Introducing spatial availability, a singly-constrained measure of competitive accessibility

Abstract

Accessibility indicators are widely used in transportation, urban and healthcare planning, among many other applications. These measures are weighted sums of reachable opportunities from a given origin, conditional on the cost of movement, and are estimates of the potential for spatial interaction. Over time, various proposals have been forwarded to improve their interpretability: one of those methodological additions have been the introduction of competition. In this paper we focus on competition, but first demonstrate how a widely used measure of accessibility with congestion fails to properly match the opportunity-seeking population. We then propose an alternative formulation of accessibility with competition, a measure we call spatial availability. This measure relies on proportional allocation balancing factors (friction of distance and population competition) that are equivalent to imposing a single constraint on conventional gravity-based accessibility. In other words, the proportional allocation of opportunities results in a spatially available opportunities value which is assigned to each origin that, when all origin values are summed, equals the total number of opportunities in the region. We also demonstrate how Two-Stage Floating Catchment Area (2SFCA) methods are equivalent to spatial availability and can be reconceptualized as singly-constrained accessibility. To illustrate the application of spatial availability and compare it to other relevant measures, we use data from the 2016 Transportation Tomorrow Survey of the Greater Golden Horseshoe area in southern Ontario, Canada. Spatial availability is an important contribution since it clarifies the interpretation of accessibility with competition and paves the way for future applications in equity analysis (e.g., spatial mismatch, opportunity benchmarking, policy intervention scenario analysis).

Multimodal spatial availability: A singly-constrained measure of accessibility considering multiple modes

“…If we understand opportunities to be finite and/or subject to some levels of congestion, it is possible for an accessibility measure to take on a crisper meaning. Accessibility research has a history of considering opportunity competition, especially regarding school-seats, hospital capacity, and employment opportunities [14,15,[17][18][19][20][21][22][23][24][25][39][40][41][42]. If one person reaches an opportunity-it is taken: the supply of an opportunity and the demand for that opportunity are the nodes in accessibility analysis.…”

“…the Hansen-type measure [1]: these measures sum "weighted" opportunities around a focal point (i.e., a potential origin), based on how expensive it is to reach them. Recent research in accessibility analysis has explored the implications of methods by which opportunities are summed, especially in the context of competitive accessibility [12][13][14][15]. In a typical Hansen-type accessibility measure, the sums around origins are not constrained: the same opportunity can enter the sum for different origins.…”

“…Pa ´ez et al (2019) [12], for example, focuses on floating catchment area methods and introduces a normalization of the impedance matrix to allocate the population and then the level of service (i.e., the supply to demand) proportionally. More recently, Soukhov et al (2023) [15] introduced a singly-constrained measure of accessibility, called spatial availability, that employs a similar but more sophisticated proportional allocation mechanism. The work of these authors show that floating catchment area methods can be seen as singly-constrained accessibility measures and improve on existing approaches by guaranteeing that each opportunity is counted only once.…”

“…A limitation of spatial availability as introduced by Soukhov et al (2023) [15] is that it was developed for the case of a homogeneous population, for example for the case of a single mode of transportation. However, the finite nature of opportunities makes the analysis of heterogeneous populations very relevant.…”

Desigualdades de classe, raça e gênero no acesso ao transporte e ao espaço urbano em cidades brasileiras: análises empíricas e métodos para políticas e planejamento.

“…In education or healthcare, measuring the time it takes for children or people to get to the closest school or healthcare facility may be helpful to unfold inequalities, especially when households are linked to school or health districts. However, the number of people who can access them is constrained by the number of teachers or doctors available in each facility and its infrastructure (Paez et al, 2019;Soukhov et al, 2023). Also, the quality of the service provided in each location varies significantly in the territory (UNESCO, 2019), which may also play a role in accessibility levels (Pizzol et al, 2021).…”