### Mathematics and scheduling of buses

Image courtesy of welshmackem

I found this article via Math Teachers at Play carnival... it talks about a new method of scheduling buses, which uses mathematics, namely Markov Chains.

I'm not personally familiar with Markov chains, but whenever mathematics solves a problem in real life, I find it fascinating!

The mathematical method "evens out" the headway (the spacing between buses) by holding each bus at the start of the route a specified amount of time. That avoids "bus bunching", and it also makes it where the bus drivers don't need to adhere to any schedule--reducing their stress.

The researcher John Bartholdi says

The trick is to hold the bus for an adjustable amount of time at one stop. We simply control how long they wait at the end of the route, and then we tell them, ‘drive comfortable with the traffic to the other end. Don’t worry about where you are. Just flow with the traffic.’

Read more: Markov Chains avoid buses arriving in threes
Sounds cool!