Math explains why your bus route is so unreliable (TheConversation)

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Have you ever waited for your bus at a bus stop for a very long time – only to be greeted by two or more buses arriving together?

This phenomenon, known as “bus bunching,” is a problem that bus transit systems around the world have been trying to solve for decades. During this time, researchers have used mathematical models to study the behavior of bus transit systems to better understand why this happens. The mathematics identify what causes this problem – and also suggests that bus-tracking technology can be combined with simple control algorithms to improve the situation.

Bunching is annoying for riders, since it increases both the average time spent waiting for the bus and the variability in this waiting time. Bunching also makes the bus system less reliable, because it causes buses to get off schedule. The long waits induced by bunching can also cause people to shift away from buses toward other, less sustainable modes of transportation.

Bus bunching occurs because bus routes are inherently unstable. When the buses are on schedule, everything seems to work fine. They travel from stop to stop, waiting at each for passengers to exit or climb aboard. However, once a bus gets behind schedule, it’s nearly impossible for it to get back on track. It will continue to get further and further behind schedule until the next bus on the route catches up.

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Written by Long Branch Mike