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A new model for "self-equalizing" bus routes may reduce wait time and increase reliability.

Bus bunching is a regular source of frustration for riders and city transit agencies alike. When buses on a particular route clump together it means crowding for the lead bus (as it stops longer to pick up more passengers), slower speeds and wasted capacity for the one behind (as it waits for the bus ahead of it and carries fewer riders), and a less reliable schedule for riders in general.

Usually transit agencies address bunching by building in slack time at certain "control points" on a bus route. That gives buses the chance to get back onto a fixed schedule or headway (the amount of time between buses). This approach can help alleviate bunching some, but it often requires a good bit of work on the part of drivers in terms of making adjustments, and it's often ineffective in cases of serious disruptions, such as a breakdown or inclement weather.

In an upcoming issue of Transportation Research Part B, John Bartholdi III and Donald Eisenstein propose a method of bus coordination that abandons the concept of tightly-managed headways or schedules. Without the restriction of meeting pre-specified targets, drivers instead follow the flow of traffic, and natural headways emerge over time. The result is a "self-equalizing" system with less bunching and more reliability, the authors write:

Under our scheme headways are dynamically self-equalizing and the natural headway of the system tends to emerge spontaneously. Headways also become self-correcting in that after disturbances they reëqualize without intervention by management or even awareness of the drivers.

The system outlined by Bartholdi and Eisenstein imposes simple adjustments at control points based on an equation whose goal is to both reduce the mean headway on a line and increase overall uniformity of headways. Because the calculation operates independent of a fixed schedule, adjustments can be made at any number of control points. When systems want more headway stability, say for longer routes, all they have to do is add more control points.

"The result is that headways are constantly adjusted to become more nearly equal," the authors write.

The researchers recently tested their model on the most popular bus line on the campus of Georgia Tech (Bartholdi's affiliation). The 3.3-mile looped route carries 5,000 riders a day and experiences both morning and evening rushes as well as heightened congestion near class change. The route strives for a constant 6-minute headway by giving several minutes of slack at two control points, but even with those provisions it usually falls behind its preset pace.

For the study, Bartholdi and Eisenstein told drivers to abandon their schedule, ignore headways, and drive with the flow of traffic. When they reached a control point the "self-equalizing" equation computed their next departure time. Compared to average headways recorded on the same day for two weeks prior to the experiment, the new system reduced headway and increased stability (the "self-equalizing" model appears in red):

The model held up to subsequent studies as well. In one case the researchers tested the severity of their "self-equalizing" system by taking an entire bus out of operation. While headways are expected to rise to around 18 minutes in such a situation, their model achieved gaps of 17 minutes. And in simulated tests of an 18-mile bus route in Chicago (Route 63), the new model outperformed target-schedule systems in both light and heavy ridership conditions.

Bartholdi and Eisenstein attribute the success of their system to its flexibility. Rather than relying on accurate forecasts of headway, which requires guessing at traffic flows, the "self-equalizing" system responds to traffic in the moment. Bus drivers seem to like it, too; after the Georgia Tech experiment, drivers told the researchers they enjoyed focusing on safe driving as opposed to worrying about a predetermined schedule. And because it's less bunchable, riders will consider the system more reliable. The authors conclude:

This [system] reduces work for management, and simplifies the job of the drivers, who can focus purely on flowing with the traffic. And most importantly, it provides better service to riders.

Top image: Flickr user ansoncfit, via Creative Commons

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