Spatial and Social Equity in Access to Emergency Service Facilities—An Opportunity–Outcome Perspective

Abstract

Equity in access to emergency service facilities (ESFs) is essential for ensuring residents’ safety and well-being. Previous studies on equity in access to ESFs have mainly focused on individual facilities or single dimensions, failing to capture the overall fairness of the emergency service system as an integrated entity. This study introduces an integrated opportunity–outcome evaluation framework to examine spatial and social equity in access to ESFs at the community scale, with particular attention to disparities across facility types, spatial levels, and socioeconomic groups. A machine learning-based approach combining XGBoost and SHAP is employed to identify key spatial and non-spatial factors influencing ESF accessibility. The results indicate that: (1) In terms of opportunity equity, spatial accessibility to ESFs varies significantly, with lower accessibility in southwestern Yongdeng County and northern Gaolan County. (2) Regarding outcome equity, a significant spatial mismatch exists between emergency resource distribution and population demand, resulting in polarization between oversupply and insufficiency, with the FSs supply–demand imbalance being the most pronounced. Low-income groups, rural residents, and the elderly face greater difficulty accessing ESFs compared to the general population. Among all variables, average elevation is found to be a decisive factor affecting accessibility. Based on these findings, the study proposes a zoning-based planning strategy for ESFs in Lanzhou. This strategy offers practical guidance for improving future regional ESF planning, enhancing urban emergency response capacity and resilience.

1. Introduction

Against the backdrop of accelerated urbanization, emergencies have become increasingly frequent and intense, posing significant threats to residents’ lives and social stability [1,2,3]. Consequently, mitigating the adverse impacts of such events and strengthening disaster response capacities have become essential priorities in urban development.

Emergency service facilities (ESFs), integral components of regional disaster prevention and mitigation systems, play a pivotal role in providing critical services such as emergency rescue and shelter during crises, thereby significantly mitigating disaster risks [4,5]. Emergency medical services facilities (EMSFs), fire stations (FSs), and emergency shelters (ESs) play a more critical role in emergencies, as they are directly related to the safety and well-being of residents, surpassing the importance of other emergency service facilities (ESFs), such as emergency command centers [6,7]. Therefore, EMSFs, FSs, and ESs are commonly classified as “critical emergency service facilities” [8]. EMSFs provide timely and effective medical treatment, minimizing the degree of lesions and even the death toll [9,10,11]. ESs are facilities or designated locations used for evacuating, assisting, and resettling individuals affected by sudden disasters, such as earthquakes and fires [12]. ESs protect residents from both direct and indirect harm caused by emergencies, ensuring basic living conditions [13,14,15]. FSs provide firefighting, rescue, and disaster relief services, along with search and rescue operations and the evacuation of trapped individuals [16,17].

The optimal layout of ESFs is one of the most effective and cost-efficient strategies for mitigating the risks of natural disasters and public safety incidents [18,19,20]. Research indicates that equity in access to ESFs significantly contributes to minimizing casualties and losses in emergencies [21,22,23]. Failing to recognize equity in access to ESFs could exacerbate the disaster impact and hinder recovery processes, which in turn, reduces future resilience and leads to a vicious cycle that leads to more severe casualties [24,25]. Recently, scholars have argued that equitable access to ESFs directly reflects a city’s emergency management capacity and disaster resilience [4,26,27,28,29]. Therefore, to optimize the use of ESFs, planners must incorporate equitable access into spatial planning to minimize casualties.

Equity in access to ESFs refers to the impartial distribution and just accessibility of resources, opportunities, and outcomes, which strive for fairness regardless of location and social group [30,31]. Equity in access to ESFs ensures that everyone in the community, regardless of their demographic background, geographic location, level of community status, and internal capabilities, have access to and benefits from emergency services. In this context, equity refers to relative fairness rather than absolute fairness. Pre-assessing equity in access to ESFs enables the evaluation of a city’s emergency service capacity before disasters occur [32]. It also assists decision-makers in optimizing the allocation of ESFs and enhancing urban emergency response capacity [33].

Related research on equity in access to ESFs can be categorized into two main aspects: assessing the spatial equity of facility supply and evaluating social equity by accounting for differences in population demand. Accessibility measures are used to quantify both spatial and social equity in urban facilities [34,35,36]. For example, Jones assessed the accessibility of EMSFs in Norfolk County, UK, by estimating response times based on road network distances [37]. Jiang measured accessibility to emergency shelters based on the minimum cost distance in Futian, China [38]. These studies primarily focused on resource supply fairness but overlooked the supply–demand relationship in ESFs. To address this limitation, scholars introduced methods like the gravity model and the two-step floating catchment area (2SFCA) method. For example, Dou applied a potential model to evaluate the accessibility of ESs in Wuhan, China [39]. KC used the E2SFCA method to assess FS accessibility in specific regions of Australia, identifying areas with potentially low future spatial access to firefighting services [40]. Li investigated the impact of urban dynamics and emergency incidents on EMSFs accessibility [41]. Su proposed a variable-radius 2SFCA method to assess the spatial rationality of ES layouts [42]. These studies evaluated residents’ equitable access to ESFs by incorporating both facility supply capacity and minimum emergency needs. However, these studies generally do not account for the specific needs of different social groups in accessing ESFs.

With the development of society, scholars have increasingly emphasized outcome equity in access to ESFs. Research suggests that during emergencies, vulnerable groups—including the elderly, children, women, migrants, and low-income workers—experience higher mortality rates than the general population [43,44]. Similarly, underdeveloped areas exhibit greater vulnerability, such as suburban and rural regions [45,46,47]. Consequently, vulnerable groups and residents of underdeveloped areas have attracted growing attention. For instance, Shi evaluated EMSF accessibility for kindergartens and nursing homes in Lanzhou, China, considering the increased demand for EMSFs among vulnerable groups, such as children and the elderly, during urban flood disasters [48]. Su developed an age-integrated accessibility assessment method to examine the accessibility and equity of ESs in the main urban area of Lanzhou, China [49]. Nakai H. used network analysis to assess ES accessibility for children’s homes along Japan’s Pacific coast [50]. Li applied an improved 3SFCA method to evaluate the equity of villagers’ access to medical facilities in Qin’an County, Gansu Province, China [51].

