Congestive Mode-Switching and Economies of Scale on a Bus Route

This paper introduces a type of circular causation called Congestive Mode-Switching (CMS) that may arise when an increase in congestion penalizes transit relative to driving. If demand is also elastic, rising congestion persuades some transit riders to drive, which exacerbates congestion further, and so on. The paper explores this logic with a static model of a bus route. When the bus fleet size is fixed, CMS applies because congestion raises the bus cycle time and thus lowers bus frequency, resulting in higher wait times. When the fleet size depends on bus ridership, CMS is joined by economies of scale as a second source of circular causation. We characterize the system's equilibria in ways pertinent to stability and comparative static analyses. The comparative static exercise shows feedback may variously mute, amplify or reverse first-order effects of a road improvement