The Time Between: Continuously-defined accessibility functions for schedule-based transportation systems

Accessibility is traditionally considered to be a property of a point or region in space, and to be invariant over time (or at least over some computationally convenient time interval). How- ever, a locations accessibility can vary over time on a wide range of scales. This temporal variation is especially significant for schedule-based transportation systems. Current measures of accessibility generally reflect the accessibility only at points in time corresponding to the departures of one or more trips; accessibility between these time points remains unconsidered and undefined. Consequently, these measures are insensitive to changes in route frequency and the distribution of trip departure times. Furthermore, these approaches ignore the disutility experienced by a system user who is limited to departing or arriving at scheduled times rather than at preferred times. As a result, they systematically overestimate the accessibility experienced by users of scheduled transportation systems. We establish new methods for representing the accessibility provided by a schedule-based transportation system from a specific location as a continuously-defined accessibility function (CDAF) of desired departure time, defined for all time points. Using schedule and route information from metropolitan transit providers, we demonstrate the application of these methods to gain new insight into the accessibility provided by real-world transportation systems. Four examples are developed to represent common service types in metropolitan transit networks. The results confirm that accessibility is significantly overestimated by measuring single points and show that trip frequency is more valuable for sustained accessibility than high accessibility on individual trips.