Despite significant progress in studying equity in access to ESFs, several limitations remain. First, previous studies on equity in access to ESFs have focused on a single facility type or dimension, often restricting the study area to specific urban regions. These studies may fail to comprehensively capture the diverse emergency needs during disasters and do not reflect a city’s overall emergency service capacity. Second, studies often assume a homogeneous population, neglecting disparities in resource access caused by factors such as age, gender, and income [52]. Third, Euclidean or network distances are commonly used to measure residents’ travel impedance [38,53], which may lead to discrepancies between predicted and actual response times.

Building on this foundation, a comprehensive evaluation framework for ESFs is developed from the dual dimensions of opportunity equity and outcome equity. Lanzhou, a representative mountainous city in underdeveloped northwestern China, serves as the study area. The analysis focuses on three types of critical ESFs directly related to life safety: EMSFs, FSs, and ESs. Employing the proposed methodology, the study conducts a community-level assessment of equity in access to ESFs. The study is guided by the following questions:

(1)

Do spatial disparities exist in equitable access to different types of ESFs in Lanzhou?

(2)

How does spatial heterogeneity in ESF accessibility vary across different spatial scales?

(3)

Does the current allocation of ESFs in Lanzhou exhibit patterns of social inequity?

(4)

How do spatial and socioeconomic factors influence equitable access to ESFs in Lanzhou?

This study aims to clarify the mechanisms driving inequitable access to ESFs in river-valley city of western China, and to offer concrete evidence for understanding urban–rural equity in similar topographic contexts. By analyzing how policy-led planning interacts with terrain-related constraints, it further seeks to support the design of spatially differentiated ESF strategies and to enhance resilience at the community level.

2. Materials and Methods

2.1. Conceptual Framework

Over time, research on equity in access to ESFs has evolved, shifting its focus to a more in-depth and progressively refined theoretical exploration [54]. This study posits that equity is a multidimensional concept and presents two core evaluative perspectives: “opportunity equity” and “outcome equity”. Opportunity equity underscores the potential for accessing services, whereas outcome equity focuses on the actual benefits derived from such access. Building on this framework, the study further operationalizes these two theoretical perspectives into two assessable dimensions: Opportunity equity is reflected in “spatial equity,” where the distribution of ESFs directly determines residents’ initial access to services. Outcome equity is assessed through “social equity”, which examines how socio-economic heterogeneity affect the ability of different groups to convert spatial opportunities into actual service outcomes.

Research on equity in access to ESFs has effectively validated this framework. Initially focused on the equity of resource quantity, the research has shifted toward addressing the equal opportunities for residents to access emergency resources [5,49,55], marking a deepening of the opportunity equity perspective. Subsequently, the social dimension was gradually incorporated, considering the disparities in supply and demand between different groups [56], signaling an expansion of the research focus to outcome equity.

From the perspective of opportunity equity, equity in access to ESFs encompasses two fundamental dimensions. The first dimension is spatial accessibility, which refers to the time or distance needed for any demand point within a designated area to reach the nearest ESF [57]. This study adopts the fastest response time as a primary indicator of equity in access to ESFs, concentrating on the supply characteristics of these facilities and conducting a quantitative analysis of service capacity across different regions. The second dimension is spatial usability, which refers to the service capacity and operational effectiveness of ESFs [58]. This dimension incorporates considerations of supply–demand alignment. The study employs a non-discriminatory approach, integrating factors such as residents’ travel costs, and the quality of ESFs, into the equity assessment. Additionally, inequalities in the usability of ESFs are evident across different spatial scales. Therefore, the study also examines the equity characteristics of accessibility at multiple spatial levels, including community, district, and central vs. non-central urban areas.

From the perspective of outcome equity, the focus shifts from “indiscriminate spatial units” to “differentiated social individuals”, incorporating socio-economic and individual differences into the assessment. These differences include variations in population density, biological factors such as gender and age, disparities in social resources like income, local residency status, and residential location, as well as cognitive differences, such as religious beliefs. The core objective is to analyze how the inherent differences among social individuals influence the equity of the outcomes in ESFs. Therefore, this study adopts the equity of access to ESFs across different socio-economic groups as an evaluation metric, aiming to identify groups that experience inequities in the provision of ESFs.

2.2. Study Area

This study was conducted in Lanzhou, Gansu Province, China. Lanzhou is a representative city in the underdeveloped region of northwest China, with a total area of 13,100 km² (Figure 1). By 2022, the total population was 4.4153 million, with an urbanization rate of 84.07%. The topography of Lanzhou is complex, with significant differences in natural geographical conditions across different regions. The central urban area exhibits a typical “two mountains surrounding one valley” landform, where mountains flank the city to the north and south, and the Yellow River valley runs through the city. The urban development follows a linear pattern along the river valley. This unique topography severely limits the continuous expansion of built-up areas and has a profound impact on the spatial distribution and transportation infrastructure for ESFs. Moreover, Lanzhou faces significant disaster risks, with a high concentration of population and economic activities in the central urban area, resulting in enormous emergency demands that pose a severe challenge to the city’s emergency response capacity [59,60].

2.3. Data Sources and Processing

ESFs data. We selected EMSFs, FSs, and ESs for a comprehensive evaluation of equity in access to ESFs (Figure 2a). (1) EMSFs: Data for EMSFs were sourced from the Baidu Maps API (https://ditu.amap.com/, accessed on 5 May 2022) and cross-verified with information from the Gansu Provincial Emergency Medical Rescue Center in 2022. Lanzhou has one emergency medical center and 24 sub-stations in total. The central urban area has 7 direct sub-stations and 15 network sub-stations, with a total of 54 ambulances, serving a targeted population of over 2 million. (2) FSs: Data for FSs were extracted from the Baidu Maps API in 2022. Lanzhou has 53 fire stations and units. (3) ESs: Data for ESs data were obtained from information provided by the Lanzhou Earthquake Bureau in 2022. Lanzhou has a total of 863 ESs, primarily including urban parks, green spaces, plazas, parking lots, and school playgrounds. The total effective shelter area covers 16 km², with a per capita effective area of 4.06 m².

