Comment by IIAOPSW

6 days ago

It can work on a subway system because there are skip-stop service patterns on J/Z line in New York.

In terms of needing extra track, that's the brilliant part of it. Even though the different services all make different stops in my proposal, so long as they depart in a certain order they will never need to pass each other.

In the 2-in-3 stops example I gave, suppose that at the present moment there's an (AB) train at station [A], a (BC) train at station [B], and a (AC) train at station [C].

If they all depart at the same time then (AB) goes one stop to the next [B] at the same time as (BC) goes one stop to the next [C] and (AC) goes one stop to the next [A].

Then they should all depart again at roughly the same time (since they all presumably took the same amount of time to go one stop).

So (AB) goes two stops from [B] to the next [A] station at the same time as (BC) goes two stops from [C] to the next [B] station and (AC) goes two stops from [A] to the next [C] station.

Then the cycle repeats.

All three service run at the same time without ever catching up or passing each other.

If you use my two-boarding-area trick then the constraint can be loosened to allow different services to catch up (but not pass) each other, which then makes it possible to run 2-in-5 stops without adding a passing track.

To elaborate a bit, on the face of it the 2-in-5 system has 10 different services running on the line at the same time, because there's 10 possible unique combinations of 2 out of 5 things.

However, just like in the 2-in-3 example, many of these services can be run at the same time without passing or catching up because they are scheduled to move and stop in the same pattern (just offset from a different starting station.

Every single train in the 2-in-5 system can be categorized as either moving 1 stop then 4 stops, or moving 2 stops then 3 stops. Two services in the same category never catch up or pass each other. If you have two subsequent services in a different category then they simply take turns catching up and falling back behind (but ultimately never passing each other).

Here's a (rough) line diagram I calculated showing where each train is at every 3-min interval in the 2-in-5 system. Notice how they meet but never pass.

https://ibb.co/4R9nQsQd

In terms of confusing people and knowing which train to get on, this is what I've come up with as a signage convention. All that's necessary to know what train to get on is the symbol on the map of your destination. If a train has the same symbol on it then it goes there.