Not quite 3 minutes, but occasionally I've seen trains leave 1-2 minutes early where the platform clocks aren't easily visible where the guard is - e.g. Cathays, where the displays are primarily aimed at the platform entrances, and rather obscured by the shelter canopies at some points on the platforms.
I've also seen 2-3 minutes early where trains haven't needed to stop at request stops. Naturally trains don't wait time if not called to stop (and perhaps staff don't perceive a need to wait even if stopping), and similarly might not wait time at the next mandatory stop if it's also quite a small station.
GWR▸ and TfW now generally time for full 30 second (sometimes even 1 minute) dwells at request stops, and often the advertised times match the working times. So it's quite possible that a train will leave a main stop 30s early if the working departure time is on the half-minute, and then recover some time by missing a request stop or two. Compare this to the Far North Line where there are still zero dwells at request stops (given that up there the chance of not needed to stop is much higher) and the advertised time is slightly before the working time.
I think the right solution for GWR & TfW, where request stops are fairly well used, is to have the 30s dwells, but make the working times realistic times passengers need to be there to hail the train, and factor in non-stopping - so maybe 30s before the working arrival time, and 1m earlier, for example, if there are two preceding 30s dwells that might not be needed. So the train will appear late by passenger times if making the stops, but will be back to right time at the next mandatory stop.
As far as I'm concerned an early departure should be considered the same as a cancellation for Delay Repay purposes - and I imagine (hope) a
TOC▸ wouldn't fight that if the train genuinely left early.
You could say that this happens by design at some London termini when doors are closed up to 2 minutes before the train is timetabled to leave for platform and on-train staff to check all the doors are closed, effectively meaning that the train has left so far as any intending passengers still on the platform are concerned. Somehow staff at intermediate calling points normally seem to carry out that process starting at the time shown in the timetable, which presumably has it built in. Do any non-London stations have similar pre-timetabled departure time boarding restrictions?
IMX staff routinely start the process before departure time where the train is ready to go, such that it can leave bang on the advertised time, and TOC posters variously advise passengers that dispatch begins 30-40 seconds before departure time. At quiet self-dispatch locations it's perhaps more like 15-20 seconds, given that dwell times may only be 30s!
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