Census data. Using community-scale data, this study precisely analyzes the equity in access to ESFs. There are 433 communities under the jurisdiction of 114 sub-districts (towns) of 8 districts in Lanzhou, with a total population of 4.42 million, 84.07% of whom reside in urban areas (Figure 2b). The data, primarily from the Gansu Provincial Health Commission (2020), includes demographic and socio-economic information such as population size, age, gender, ethnicity, and household registration (hukou) status (Table 1). Population centroids are used to designate the locations of the Community Residential Committees (CRCs), which are familiar to residents. To assess outcome equity in access to ESFs, we selected six population groups: the elderly (aged 65 and above), children (aged 14 and below), males, females, migrant groups (non-local registered population), and ethnic minorities (Figure 3).

Travel time. Travel time, rather than travel distance, more accurately reflects travel costs [61,62]. Therefore, in this study, travel time extracted from online maps was used to measure travel costs for accessibility. In reality, travel costs are influenced by various factors. As a result, traditional calculation methods tend to overestimate the accessibility of ESFs. The route planning module of the Baidu Maps API provides accurate and comprehensive road information and route planning, closely reflecting actual travel times in accessibility studies, thus enhancing credibility and accuracy. Using the Baidu Maps API’s route planning module, travel times from each community to ESFs are automatically calculated travel time data for multiple passages between supply and demand points were obtained through the route planning interface, and the average travel time for each origin-destination (OD) pair was calculated based on repeated measurements. This methodology provides a more reliable travel time, which is then used in the analysis of ESF accessibility.

Road network data. Road network data from OpenStreetMap (https://www.openstreetmap.org/, accessed on 15 May 2022) were used to evaluate the density of road network.

2.4. Methods

This study analyzes the equity in access to ESF in Lanzhou from an opportunity–outcome perspective. The research workflow is illustrated in Figure 4.

2.4.1. Accessibility Calculation of ESFs

(1)

The Gaussian 2SFCA method

The Gaussian 2SFCA method introduces the decay law of residents’ travel distances and considers the supply-service capacity of public service facilities [63,64,65]. In recent years, many scholars have used this method to analyze the accessibility and social equity of various facilities. Therefore, in this study, we chose Ga2SFCA to measure accessibility to ESFs. The method consisted of the three steps listed below.

The first step is calculating the supply-to-demand ratio $R_j$.

$$R_j={\displaystyle \frac{S_j}{\sum _{i\in \left\{t_{ij}\le t_0\right\}}G\left(t_{ij}{,t}_0\right)D_k}}$$

(1)

$$G\left(t_{ij}{,t}_0\right)=\left\{\begin{array}{cc}{\displaystyle \frac{e^{-1/2\times {\left(t_{ij}/t_0\right)}^2}-e^{-1/2}}{1-e^{-1/2}}}, \hfill & t_{ij}\le t_0\hfill \\ 0,\hfill & t_{ij}>t_0\hfill \end{array}\right.$$

(2)

where $S_j$ is the supply capacity of ESFs; $D_k$ denotes the population size of community $k$; $G\left(t_{ij}{,t}_0\right)$ is the time distance decay function; $t_0$ refers to the spatial search threshold, measured by time cost in this study; $t_{ij}$ is the travel time between community $i$ and facility $j$.

The second step is to calculate the accessibility value $A_i$ of the community.

$$A_i=\sum _{j\in \left\{t_{ij}\le t_0\right\}}{R}_j{w}_{ij}$$

(3)

where Ai refers to the accessibility index of ESFs within the spatial search threshold $t_{ij}$ centered on community $i$.

In the third step, comprehensive accessibility index $C_i$ of MESFs is calculated.

This study adopts an integrated subjective and objective weighting method to determine the weights associated with different types of ESFs. First, the relative importance of each ESF was first established through structured expert consultation, involving six scholars in the field of urban and rural planning. Subsequently, the relative weights of each facility type were determined using the Analytic Hierarchy Process (AHP). To further reduce subjectivity in the weighting process, we then applied the entropy method for objective weighting. Finally, the comprehensive weights were calculated using Formula (4).

$$w_i={\displaystyle \frac{v_i{\times y}_i}{\sum _i^n{v}_i{\times y}_i}}$$

(4)

$$C_i=\sum _i^n{w}_i\times A_i$$

(5)

where $v_i$ denotes the weight of AHP; $y_i$ is the weight of the entropy method; $w_i$ denotes the weight of the combined index. The finalized combined evaluation weights were 0.491 for EMSFs, 0.311 for FSs and 0.198 for ESs.

(2)

Setting of service thresholds and supply capacity for urban and rural ESFs

This study adopted varying service thresholds for ESFs (Table 1). The previous “one-size-fits-all” approach to public service allocation has led to a pronounced mismatch and inadequacy of ESFs between urban and rural areas [45,46,47]. Urban and rural areas differ significantly in scale, spatial layout, population density, and emergency service demand [66]. Therefore, differentiated service thresholds must be set for urban and rural facilities, considering the characteristics of both service units and target groups.

Table 1. Setting of service threshold ESFs.

ESF	Service Threshold (min)		Travel Mode	Reference
EMSF	Urban area	15	Driving	(Health Commission of Gansu Province, 2020)
	Rural area	45
FS	Urban area	10	Driving	[67]
	Rural area	20
ES	Temporary shelters	15	On foot	Standard for Urban Planning on Earthquake Resistance and Hazardous Prevention (China)
	Fixed shelters	60

Table 1. Setting of service threshold ESFs.

ESF	Service Threshold (min)		Travel Mode	Reference
EMSF	Urban area	15	Driving	(Health Commission of Gansu Province, 2020)
	Rural area	45
FS	Urban area	10	Driving	[67]
	Rural area	20
ES	Temporary shelters	15	On foot	Standard for Urban Planning on Earthquake Resistance and Hazardous Prevention (China)
	Fixed shelters	60

We adopted different calculations for these service capacities. The number of beds, effective area, and number of fire trucks were selected to represent the service capacities of EMSFs, ESs, and FSs, respectively.

