Equality of access and resilience in urban population-facility networks

The study investigates how the spatial distributions of populations and urban facilities interact to shape equality of access and resilience in cities. Urban systems face risks from natural and man-made shocks that disrupt access to essential services. Prior work has largely assessed resilience of physical systems while overlooking population–facility interactions and equality of access. The authors hypothesize that improving equality of access—by aligning facility distributions with population distributions and reducing travel costs—also enhances the resilience of population–facility networks during crises. Leveraging large-scale smartphone mobility data, the study aims to optimize facility distributions to minimize total population travel distance and to quantify how such equality improvements affect resilience under disruptions.

The paper reviews streams of work on: (1) definitions, indicators, and metrics of inequality in urban contexts (e.g., neighborhood isolation, mobility segregation, spatial inequality), often stratified by socio-demographics; (2) disaster-related disparities in impacts and evacuation patterns; (3) accessibility optimization methods (e.g., particle swarm optimization, p-median problems) applied to facility siting to improve equity; and (4) resilience modeling of complex systems and urban networks, including transportation and mutualistic networks. Existing literature reveals widespread spatial mismatch between populations and facilities and inequality that intensifies during crises, but offers limited tools to jointly optimize equality and resilience using granular mobility data. The rise of smartphone-based mobility datasets offers opportunities to overcome past data granularity and noise limitations and to integrate accessibility and resilience analyses.

Data and preprocessing: The study integrates multiple datasets at county scale, standardized onto a ~0.5 km x 0.5 km grid: (a) Population from the US Census (2014–2018 ACS) apportioned to grids using anonymized smartphone mobility data (Veraset; Jan 27–Feb 23, 2020) and home-location inference via DBSCAN on night-time pings. An amplification factor (ratio of devices to census population) rescales device-based measures to population estimates. (b) Facility locations and categories from SafeGraph (NAICS), focusing on ten common categories (e.g., retail trade, finance and insurance, health care, education, arts & entertainment, etc.). (c) Road networks from OpenStreetMap (highways and primary roads) to compute travel costs between grid cells via neighbor-grid path aggregation to approximate shortest paths efficiently. Demand and capacity estimation: Device visits to facility categories over four weeks estimate device-level demand by grid of residence; demands are scaled by the amplification factor to population demand. Total facility capacity per category in a county is approximated as equal to total estimated demand and is distributed equally across facilities in that category; grid-level capacity aggregates facilities in the grid. Urban Centrality Index (UCI): UCI = LC × PI, where LC = 1 - Σ k_i^2 / N captures distributional inequality across N grids (k_i is share of quantity in grid i), and PI = 1 - V/V_max captures spatial separation with V = K^T D K (D is inter-grid distance matrix). V_max is approximated by uniformly distributing quantity along county boundaries. UCI ranges from 0 (polycentric) to 1 (monocentric). Equality optimization: Formulated as a p-median location problem to minimize total population-weighted travel distance from residential grids R to facility grids F. Decision variables: r_ij ∈ {0,1} assign each residential grid j to one open facility grid i; y_i ∈ {0,1} indicates facility open. New facilities (~10% of existing count) are included as candidate grids. Objective: minimize Σ_{i∈F, j∈R} d_ij r_ij p_j subject to assignment and facility-open constraints. Solved using a fast swap-based local search heuristic (fast interchange) to insert/swap facilities based on distance gain/loss. Resilience model: Defines a bipartite population–facility (PF) network with dynamic mutualistic interactions. Let S_i and U_i be satisfied and unsatisfied demand at facility grid i. Dynamics: ∂S_i/∂t = -λ S_i + α Σ_j w_ij S_j U_j - y_i; ∂U_i/∂t = λ S_i - α Σ_j w_ij S_j U_j, where λ is the rate of demand-pattern change, α is a fitted parameter, and w_ij is road-network distance between facility grids i and j. Dimension reduction aggregates to effective variables: w_j = Σ_i w_ij; W = Σ_j w_j; S_eff = (Σ_j S_j w_j)/W; U_eff = (Σ_j U_j w_j)/W; W_eff = (Σ_j w_j^2)/W, yielding ∂S_eff/∂t = -λ S_eff + α W_eff S_eff U_eff and ∂U_eff/∂t = λ S_eff - α W_eff S_eff U_eff. At steady state (∂S_eff/∂t = 0), the fraction satisfied is S_eff = 1 / (1 + (1/(α W_eff))^{1/(1-λ)}). Resilience is assessed by random perturbations removing a fraction f of facility grids (and their roads) and tracking W_eff and the implied S_eff. Each perturbation scenario is run 100 times for both existing (empirical) and optimized facility distributions. Evaluation: (1) Compare average travel distances under existing, optimized, and random-placement baselines; (2) UCI of population and facilities in existing vs optimized scenarios; (3) Analyze PF network structures; (4) Resilience via changes in W_eff and resulting S_eff as f increases.

