Bus bunching has a mathematical explanation

Waiting at the bus stop can be frustrating, especially if your bus is late. You wait, and wait – and often, when your bus finally arrives, there’s another close behind. It’s not just coincidence. Turns out, a phenomenon known as bus bunching is to blame.

It’s a problem that transit systems all over the world have been trying to solve for years. Now, a pair of mathematicians may have a potential answer.

“Bunching is annoying for riders, since it increases both the average time spent waiting for the bus and the variability in this waiting time,” Drs. Vikash V. Gayah and S. Ilgin Guler, both professors of civil engineering at Pennsylvania State University, wrote for The Conversation.

The problem comes when a bus gets off schedule for any reason. A late bus is likely to get later and later as it travels its route, waiting for passengers to climb off or board. At the same time, an early bus gets earlier with each stop.

That’s because the later a bus is, the more time passengers have to gather at the stop, and the more time it takes them to board. Early buses see fewer passengers and shorter boarding times.

“Bus bunching occurs because bus routes are inherently unstable,” Gayah and Guler wrote.

In the end, it can lead riders to lose faith in the transit system and turn to less sustainable forms of transportation, like personal vehicles.

Gayah and Guler suggested some possible solutions to prevent bus bunching. One would be to instruct bus drivers to skip stops if they’re running late and no one needs to get off, but this would leave riders who need to board the bus stranded, the pair admitted.

Another strategy builds “slack” – extra time – into the bus schedule to prevent late buses. Early buses simply wait at each stop until the scheduled departure time. But if a bus does run late, it’s still difficult for the driver to make up time, the mathematicians said.

New technology that allows bus dispatchers to watch buses in real time and offer up feedback may help ease bus bunching, the pair wrote.

“These novel strategies treat consecutive buses as if they were all connected by springs. Buses that are too close together along the route are given instructions to help ‘push’ them apart, while buses that are too far apart are given information to help ‘pull’ them back together,” Gayah and Guler said.

The researchers are now using modeling and algorithms to test how the latter strategy could be used in the field, so for now, bus riders may have to continue dealing with bunching. But at least now you know there’s a mathematical explanation.

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By Kyla Cathey, Earth.com staff writer

Image credit: lena1790, Pixabay