Was on a Swiss train that did exactly this yesterday. To be fair, the delay originated in Italy (20 minutes late)and there was a minimal impact for people wanting to get to or leave from that city (Bern) as passenger on the affected train could get off one stop early and then catch another train to finish their leg and passengers trying to board the train in Bern just had to catch another train to the subsequent stop (Olten) to get on the late train there.

Finally, this was the first time in over 20 years of light rail use in Switzerland that I experienced this.

> Was on a Swiss train that did exactly this yesterday.

Though there's usually replacement trains for those use cases. The main stations have a standby train (Dispozug) ready to immediately replace any train that's cancelled or delayed (and avoid propagating delays).

https://twitter.com/SBBTrainDriver/status/150809526141493657... (is an example, the driver spends 3h+ just waiting in the train in case it needs to replace another train)

I don't know about the statistics reported to the European level but most Dutch railways don't take into account "cancelled" trains when determining punctuality. A train is "cancelled" when it's 30 minutes late and therefore doesn't alter the punctuality scores.

It does stop at all stops unless it's really late and passengers might as well get out at a stopover station and transfer trains, however if it's sufficiently delayed it may be put on side tracks to let other trains pass to prevent a ripple effect, delaying the train even more to keep the rest of the system working well.

German rail has what we call the Profalla-Wende (a "turn" named after the former minister of transport). If a train is sufficiently delayed, and at the final destination would turn around to do the same trip in the other direction, it might skip the last few stops and just turn around earlier. Now the train is on time, skipped stops aren't counted in the statistic, the ripple effects from tracks and stations blocked by the delayed train are gone, and everyone who wanted to go to the final destination is skrewed.

In my European country if a train was running very late they could turn around the train some stops earlier, thereby not servicing the stations further down the track. Since the train would never arrive there it implied it also couldn't be late and thus it would not be counted in the statistics as such.

The rail company has a government-imposed punctuality target and their result is used in the calculation of how much money they get from the government the next year, i.e. the usual "once a KPI becomes a target..."

German Rail did that: translated presentation from German: https://www.youtube.com/watch?v=AGCmPLWZKd8 (with a translator that sadly breathes into the mic...)