• Population–facility spatial mismatch: Across ten US metropolitan counties, population distributions are relatively polycentric (UCI ≈ 0.2), while many facility categories are more monocentric (facility UCI spanning ~0.2–0.8; education, finance and insurance, and professional services often near ~0.8). Facility CCDFs approximate power-law-like distributions, with many facilities concentrated in few grids.
• Inequitable travel costs: Travel distances to nearest facilities vary widely; in some counties, residents in certain areas must travel >10 km to access health care. The unequal travel costs stem from spatially variant facility distributions.
• Equality optimization performance: Minimizing total travel distance (p-median) reduces average travel distances to all ten facility types compared to existing and random scenarios across all counties. The optimized scenario improves equality of access (more balanced service communities) while largely preserving overall spatial structure (radar-chart shapes similar across scenarios).
• UCI convergence: In optimized scenarios, facility UCIs decrease and move closer to the population UCI (~0.2), indicating more balanced, polycentric facility distributions aligned with population patterns.
• Resilience benefits: Higher facility capacity generally improves resilience but is not solely determinative. Effective distance embeddedness (W_eff) is the key factor. Under random facility-grid removals, optimized scenarios exhibit W_eff increases of roughly 10–30% relative to existing distributions (e.g., retail trade in Suffolk and San Francisco ~20% higher), maintaining higher S_eff (fraction of satisfied demand) for the same perturbation levels. W_eff declines as more facilities are removed, but remains consistently higher in optimized cases, indicating enhanced resilience.
• Generality: Patterns and improvements hold across diverse county sizes, shapes, and locations.

The findings support the hypothesis that enhancing equality of access through better-aligned, more polycentric facility distributions also strengthens the resilience of population–facility networks. By reducing average and disparate travel distances, optimized distributions mitigate vulnerabilities inherent to monocentric facility clusters, easing transitions to substitute facilities when disruptions occur. The effective-distance mechanism demonstrates how spatial dispersion increases the likelihood that unaffected, distant facilities can serve disrupted areas, sustaining higher fractions of satisfied demand during shocks. Practically, the models offer a data-driven pathway for urban planners to co-optimize facility siting and transportation planning, informing investments that improve daily access while bolstering system performance under crises. The work underscores the need to jointly consider equality and resilience rather than addressing them in isolation.

This study integrates large-scale smartphone mobility, facility, and road-network data with optimization and resilience modeling to jointly address equality of access and resilience in urban population–facility networks. It (1) documents a general population–facility spatial mismatch across US metropolitan counties; (2) provides an optimization framework that reduces travel distances and brings facility centrality closer to polycentric population patterns; and (3) shows that equality improvements increase effective distance embeddedness and, consequently, resilience under disruptions. The models can guide siting of new facilities, redistribution strategies, and transportation network planning. Future research should incorporate multimodal travel times and congestion, explicit road-disruption dynamics, facility relocation costs and land-use constraints, and equity-aware objectives that prioritize vulnerable populations and heterogeneous needs.

• Accessibility measured solely by travel distance; does not model multimodal travel times, congestion, or varying travel costs by mode.
• Facility capacities assumed equal within a category and constant over time; real capacities and service heterogeneity may vary.
• Socio-demographic and equity considerations (e.g., low-income, elderly, minority needs) not explicitly integrated; equal distributions may not ensure equitable outcomes.
• Resilience simulations focus on short-term facility-grid shutdowns; road-only disruptions and behavioral adaptations are not fully modeled.
• Practical constraints (relocation costs, land availability, zoning) limit redistributions; results assume feasibility of adding/relocating facilities (~10%).
• Smartphone data represent a subset of the population and a one-month period (pre-pandemic early 2020); despite scaling, potential sampling biases remain.