Accessibility Analysis of Multi-Type Public Service Facility in Beijing Based on the MRGS2SFCA Model

TIAN Haozheng¹  JIANG Xiaohan²  ZHANG Ning^3,4*  Abudoula Alimujiang⁵  WANG Shaohua¹

1. State Key Laboratory of Remote Sensing and Digital Earth, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100101, China; 2. Faculty of Architecture and Urban Planning, Lanzhou Jiaotong University, Lanzhou 730070, China; 3. China Academy of Urban Planning & Design, Beijing 100044, China; 4. Remote Sensing Application Center, Ministry of Housing and Urban-Rural Development of P. R. China, Beijing 100835, China; 5. Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China

Abstract: The spatial equity of public service facility allocation is directly related to urban operational efficiency, residents’ quality of life, and the fairness of public service provision. To address the limitations of existing studies, which mainly focus on single facility type, lack a unified parameter framework, and have difficulty capturing differentiated service processes among multiple facility types, this study takes the built-up area of Beijing as the study area and selects 6 categories of public service facilities—medical care, education, transportation, commercial shopping, leisure and entertainment, and life services—as the research objects. By integrating multi-source spatial data, including road networks, population distribution, built-up areas, and points of interest, a Multi-Radius Gaussian Two-Step Floating Catchment Area (MRGS2SFCA) model was constructed to systematically analyze the coverage pattern and accessibility characteristics of public service facilities. First, a unified parameter system was developed based on POI semantic cleaning and hierarchical mapping, transforming differences in service radius, distance decay, and supply capacity among facility types into comparable model parameters. Then, the accessibility levels of the six facility types were measured on unified demand spatial units, and their spatial distribution patterns and structural differences were comprehensively compared. The results show that public service facilities in Beijing exhibit a significant “core concentration-peripheral decline” pattern overall. Areas with high coverage and high accessibility are mainly concentrated in the core urban districts, including Dongcheng, Xicheng, central Chaoyang, and southern Haidian, whereas peripheral areas such as Shunyi, Tongzhou, Daxing, Fangshan, Yanqing, and Mentougou experience varying degrees of service insufficiency. Although all six facility types follow the overall gradient structure, their spatial organization patterns differ significantly: medical and educational facilities exhibit strong hierarchical and core-concentrated characteristics; Transportation facilities show strong network continuity; Commercial shopping facilities display a multi-centered nodal expansion pattern; Leisure and entertainment facilities are relatively dispersed; and life service facilities are characterized by high density, wide coverage, and strong grassroots-level balance. The results further indicate that the MRGS2SFCA model can effectively overcome the limitations of the traditional Two-Step Floating Catchment Area (2SFCA) method under fixed thresholds and uniform service radii in representing multiple facility types, enabling comparable expressions of different facilities within a unified analytical framework. This study provides methodological support and empirical evidence for optimizing public service facility allocation, promoting 15-minute living circle construction, and advancing refined urban governance in Beijing.

Keywords: public service facilities; POI; accessibility; MRGS2SFCA model

DOI: https://doi.org/10.3974/geodp.2026.05.04

1 Introduction

Public service facilities, as fundamental elements supporting urban development, play a critical role in sustaining urban operations, enhancing residents’ well-being, and promoting social equity. These facilities cover multiple sectors, including education, medical care, transportation, commercial shopping, life services, and leisure and entertainment, directly serve residents’ daily needs^[1]. Achieving the spatially balanced allocation of public service facilities and the coordination between supply and demand is an important pathway toward improving urban livability and promoting sustainable development^[2]. At the global level, this goal is highly consistent with the United Nations Sustainable Development Goals, particularly SDG 11 on sustainable cities and communities^[3]; at the national level, it also responds to China’s new urbanization strategy, which emphasizes equalization and inclusiveness in public service provision^[4,5].

Against the backdrop of rapid urbanization, public service demand in Beijing has become increasingly diverse and dynamic, while the spatial imbalance of facility supply has become more pronounced^[6,7]. As a typical megacity, Beijing is characterized by a large spatial extent, complex functional zoning, and a marked core-periphery structure. Significant differences exist across areas in terms of population density, employment activities, transport conditions, and service demand, making the mismatch between facility supply and demand even more prominent. Reliance solely on facility counts or per capita indicators is no longer sufficient to accurately identify real differences in service access within the city.