2.4.2. Gini Coefficient and Lorenz Curve

This study employed the Lorenz curve and Gini coefficient to quantify the equity of ESFs accessibility. The Gini coefficient ranges from 0 to 1, with lower values indicating a more equitable distribution of resources [68]. Generally, 0.4 is regarded as the “warning line” for distribution disparity [40,41].

$$G=1-\sum _{i=1}^n\left(x_{i+1}-x_i\right)\left(y_{i+1}+y_i\right)$$

(6)

where $G$ represents the Gini coefficient of ESFs; $x_i$ denotes the cumulative population ratio; $y_i$ denotes the cumulative accessibility ratio of ESFs.

2.4.3. Bivariate Local Moran’s I

The bivariate local Moran’s I is commonly used to detect spatial relationships between two variables [69]. The formula for the bivariate local Moran’s I statistic is as follows:

$$I_{xy}^i=z_x^i\sum _j{w}_{ij}{Iz}_y^j,\sum _j{w}_{ij}=1$$

(7)

where $z_x^i$ is the standardized value of variable $x$ (accessibility index of ESFs) for area $i$; $z_y^i$ is the standardized value of variable $y$ (population density) for area $\mathrm{y}$; $w_{ij}$ is the spatial weight matrix between areas $i$ and $j$.

2.4.4. Share Index and Locational Entropy

This study used the share index and zone entropy to evaluate social equity in ESFs accessibility for different social groups.

In the first step, the share index was calculated. This method evaluates social equity by measuring the gap between the access levels of different social groups and the average access level in society [70]. When the share index R > 1, it indicates that the specific social group has above-average access to emergency services.

$$R=\sum _{j=1}^n{P}_j{X}_{j}100\%$$

(8)

$$F={\displaystyle \frac{R}{P}}$$

(9)

$P_j$ represents the proportion of a particular social group in the resident population of community $j$; $X_j$ represents the ratio of a is the ratio of emergency resources in community $j$ to the total emergency resources in the study area. $P$ represents the proportion of a particular social group in the total population of the study area.

The second step is to calculate the zone entropy. To further assess the relationship between the distribution of ESFs and various social groups, we clarified it through calculation. The formula is as follows:

$$Q_j={\displaystyle \frac{T_j/P_j}{T/P}}$$

(10)

$Q_j$ is the zone entropy of community $j$. $P_j$ is the population size of a particular social group in community $j$. $T$ represents the total sum of emergency services across all communities in the study area. $P$ is the total population of that particular social group in the study area. When $Q_j$ > 1, it indicates that the supply capacity of emergency services exceeds the demand of that social group; when $Q_j$ < 1, the opposite is true [71].

2.4.5. XGBoost Model and Explanatory Model

This study employs the XGBoost algorithm as the primary model to analyze the relationship between the accessibility of ESFs and their influencing factors. XGBoost offers strong generalization capabilities, efficient computation, and excels at capturing the nonlinear, high-dimensional relationships that characterize the factors affecting equitable access to ESFs [72]. Beyond its predictive power, XGBoost is highly compatible with post hoc interpretability techniques, such as Shapley Additive Explanations (SHAP), allowing for the quantification of the marginal impact of each input variable on the model’s output.

The XGBoost computation formula is as follows:

$$L\left(\varphi \right)=\sum _{i=1}^{n}l\left({\widehat{y}}_i,y_i\right)+{\sum }_{k=1}^k\mathsf{\Omega }\left(f_k\right)$$

(11)

where $L$ represents the loss function (e.g., mean squared error), ${\widehat{y}}_i$ is the predicted value, $y_i$ is the actual value, and $\mathsf{\Omega }$ is the regularization term, which generalizes the model complexity to prevent overfitting. The prediction of the model is expressed as follows:

$${\widehat{y}}_i=\sum _{k=1}^k{f}_k\left(x_i\right), f_kϵF$$

(12)

where $f_k$ represents a decision tree, and $f$ is the set of all possible trees. $x_i$ denotes the feature vector of the $i$th sample, $k$ is the total number of trees. In this study, the objective function used is the accessibility of ESFs.

The dataset was divided into 80% for training and 20% for testing, with both linear and nonlinear regression models used for performance comparison. The XGBoost model was optimized using hyperparameter tuning, guided by principles of gradient boosting and decision tree regularization [73]. The learning rate was set between 0.1 and 0.3 to balance convergence speed with model generalizability, in line with Friedman’s framework. Tree depth (max_depth) was limited to a range of three to six to prevent overfitting, and the ensemble size was set at 500 based on convergence behavior [74,75]. The final configurations are as follows: n_estimators = 500, learning_rate = 0.2, max_depth =5, random_state = 42.

This study evaluates the model performance using complementary metrics from five-fold cross-validation. The performance results are shown in

Table 2. Optimal parameters and performance of the XGboost model.

N_Estimators	Random_State	RMSE	MAE	R2
500	42	0.0664	0.0499	0.8360

.

$$R^2=1-{\displaystyle \frac{\sum _i{\left(y_i-{\widehat{y}}_i\right)}^2}{\sum _i{\left(y_i-{\overline{y}}_i\right)}^2}}$$

(13)

$$RMSE=\sqrt{\sum _{i=1}^n{\displaystyle \frac{{\left(y_i-{\widehat{y}}_i\right)}^2}{n}}}$$

(14)

$$MAE={\displaystyle \frac{{\sum }_{i=1}^n\left|y_i-{\widehat{y}}_i\right|}{n}}$$

(15)

SHAP (SHapley Additive exPlanations) is a Python (3.7)-based interpretability framework that clarifies machine learning model predictions by decomposing each prediction into feature-specific contributions [76,77]. The SHAP explanation model can be mathematically represented as:

$$g\left(z^{\prime }\right)={\varphi }_0+{\sum }_{j=1}^M{\varphi }_j{z}_j^{\prime }$$

(16)

where $g$ represents the explanation model, $z^{\prime }\in {\left\{\mathrm{0,1}\right\}}^M$ represents the coalition vector, $M$ represents the maximum coalition size, and ${\varphi }_j\in R$ represents the feature attribution for a given feature $j$, indicating its contribution.

