Now, the layout above explains things analogously to a plate-stack, but actually that layout isn't the most efficient one, since it (a) wastes twice as much corridor-facing space as it needs to and (b) requires the Ready cab to move when a replacement Standby cab arrives or an Overflow cab needs to leave. A better default layout would be this:
With this improvement, a Standby or Overflow cab can slide in or out even when passengers are entering/exiting the Ready cab, hesitating while thinking about their destination, holding the door for a straggler, etc., and the configuration only chews up one additional cab-width of potential corridor access instead of two.
With this setup, you can even handle a fourth cab arriving when your Overflow is already full, by having all four cabs simultaneously rotate one space counter-clockwise so the occupants can exit (this would require the tube outline to be more circular than I have depicted it). Conversely, if the hypothetical predictive traffic-optimization algorithm anticipates lots of departures from a particular terminus, it can pre-stage a third cab in the Overflow and even a fourth in the tube (adjacent to both Overflow and Ready) and then do the little rotation-shuffle as the first of the four cabs leaves.
Quite a bit of flexibility there, in a small space, I think.