Science explained: The U1

The horror of the U1 is probably one of the few things every Warwick student can agree on. We’ve all done it: stood at the campus interchange in the dark and cold waiting for the U1. You wait and wait then two buses, sometimes more, show up at the same time. Now this could be due to some masterplan from Stagecoach but it is far more likely to be a simple mathematical inevitability.

Image: JThomas

This is hardly a unique phenomenon, called bus bunching by those with PhDs in transport engineering, but why does it happen? Considering the amount of points things can slow down even on the reasonably simple U1 route (let’s not even start on the U12) we’ll have to simplify things slightly. Our model will have two buses, bus A and bus B, going around a circle with two stops.

To start with, our buses are on opposite sides of the circle and are picking up the same number of passengers at the same rate- there are no delays. If you introduce a delay to bus A, say there were too many passengers at a stop, then bus B will start catching up with bus A.

This is where it gets interesting. As soon as there is a delay for either bus, bus bunching is inevitable (in this simple model anyway).

As bus B has caught up slightly with bus A, bus B will reach the stop bus A was delayed at before the stop has fully refilled with passengers. This means bus B will fill up quicker and catch up with A slightly more. At the same time, bus A is late to its next stop so this stop has too many passengers, slowing it down further. This process continues until bus B catches A – giving the wonderful sight of two U1s after a half hour wait.

Remedying this situation involves introducing slack to the system. Ideally this means open stretches of road where delayed buses can catch up with the timetable. Now considering the state of the roads between campus and Leamington, you can see why this doesn’t happen. The other option is to lay on more buses, reducing the chance that stops get too full….

I’ll believe it when I see it.