3. Results

3.1. Opportunity Equity in Access to ESFs

3.1.1. Disparities in ESF Response Times

A shorter response time is associated with a lower risk of loss of life in emergencies [20,66,78,79,80]. We analyzed and visualized the shortest times required for residents to access various ESFs. The results reveal significant disparities in access times across regions (Figure 5). Areas with higher inequality are typically located in peripheral clusters and remote suburban counties, where harsh topography and weak economic foundations contribute to longer response times. For example, the southwestern part of Yongdeng County and the northeastern part of Gaolan County.

We conducted a statistical analysis of the shortest times required for urban and rural settlements to access ESFs. Statistics indicate that urban residents take an average of 12.88, 10.22, and 11.08 min to reach the nearest EMSFs, FSs, and ESs, while the average time for rural residents is 3.1, 3.3, and 1.9 times longer than in urban areas. Additionally, 84.4% of urban residents reach EMSFs within 15 min, whereas 34.9% of rural residents take over 60 min. 85.7% of urban residents reach an ES within 15 min on foot. 92.1% of urban residents receive firefighting support within the golden hour. In rural areas, 68.2% of residents wait more than 20 min for fire truck arrival.

3.1.2. Differences in Spatial Distribution of Accessibility to ESFs

Accessibility is a key indicator of opportunity equity in access to ESFs for residents. Figure 6 shows significant differences in the accessibility of ESFs across different regions and types in Lanzhou.

The spatial distribution of EMSF accessibility follows a ‘dual-center’ pattern, with values gradually decreasing from the central urban area and the county center of Yongdeng County toward the city’s periphery (Figure 6a). This pattern is attributed to the centripetal distribution of high-level emergency medical resources, which gives these areas with stronger service capabilities. Supply gaps are located in the southwestern part of Yongdeng County, rural areas of Yuzhong County, and the northern part of Gaolan County.

The distribution of FS accessibility is heterogeneous and polycentric (Figure 6b). High accessibility values are distributed in Anning District, the western part of Qilihe District, and Lanzhou New Area. This is because Anning District, within the central urban area, has a lower population density than Chengguan District, adequate firefighting resources, and convenient transportation, ensuring residents’ fire protection needs are met. Inaccessible areas are widespread in rural areas.

Compared to other ESFs, ESs exhibit more dispersed high accessibility values (Figure 6c). High values are distributed in communities nearer to ESs, following a spatial layout similar to that of highways. Low accessibility values are primarily found in extensive, mountainous rural areas, particularly in the southwestern part of Yongdeng County. Notably, some areas still experience relatively poor accessibility in the central urban area, although the total area of ESs is 12.13 hm². This suggests that the high population density increases evacuation demand, offsetting the benefits of proximity and available resources.

The spatial distribution of accessibility of MESFs follows a “high in the center, low at the edges” pattern (Figure 6d). High accessibility values are primarily concentrated in the central urban area, the county center of Yongdeng County, and Lanzhou New Area. Accessibility gradually declines as the distance between residential areas and MESFs increases.

The accessibility of ESFs is divided into five levels by the natural fracture point method, namely, low, higher low, medium, high, higher high. Figure 6e–f compares the proportions of communities and areas with different levels of accessibility to various ESFs. EMSF accessibility is relatively good, with about 45% of residents having effective access. In contrast, FS and ES accessibility are lower, with only 3% and 8% of residents, respectively, living in areas with high accessibility.

3.1.3. Inequity in Access to ESFs at Multiple Scales

(1)

Inequality among communities

To further assess opportunity equity in access to ESFs, we calculated the Gini coefficient and plotted the Lorenz curve. All Lorenz curves show a significant deviation from the line of equality (Figure 7a). The Gini coefficients for the EMSF, ES, FS and MESFs are 0.456, 0.731, 0.748, and 0.529, respectively, all significantly above the internationally recognized warning threshold of 0.4. These findings quantitatively confirm the severe inequality in Lanzhou, where most services are concentrated in a small portion of the population.

(2)

Inequality among central and non-central urban areas

Figure 7b shows that the accessibility of ESFs is inequitable in both central and non-central urban areas (comprising sub-districts or town units), though with significant differences between the two. The Gini coefficients for EMSFs and MESFs exhibit a broader range from non-central to central urban areas. Both two areas show clear inequalities in FS, with only one town in the non-central area having a Gini coefficient below 0.4, and only 11 sub-districts in the central urban area showing relatively equitable accessibility. Notably, the greatest disparity in ES fairness exists between the two areas. In the non-central area, only two towns have a Gini coefficient below 0.4, ranging from 0.287 (comparative equality) to over 0.9 (severe inequality), highlighting the most inequitable spatial distribution of ESs in this region.

(3)

Inequality across districts

The inequity in access to ESFs across Lanzhou’s districts and counties is substantial (Figure 7c). Only Chengguan District has a Gini coefficient for EMSF and MESF below 0.4, indicating relatively better equity. Chengguan District has significantly more emergency resources than other three core districts (Qilihe, Anning, and Xigu), yet its equity is lower. This suggests that the excessively high population density creates immense potential demand for emergency services, making it difficult to allocate limited resources equitably. In contrast, Yongdeng County has a low population density and no significant shortage of emergency resources. Yongdeng County People’s Hospital, designated as a provincial 120 emergency network hospital by the Gansu Provincial Health Department, serves 280,000 county residents and those from nearby areas. However, the equity of ESFs remains low. This is due to Yongdeng County’s vast size and dispersed population, which make it difficult for some areas to access ESFs.

3.2. Outcome Equity in Access to ESFs

3.2.1. Spatial Mismatch Between ESF Accessibility and Population Density

To better understand the outcome equity in access to ESFs, we further analyzed the relationship between population density and accessibility. The high accessibility–low population density (HL) cluster represents a positive spatial mismatch, where supply exceeds demand, while the low accessibility–high population density cluster indicates a negative spatial mismatch, where demand exceeds supply. The ideal scenario is that areas with high population density should have higher accessibility to ESFs and vice versa.