In recent years, spatio-temporal big-data-based spatial heterogeneity analysis, statistical modeling, and indicator system construction have gradually become important technical approaches for monitoring public service facility coverage and supply-demand relations. Related studies have mainly focused on 3 aspects: first, methods for characterizing spatial heterogeneity, such as service evaluation from the perspective of living circles and demand density analysis based on mobile data^[6,7]; second, the application of intelligent algorithms in facility optimization, such as commercial solvers, heuristic algorithms, deep reinforcement learning, and graph convolutional networks^[6,8–10]; and third, the integration of GIS and spatial statistical methods to quantify public service inequalities^[8,9]. Meanwhile, POI data can be used to finely depict the spatial distribution of facilities, population data can reflect potential demand, and road network data provide the basis for accessibility analysis. The integration of multi-source data has thus become an important approach for studying urban public service supply-demand relations^[11–13].

Nevertheless, existing studies still face 2 key limitations in the analysis of multi-type public service facilities. First, different facility types are usually measured separately, lacking a unified parameter framework. As a result, although the findings can describe the distribution of individual services, they are difficult to compare horizontally on the same scale, thereby weakening the explanatory power regarding the overall urban service structure. Second, although the traditional Two-Step Floating Catchment Area (2SFCA) method has been widely used because it balances supply-demand considerations with computational feasibility, it relies on a fixed service radius and a binary distance threshold, that is, locations within the service range are regarded as fully accessible, whereas those outside are regarded as inaccessible. This “covered versus uncovered” treatment ignores the objective fact that service effects decay continuously with distance, and it tends to produce a large number of zero or near-zero values in peripheral and low-density areas, thereby underestimating the actual service level in outer areas^[14,15].

This limitation is particularly evident in the context of Beijing. The city exhibits a pronounced core-periphery structure, with dense facilities and highly concentrated population activities in the central urban area, whereas peripheral areas are relatively sparsely served and characterized by longer commuting distances. If fixed thresholds and uniform service ranges are still adopted, the advantages of the central area may be overstated, while the possibility for peripheral areas to obtain services from secondary facilities may be underestimated^[16]. This problem becomes even more acute when the research object is extended to 6 types of facilities, namely education, medical care, transportation, commercial shopping, life services, and leisure and entertainment. These facility types differ significantly in service coverage scale, supply capacity, frequency of use, and spatial attractiveness. If a uniform radius or a uniform decay mechanism is applied, it is difficult not only to reflect hierarchical differences among facilities but also to accurately characterize the composite structure of urban public services^[17–20].

In this context, the Multi-Radius Gaussian Two-Step Floating Catchment Area (MRGS2- SFCA) model provides a more interpretable methodological pathway for analyzing public service accessibility in complex urban settings. Compared with the traditional 2SFCA, MRGS2SFCA introduces a Gaussian distance-decay function, multi-level service radii, and differentiated facility weights, thereby structurally improving the conventional model. It transforms accessibility from a binary judgment of “covered or not” into a weighted process that changes continuously with distance, effectively alleviating the truncation effect caused by fixed thresholds. At the same time, it captures the spatial influence of facilities at different levels through multi-scale service ranges and reflects differences in service capacity through hierarchical weights, thus providing a more realistic description of the spatial interaction between service supply and demand within the city. Overall, MRGS2SFCA offers a more suitable methodological foundation for analyzing the supply and demand of multi-type public service facilities in Beijing and provides a new analytical framework for revealing spatial heterogeneity and supply-demand mismatches.

2 Methods

2.1 Research Design and Overall Framework

This study takes the built-up areas of Beijing’s 16 districts as the research scope and develops an analytical framework integrating multi-source data and multiple methods to characterize the spatial relationships between public service supply and demand (Figure 1). First, population data, road network data, building footprint data, and POI data for six categories of public service facilities are integrated, and all datasets are uniformly clipped and preprocessed according to Beijing’s administrative boundary and built-up area extent. On this basis, the built-up area is subdivided into block units using the road network, and blocks with a population greater than 100 are selected as the research units to ensure that the analytical units can realistically reflect residents’ activity spaces and service demand. Second, the POI data are semantically cleaned and reclassified into 6 categories of facilities: transportation, medical care, education, commercial shopping, services, and leisure and entertainment. A hierarchical parameter system is then constructed by incorporating differences in service range, service targets, and supply capacity among facilities. Subsequently, in the spatial analysis stage, built-up area analysis, kernel density analysis, and the MRGS2SFCA model are jointly applied to examine public service facilities in

Figure 1  Research framework

Beijing. Specifically, built-up area analysis is used to define the effective study space, kernel density analysis is used to reveal the spatial agglomeration patterns of the six facility types, and the MRGS2SFCA model is used to measure accessibility and supply-demand matching relationships for different facilities under a unified spatial scale. Finally, the results are comprehensively analyzed and evaluated from 3 aspects: the distribution characteristics of the six categories of public service facilities, their accessibility patterns, and the applicability of the MRGS2SFCA model in the study of multiple facility types in Beijing, thereby providing methodological support for the optimization and refined governance of public service facility allocation in Beijing.

