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why do three come along at once?

To see why buses often arrive in groups, think about the gaps between various buses running the same route. If all the buses are on time, the gaps should be roughly equal - say, one bus every ten minutes.

If one bus is delayed for some reason, the gaps will change - now there is a gap of twelve minutes to the bus in front, and only eight minutes to the bus behind. Since people must now wait twelve minutes for the bus to arrive, there is more time for people to turn up at the stop, and more people are likely to be waiting. This will mean the bus has to wait longer at the stop whilst the extra people get on, which is likely to delay it still further and make the problem worse.

The reverse is true for the bus behind. It is only eight minutes behind, so there is less time for people to arrive at the bus stop. When it arrives, it will have less people waiting, and be able to leave quicker, so it tends to catch up more and more.

This is called "positive feedback" and is the reason why three come at once!

EPSRC