Bivariate local spatial autocorrelation results reveal significant spatial mismatches between the accessibility of different emergency resources and various socio-economic characteristics (Figure 8). Low–high clustering of EMSFs and population density is concentrated in the northwest of the central urban area (Figure 8a). The high–low association between FS accessibility and population density is primarily found in Lanzhou New Area, where several large fire stations are located and resources are sufficient (Figure 8b). Low–high residential areas are located in the central and eastern parts of the urban area, where the population density exceeds 50,000 people per square kilometer, accounting for 13.38% of the total population. Low–high clustering of ES residential areas is found in the central urban area, which accounts for 22.31% of the total population, while high–low clustering is scattered across non-central areas (Figure 8c). The low–high association of MESF accessibility is located in central Chengguan District, with the high–low association resembling that of EMSF (Figure 8d). To improve the accessibility and equity of ESFs, it is crucial to optimize resources in high–low and low–high associated areas.

3.2.2. Inequity in Access to ESFs Among Socioeconomic Groups

To assess equity in access to ESFs among different social groups in Lanzhou, we calculated the share index of ESFs for the elderly (aged 65 and above), children (aged 14 and below), males, females, migrants, and ethnic minorities. The results (

Table 3. The share index of various social groups.

	EMSF	FS	ES	MESF
The elderly	0.968	1.011	0.957	0.968
Children	1.037	1.212	1.072	1.048
Male	1.021	0.742	1.006	1.009
Female	0.982	1.229	0.995	0.992
Migrants	0.901	0.546	0.772	0.870
Ethnic minorities	0.168	0.411	0.573	0.322

) indicate that social equity in access to ESFs differs among these groups.

Generally, vulnerable populations (non-local residents, individuals with lower education, and those with limited self-protection capabilities) in Lanzhou have higher emergency demand and lower accessibility to ESFs compared to advantaged groups. The equity performance index for EMSFs, ESs, and MESFs is close to 1 for the elderly. The share index for EMSFs and ESs is slightly higher for females than for males; however, males have a slight advantage in accessing FS. The share index for migrant groups is below average, comprising approximately 23.29% of Lanzhou’s population, predominantly migrants from less developed regions [81]. Minority groups have significantly less equitable access to ESFs compared to the Han population, highlighting a substantial gap between these groups and the average social equity standards. Notably, children have better access to ESFs than the societal average, contradicting the common assumption that children are a vulnerable group in both research and real-world settings. Overall, the accessibility of ESFs for different groups in Lanzhou requires significant improvement.

We further use the locational entropy formula to analyze the spatial distribution of social equity in access to ESFs for different social groups. Figure 9 illustrates the differences in locational entropy across social groups accessing ESFs. Regions exhibit varying levels of locational entropy, influenced by specific factors contributing to extremely high or low values.

Figure 9a–d shows that the spatial distribution of the entropy location of elderly, children, male and female is generally similar to the spatial distribution of their accessibility. In contrast to accessibility patterns, some areas in the central urban zone show poor social equity. For example, residents of Chengguan District experience significantly lower fairness in accessing FS and ES compared to the general population. Although the share index for the four groups is slightly above or below 1, urban groups consistently experience more equitable access to ESFs than rural groups.

3.3. Analysis of Factors Influencing Equity in Access to ESFs

3.3.1. Correlation Analysis

In recent years, accessibility has become a key indicator in studies of spatial equity [82]. Accessibility is a multidimensional concept [83], influenced by both spatial and non-spatial factors [84]. To identify the factors affecting accessibility, this study selected 17 potential indicators based on a literature review that may influence the accessibility of MESFs. A multicollinearity diagnostic was conducted on the selected indicators, and those with a variance inflation factor (VIF) greater than 10 were removed to ensure parameter stability in the machine learning model [85]. Given the limitations of VIF in detecting nonlinear relationships, Spearman’s rank correlation was employed to examine potential nonlinear dependencies. After optimization, variables with a VIF below 10 and a Spearman correlation coefficient below 0.8 were retained (Figure 10).

3.3.2. Global Feature Importance

In the SHAP summary plot, variables are ordered based on their mean absolute SHAP values, thereby positioning the most influential predictors at the top (Figure 11). As illustrated in Figure 11, average elevation emerges as a dominant predictor of equity in access to MESFs. In addition to elevation, other salient explanatory variables—such as the response times of EMSFs and FSs, the proportions of migrant and child populations, and the level of transportation accessibility—jointly contribute to inequities in access to MESFs.

3.3.3. Spatial Heterogeneity of Key Influencing Factors

This study further analyzes the spatial variations in the impact of different factors on spatial equity in access to MESFs across various regions of Lanzhou. The SHAP values for average elevation, the proportion of migrant populations, the proportion of children, and road density are visualized. Figure 12a illustrates the effect of average elevation on accessibility to MESFs, revealing a significantly positive influence in the central urban area and county centers of Yongdeng County, whereas higher elevations in the expansive rural areas exert a severe negative impact. Figure 12b highlights the negative impact of a higher proportion of migrant populations on accessibility to MESFs in the northern part of Xigu District and suburban areas, primarily due to the concentration of industrial hubs that attract migrant workers. With limited emergency response capabilities, the migrant population is more dependent on the city’s MESFs. Figure 12c shows that a higher proportion of children negatively affects access to MESFs in the southwestern part of Yongdeng County, the northern part of Yuzhong County, and the northern part of Gaolan County. Figure 12d illustrates the influence of road density on accessibility to MESFs, with suburban areas and Gaolan County demonstrating a greater reliance on road density for access to these services.

4. Discussion

4.1. Spatial Heterogeneity and Underlying Mechanisms of Equity in Access to ESFs

This study investigates the spatial equity of ESF accessibility in Lanzhou. The findings reveal significant inequities in access to ESFs, particularly in rural areas. Furthermore, this issue is not only prevalent in other Chinese cities but also aligns with a common issue faced by many developing countries and regions with complex terrain [24,47,65,86,87].

The inequitable access to ESFs in rural areas in Lanzhou is shaped by both natural terrain and policy constraints. The city’s distinct “linear-concentration and peripheral-dispersion” spatial structure, molded by its river–valley topography, intensifies gradients in facility accessibility compared to more isotropic or polycentric cities like Chongqing. Similar challenges are observed in geographically comparable settings such as the Swiss Alps [88] and Norwegian settlements [89].

