Figure 1: A tablet computer mounted beside the bus driver signals when to go.
It is hard for buses to adhere to a schedule because there is a tendency to bunch. The result is that riders experience a long wait, after which several buses may arrive together.
Worse, a schedule is inflexible. If a bus breaks down it leaves a gap in service and this gap tends to grow. The bus following this gap will serve about twice as many passengers as before and so will spend more time at each stop, and fall still farther behind.
Bunching is the most frequent complaint about any urban bus system, as a web search on “bus bunching” will confirm.
Abandon the schedule! No one cares about a schedule as long as the gaps between buses — that is, the headways — are small, as in a busy urban bus system. Instead control headways by strategically delaying buses at the ends of the route or at special locations such as transfer points.
My colleague Don Eisenstein (UChicago) and I have devised a new way of computing the delays so that headways equalize, without management direction or driver intention.
Our scheme requires only this: When a bus arrives at one end of the route, it “looks” at the bus immediately following and and estimates the time until its arrival. Then it performs a simple calculation that determines how long to pause. This pause changes the headway of each newly arrived bus to an average of its former headway and the headway of the following bus. If its former headway was larger, its new headway becomes smaller, and vice versa. The result is that headways are constantly adjusted to become more nearly equal.
The scheme requires only a tidbit of local information — the estimated time until the next bus arrives — but this is sufficient to coördinate all the buses on the route: The relative positions of the buses will be adjusted to be more evenly spaced, so that no one has to wait too long for a ride. Moreover, this technique works without knowing a map of the route or even the number of buses.
Read the details in our technical paper, a version of which has appeared in Transportation Research B. The final, published version, which may be found here, won the 2012 Best Paper Award from the Transportation Science and Logistics Society of INFORMS.
If you have Java enabled in your browser, you will see a live simulation of buses on a route below. The simulated buses will likely have achieved equal headways by the time you have read this far. Click anywhere on the simulation to remove one bus, leaving a large gap, and you will see that the remaining buses spontaneously re-equilibrate. In general our system can transition from n buses to n-1 or n+1 without any need for management oversight or coördination among the drivers.
Without changing operations or processes, buses can be added or removed from the route at any time; the route can be changed (for example, to detour around construction); and bus stops can be inserted or removed. After any such change the headways will autonomically re-equalize.
Thanks to the bravery of David Williamson and Aaron Fowler of Georgia Tech's Department of Parking and Transportation, we were able to test our scheme on the central bus route through the heart of campus. The results were clear: Average headways were smaller so there was less wait for a bus. And there was less variability in headways, so service was more reliable.
More importantly, tests confirmed the ability of our scheme to respond to large disturbances. We removed one bus from the route, leaving a large gap in service. Under our scheme, the headways of the remaining buses spontaneously re-equalized, thereby re-establishing regular service without intervention by management or awareness of the drivers.
Figure 1: A tablet computer mounted beside the bus driver signals when to go.
Georgia Tech students, working with the GT Department of Parking and Transportation, have built a system based on our control scheme in which each bus contains a tablet or mobile phone with GPS and wireless networking capabilities. We have been conducting live trials for over one year and held a public demonstration on 20 April 2012, which was covered by CNN and PBS. Our system began full-time use at Georgia Tech in August 2013. Look for more information here soon.
Our scheme is simple, practical, and easy to implement or adapt, so we expect it to be useful for other transportation systems with short headways, such as subway trains or airport shuttles.
Here are some frequently-asked questions and their answers.
For more information contact: John DOT Bartholdi AT GaTech DOT edu or Don DOT Eisenstein AT ChicagoBooth DOT edu