The waiting time paradox: why is my bus always late? (2018)

There's another thing that happens with busses that makes it worse.

The further behind the previous bus a bus is, the more people will arrive at the bus stop. The more people there are at the stop, the longer the bus has to spend picking them all up and selling them tickets etc. Therefore the delayed bus will tend to experience more delay. The bus behind them will have less people to pick up, so it will spend a shorter time at stops and tend to catch up with the first bus, so the two busses are dragged towards each other.

That bus with more riders on board also has a higher probability of needing to stop to let people off at each location as well, slowing it down even further!

This is part of a good route design - most bus stops should be "mandatory" - which means the bus stops there no matter what. Some bus stops are "optional" - driver only stops there if there's somebody waiting or if somebody in the bus presses the "STOP" button near the doors. It's marked on the timetable which bus stop is optional.

It's not worth it to make every stop optional because then the routes become too unpredictable and scheduling is hard. Usually there's like 5-10% of optional bus stops on each route - only in the places where very few people get in/out.

For express or intercity busses, that makes sense, but for high-frequency regular bus routes, I can't imagine that working. It means thar bus stops would have to be extremely sparse, or else the bus trips would need to be extremely slow.

Exactly the opposite. It sucks for intercity buses, cause there's no point. Bus stops are rare and buses don't "bunch up". It's essential for city buses.

This is how it works in every big city in Poland, it's working great. More cities started to use this system over time, because it improves the scheduling so much.

The point of city buses is that they drive in traffic anyway - they rarely drive over 50 km/h and they stop every 5 minutes. How regular they are is MUCH more important than how fast they drive.

If you skip 3 stops because nobody waited there - you get to the 4th bus stop 5 minutes too early and wait for 5 minutes there - potentially blocking the bus stop for others and wrecking havoc with the scheduling. Much better to split these 5 minutes between the bus stops where nobody is blocked.

It's like in gamedev - you don't want to optimize happy case cause you're making the situation WORSE. If your fastest frame takes 5 ms instead of 10 ms it changes nothing at best (and makes for more jerky movement at worst). If your longest frame takes 15 ms instead of 18 ms - it means you can keep consistent 60 FPS now - and that's a HUGE win.