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it would be incorrect for an empty bus to pass a full bus

You've got it precisely backwards.

If the empty bus passes the full bus, then the empty bus is picking up passengers, while the full bus, arriving at freshly cleared stops, only unloads.

Eventually the loading factor levels out and the problem's cleared



Indeed, so the empty bus will slow down and the full bus will speed up a little (as it still has to drop off passengers), and they will meet and switch places again; so the two buses will start leap-frogging each other all the time, as GP described. So they will tend to stay together, and not spread out as desired.


You don't permit them to switch.


That's even worse. They will just keep together, and the bus at the back (which was the initial full bus) will have to wait for the bus at the front without any good reason.


No, that's exactly what you're trying to accomplish.

You're already got a headway interruption. Both buses are arriving at stops after a longer-than-usual interval. That means there are more passengers waiting.

You've put the empty bus ahead of the full one. It picks up the waiting passengers.

The full bus trails, briefly, it discharges passengers, but loads none (or at worst, a very few).

This continues either to the end of the line (at which point regular headways are once again established), or, possibly, until the lead bus becomes full. At that point, you might swap positions, but only then.

If you were to put the full bus in the lead because it was "getting delayed", you'd only re-create the problem you initially had: of a full bus trying to load and unload passengers, which happens much more slowly than for an empty bus, while the less loaded bus that can accomplish loadings/unloadings faster trails behind.

Your letting the trailing, full bus lead doesn't save time.

Play with the sim here and see what happens.


Well, I guess you can't make it much better than your method anyway, and it does have the advantage that people will see both buses arrive at nearly the same time, so there's that.


Even in the worst case performance of leapfrogging, you still have an additional busload of throughput that you didn't have before.




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