Optimal bus stop spacing through dynamic programming and geographic modeling

A discrete approach was used to model the impacts of changing bus-stop spacing on a bus route. Among the impacts were delays to through riders, increased operating cost because of stopping delays, and shorter walking times perpendicular to the route. Every intersection along the route was treated as a candidate stop location. A simple geographic model was used to distribute the demand observed at existing stops to cross-streets and parallel streets in the route service area, resulting in a demand distribution that included concentrated and distributed demands. An efficient, dynamic programming algorithm was used to determine the optimal bus-stop locations. The model was compared with the continuum approach used in previous studies. A bus route in Boston was modeled, in which the optimal solution was an average stop spacing of 400 m (4 stops/mi), in sharp contrast to the existing average spacing of 200 m (8 stops/mi). The model may also be used to evaluate the impacts of adding, removing, or relocating selected stops.