A family of accessibility measures derived from spatial interaction principles

Transportation planning has long prioritized the efficiency of movement. However, the concept of accessibility represents a more comprehensive evolution, shifting focus from movement (i.e., trips) to the potential to spatially interact with desired destinations. Despite growing recognition of accessibility-based planning approaches, the concept remains fragmented, with inconsistent definitions and unclear interpretations. To this end, this paper makes a methodological contribution by specifying a family of accessibility measures that are grounded in the shared 'gravity-based' theoretical roots of spatial interaction models, particularly their balancing factors. From this foundation, we outline four members of the family: the 'unconstrained' measure (i.e., Hansen-type accessibility), the 'total-constrained' measure (i.e., a constrained version of the Hansen-type accessibility), the 'singly-constrained' measure (i.e., related to the popular two-step floating catchment approach - 2SFCA), and the 'doubly-constrained' measure representing realized access (i.e., equal to the doubly-constrained spatial interaction model). These measures can be interpreted as either the number of accessible opportunities or accessible population (i.e., market potential). A toy example illustrates how they produce interpretable unit-based values, offering a clearer and more coherent basis for accessibility analysis.