In terms of policy, the Chinese government employs strong planning instruments—such as territorial spatial planning and major project placement—to allocate high-quality emergency resources as strategic investments. These resources are prioritized in political–economic core areas, including central urban districts, and in strategically designated zones that function as growth engines, such as the Lanzhou New Area and the Yuzhong Ecological Innovation City. Consequently, the delivery of public services tends to follow a pattern of geographically discontinuous provision rather than a gradual, demand-aligned diffusion. Together, topographical and policy factors amplify the layered marginalization of bypassed transitional and rural areas. This development mechanism differs notably from the historically formed polycentric inequalities observed in many Western cities, which emerged gradually through market dynamics and segregationist policies [90,91]. It also contrasts with the marginalization of informal settlements in Latin American cities, a condition often resulting from governance insufficiencies [92].

Notably, the average walking time for rural residents to reach the nearest ES (21.05 min) is considerably shorter than the driving time to other ESFs (EMSF: 39.93 min, FS: 33.73 min). This is because some village committees have established small ESs, expanding their service coverage and enabling more villagers to evacuate quickly. Compared to urban areas, villages are more dispersed, making decentralized small ESs more effective in emergencies. Therefore, we conclude that significant differences in resource access and spatial structure between urban and rural areas result in distinct configurations of emergency services. Previous studies have reached similar conclusions [66].

The equitable distribution of ESFs involves a complex interplay among their spatial allocation, road network accessibility, and shifting population patterns. An analysis of the spatial heterogeneity in key influencing factors shows that in densely populated areas, the quantity and scale of facilities primarily determine service equity. In sparsely populated regions, however, a centralized facility layout often exacerbates rather than reduces inequities—a finding consistent with existing research [93,94]. In summary, the persistent and widespread disparities in ESF accessibility must be analyzed through a multi-scale perspective to guide urban governance toward more refined, evidence-informed policy interventions.

4.2. Inequitable Access to ESFs Across Socioeconomic Groups

This study also analyzed the equity in access to ESFs for different social groups. The results indicate that migrant populations and ethnic minorities face disadvantages in accessing ESFs, consistent with previous research findings [95,96]. In contrast to previous research findings, vulnerable groups such as the elderly, children, and women do not have significant disadvantages in terms of equitable access to ESFs [97]. This may be because the majority of residents in each group live in the central urban area, where they can access a large amount of emergency resources, improving overall equity.

This is primarily because the majority of elderly residents and children in Lanzhou are concentrated in the densely built-up central urban districts, where they have access to relatively abundant emergency resources—thus offsetting their individual vulnerability at the aggregate level. This reveals a core contradiction in the equity of facility accessibility: in densely populated urban cores, accessibility is largely determined by the quantity, scale and density of facilities, whereas in sparsely populated rural areas, the efficiency of spatial coverage and transportation connectivity emerge as decisive factors [93,94]. The locational advantage enjoyed by populations in central urban areas masks the vulnerability of specific groups, an advantage entirely absent in rural contexts.

However, the location entropy map (Figure 9) reveals that, rural residents face a significant disadvantage in accessing ESFs compared with urban areas [98]. Villages suffer from severe labor force loss, leaving a larger proportion of elderly and women–children groups behind. These vulnerable groups lack disaster response capabilities, leading to heavy reliance on external rescue forces for disaster prevention and mitigation in rural areas. Therefore, targeted and differentiated interventions must be adopted in the future planning of urban and rural EFSs. In urban areas, attention should be paid to vulnerable groups that may gather in facility “blind spots”. In rural areas, it is imperative to address the compound challenges arising from the interplay of regional service gaps and demographic structural vulnerability, and to prioritize enhancing equity in access to emergency resources for these populations.

In general, differences in social vulnerability due to disaster risks and the uneven distribution of ESFs are significant causes of exacerbated inequality. Vulnerable groups are more likely to be affected by the risks of emergency events, and the impact of such events further exacerbates internal societal inequalities. This will create a self-perpetuating cycle, making social inequality more complex and impossible to ignore. Focusing on equity in access to ESFs for vulnerable groups is a crucial measure to improve the resilience of urban communities. Therefore, in planning and constructing ESFs, it is essential to consider factors such as population density, demographic composition, facility scale, topography, and economic conditions to meet the emergency needs of residents in different communities [99,100]. The new challenges arising from cities with significant population density differences can provide insights into optimizing the spatial structure of ESFs in both urban and rural areas.

4.3. Establishing a Zonal Management Plan for ESFs in Lanzhou

To optimize the distribution of ESFs and promote equitable access, we propose the following recommendations based on the current state of equity in access to ESFs in Lanzhou, considering existing challenges, topographical features, and zoning variations (Figure 13).

(1)

High-density urban areas in valleys

The core strategy for this area focuses on optimizing the operational efficiency of existing resources through refined governance. (1) For EMSF: Establish emergency sub-stations at regional high-level medical institutions, and set up emergency centers (or stations) in public secondary-level hospitals or higher to expand the reach of emergency services. In communities with higher demand potential, emergency outpatient services can also be established at primary hospitals to improve the coverage of emergency services. (2) FS: A comprehensive analysis of urban structure, historical fire incidents, and the distribution of major hazardous facilities should be conducted to assess fire risks within the city. Based on this analysis, consideration should be given to establishing small-scale fire stations in high-density population areas, thereby enhancing the firefighting and rescue system in conjunction with existing facilities. (3) ES: The establishment of additional ESs should be prioritized, utilizing existing public spaces such as parks, squares, schools, and large sports venues for their repurposing and conversion. Simultaneously, the operational efficiency and functional resilience of dual-purpose facilities must be enhanced to ensure their effectiveness in both routine and emergency scenarios.

(2)

Policy-driven growth poles

The core advantage of the new urban areas lies in their high-level planning and ample spatial resources. Future ESF planning should prioritize regional coordination and adaptive configurations. Designate the new growth poles as regional emergency hubs, and establish efficient emergency routes connecting the central urban area and surrounding rural regions. Adopt a dual-purpose model by repurposing spaces such as sports facilities, parks, and school auditoriums to accommodate both regular functions and emergency shelter requirements, thereby optimizing resource efficiency.

