“A Self-Coordinating Bus Route to Resist Bus Bunching”, 2012-05 (; similar):
The primary challenge for an urban bus system is to maintain constant headways between successive buses. Most bus systems try to achieve this by adherence to a schedule; but this is undermined by the tendency of headways to collapse, so that buses travel in bunches.
To counter this, we propose a new method of coordination buses. Our method abandons the idea of a schedule and even any a priori target headway. [Specifically, we delay bus 1 at the control point for duration α · hn where 0 < α < 1 is a control parameter that determines the sensitivity of our scheme to perturbations.]
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 realize without intervention by management or even awareness of the drivers.
We report on a successful implementation to control a bus route in Atlanta. [using Georgia Institute of Technology’s campus buses]
…The computation of Equation 3.6 changes the headway of each newly arrived bus to a weighted average of its former headway and the former headway of the trailing 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. Furthermore, this adjustment proceeds from any starting positions of the buses, which means that the headways will tend to re-equalize after any disturbance, no matter how severe.