignore the fact that the timetable has to try and satisfy a huge number of people with often very different needs, on networks with some very fixed constraints that are expensive and difficult to change.

Not without passing places, because you can't miss a stop without the train in front of you also missing it, at least without an eye watering body count.

Depends on how closely you are trying to run those trains! If they are both skipping every other stop, they will both have the same mean speed, and thus shouldn't have to pass one another if there is sufficient initial spacing.

For example, in the simple case where the stations are evenly spaced, if train B arrives at station 1 at the same time that train A arrives at station 2, then they will leave at the same time and arrive at stations 3 and 4 respectively at the same time, and never catch up with each other.

Yes, this was the sort of thing I was thinking for London. Not "express" per-se, but "missing stops" (i.e. just like what happens when stations are closed for platform maintenance during normal ops).

You can definitely do that.

However on something like the underground that would complicate the "turn up and go" approach that most people take to the tube if you start skipping different sets of stations on different trains.

It's something that's done, but I'm not sure how well it would scale on the tube if you did it a lot. Each train would need to miss roughly the same number of stops to prevent blockages or you need more passing places. With the small gaps between many tube trains the margin of error for scheduling can be very small.

I think it's one of those things that works, but the advantage for the vast majority of people would be pretty small compared to the complexity and added fragility it would introduce if you tried to do it a lot.

This creates a very significant passenger challenge. How do the customers know which train to get on and what if they get on the even stop and need to get off an odd stop? They have to change train. If they can't pass each other then they don't save much time.

In NY, the expresses are easier to understand because the rules are very simple.

They used to do it in Chicago for a long time. Trains and stops are labelled A or B and some stops would be labelled AB if evens and odds both stopped.