(3)

Transition zones between the north and south mountain terraces

The fundamental issue in this area lies in its limited connectivity to the central urban area and the high vulnerability of its transportation. (1) Redundancy in transportation infrastructure. It is crucial to plan and construct backup emergency access routes that connect the area to the central urban zone, ensuring the availability of alternative routes in the event of disruptions to primary infrastructure. (2) Establishment of small-scale integrated emergency service stations at key nodes on the plateau. Site selection should follow the principles of “centrality, accessibility, and safety,” with priority given to locations at population centers, intersections of multiple internal roads, and areas characterized by stable and open geological conditions.

(4)

Urban–rural interface zones in the mid-low mountainous and remote highland rural regions

The fundamental challenge in these areas stems from the inherent tension between service costs and demand. Spatial strategies should shift away from the pursuit of “universal coverage” and, instead, implement a more adaptable and context-sensitive approach. (1) Plan the layout of ESFs based on rural natural conditions and population distribution. Lanzhou has complex geological conditions and limited land resources, with rural settlements scattered and independent in pattern. In this pattern, when planning EMSF and FS, clusters divided by terrain should be considered as the basic spatial units. Position high-level EMSF and FS at the centers of clusters, surrounded by grassroots emergency resources to improve service quality. Additionally, strengthen the interaction between rural and urban medical systems to facilitate the sharing of high-quality medical resources. To quickly enhance the emergency shelter capacity of villages, small shelters can be established in neighborhood committees to increase coverage. Simultaneously, consider reinforcing foundations and buildings, and stocking disaster-resistant supplies. (2) Improve the accessibility of rural transportation networks. Limited access to emergency service facilities in rural areas is not only due to a shortage of facilities but also due to inaccessible roads.

(5)

Disaster prevention and mitigation facilities for vulnerable groups

Analyze the distribution of vulnerable populations and urban development trends, assessing and forecasting their needs. Considering the diverse emergency needs of vulnerable populations across different age groups, integrate the designation of safe living zones and comprehensively plan ESFs along with supporting infrastructure. Critical ESFs should be located near urban public services, such as elderly care institutions and kindergartens. Enhance the efficiency of resident evacuation and medical treatment through coordinated strategies, while strengthening the emergency service capacity of these facilities.

Lanzhou, as a typical example of an underdeveloped region, faces both the geographic challenges inherent in mountainous cities and significant urban–rural disparities. Its approach to the planning of ESFs provides valuable insights for the layout of emergency infrastructure in mountainous cities and rural areas, both within China and internationally. Through the assessment and categorization of equity in access to ESFs across urban and rural communities, the government can formulate more targeted and evidence-based strategies for ESF planning, grounded in scientific spatial strategies, systematic construction plans, and effective management measures.

4.4. Advantages and Limitations

First, this study constructs a comprehensive assessment framework for evaluating the equity in access to ESF, overcoming the limitations of earlier single-dimensional approaches. This framework systematically integrates facilities, population, and road networks to assess distributional equity from both opportunity and outcome perspectives, offering a more holistic and multidimensional analytical lens for research in this field. Second, the analysis is conducted at the community scale, which not only achieves high-resolution spatial visualization of accessibility and equity but also supplies precise spatial references for grassroots disaster prevention and mitigation. This approach supports the enhancement of community disaster resilience. Third, the study employs the XGBoost along with SHAP interpretability analysis to perform attribution analysis on the factors influencing equity in access to ESFs. This methodology effectively quantifies the marginal contribution of individual variables, thereby strengthening the reliability of the findings and providing deeper mechanistic insight.

This study has several limitations that should be addressed in future research. First, this study does not simulate real disaster scenarios, leading to a discrepancy between calculated accessibility of ESFs and actual emergency demands. Second, this study relies on static population data and assumes the spatial location of neighborhood committees as demand points, simplifying accessibility calculations. When data becomes available, analyzing dynamic population distribution will enable a more precise identification of emergency demand locations and scales, thus improving the accuracy of the accessibility evaluation of ESFs. Third, this study employs the equity in access to ESFs across socioeconomic groups as a proxy for the abstract concept of outcome equity. This approach allows for quantitative analysis and incorporates group distinctions based on gender, age, income, household registration, and religion. However, it simplifies the transition from access opportunity to actual service outcomes and does not explore how such differences mediate this transition. Future research should integrate multi-source data and mixed methods to more accurately assess the fairness of ESFs attainment across different groups.

5. Conclusions

Evaluating equity in access to ESFs is essential for developing resilient cities. This study introduces a comprehensive framework for evaluating equity in access to ESFs. The aim is to improve the city’s emergency service capacity by ensuring equitable access to ESFs. This study, from the perspectives of resource–opportunity–outcome equity, selects communities as the research scale, to analyze the spatial and social equity of access to ESFs of Lanzhou, a less-developed city in Northwest China. The conclusions are as follows:

Regarding opportunity equity, ESFs exhibit a clustered and sparse distribution, with a significant urban–rural imbalance. Low accessibility values are concentrated in southwestern Yongdeng County, northeastern Gaolan County, urban fringe areas, densely populated Chengguan District, and sparsely populated rural regions. Moreover, inequality in access to ESFs is greater in rural areas than in urban areas, with significant internal disparities in both accessibility and fairness in rural regions. At the district level, fairness in ESFs is primarily influenced by the quantity and scale of ESFs in densely populated areas. In areas with dispersed populations, the centralized distribution of ESFs exacerbates inequities. This study also examines the disparities in equitable access to ESFs among different social groups. The findings indicate that marginalized groups, such as migrants and ethnic minorities, experience significant inequities in ESF access. The attribution analysis of MESF accessibility reveals that steep topography is a decisive spatial factor limiting access, while a high proportion of migrant populations and children are key non-spatial determinants. This highlights the necessity of ongoing urban and rural disaster prevention planning, prioritizing vulnerable populations and progressively expanding service coverage. This study provides decision-makers with insights to optimize the spatial distribution of ESFs and enhance equitable access. These improvements will bolster urban emergency management and enhance disaster resilience.