2.2 Data Collection and Preprocessing

2.2.1 Urban Boundary and Built-up Area Extraction

The basic datasets used in this study include administrative boundary data, population data, road network data, and multi-source remote sensing imagery. The vector data for Beijing’s administrative boundary were obtained from the National Platform for Common Geospatial Information Services[1] (accessed on 2 February 2026), and were used to define the study area and clip the relevant spatial datasets. The built-up area boundary data of Beijing were provided by the Remote Sensing Application Center of the Ministry of Housing and Urban-Rural Development and were derived for the 2025 Urban Physical Examination Program. These data were used to delineate the effective urban built-up area for this study.

To ensure spatial consistency among different datasets, the administrative boundary, built-up area boundary, population, road network, and POI data were transformed into a unified coordinate system and spatially matched. All datasets were projected into the CGCS2000 3 Degree GK CM 117E coordinate system. On this basis, the road network was overlaid with the built-up area and subdivided by roads to form urban “block” units. Population data were then linked to the block attribute table, and blocks with a population greater than 100 were selected as the final research units^[21].

2.2.2 Road Network

The road network data used in this study were obtained from OpenStreetMap[2] (accessed on 2 April 2026). First, vector road network data for Beijing were acquired from the platform and clipped according to the administrative boundary of Beijing to extract road information within the study area. Subsequently, road features were organized based on road attribute fields, and dual-line roads were merged into single-line representations to improve the consistency of the network structure.

During preprocessing, topological rules for the road network were established, and topology checking and repair were conducted to eliminate isolated road segments, dangling nodes, and broken connections, thereby ensuring network connectivity and the reliability of subsequent analyses.

2.2.3 Population Data

Population data were obtained from WorldPop[3](accessed on 2 April 2026) using the UN-adjusted “Unconstrained” product with a spatial resolution of 100 m×100 m. The data were first projected into the CGCS2000 3 Degree GK CM 117E coordinate system and then clipped according to the administrative boundary of Beijing to ensure consistency with the spatial extent of the study area.

Subsequently, the population raster data were mapped onto block units through spatial overlay, enabling consistent representation between population data and spatial analysis units.

2.2.4 POI Data

The public service facility data used in this study were obtained from the Amap Open Platform[4] (accessed on 2 April 2026). POI data within Beijing were acquired through the API interface, and coordinate transformation and format standardization were carried out so that all data were unified under the CGCS2000 3 Degree GK CM 117E coordinate system.

During preprocessing, POI data were classified and organized using a combination of keyword search and spatial filtering. Facility types closely related to residents’ daily life were selected, including education, medical care, transportation, commercial shopping, life services, and leisure and entertainment. The POI data were then cleaned, deduplicated, and spatially corrected in ArcGIS Pro to ensure data quality.

Table 1  POI types, subtypes, codes, and maximum travel times within the living circle

2.3 Data Structure and Variable Settings

On the demand side, gridded population data were used to represent spatial demand intensity. Each demand unit is characterized by the population size , whose value is derived from the field grid code. This variable directly participates in the calculation of the supply- demand ratio and is used to reflect differences in demand size among spatial units.

On the supply side, 6 categories of facilities were used. After semantic cleaning and classification, all facilities were converted into a structurally unified data format. Each facility unit contains 3 core parameters: service radius (Radius_D), distance decay parameter (), and supply capacity (Supply_C). Radius_D is used to define the service influence range,  is used to characterize the decay of service influence with distance, and Supply_C is used to reflect the relative service capacity of the facility. These parameters were assigned based on the POI category classification so as to ensure a consistent logical basis for representing different facilities in the model^[22].

2.4 Hierarchical Classification and Construction of the Parameter System

To avoid the subjectivity that may arise from assigning parameters directly according to facility categories, this study introduced a hierarchical classification scheme to uniformly represent different facility types. The hierarchy was defined according to service coverage scale and service target range, and facilities were divided into 5 levels (L1–L5). Facilities capable of providing cross-regional services with broader coverage were assigned to higher levels, whereas facilities limited to local areas and mainly serving daily needs were assigned to lower levels. This classification transforms different facility types into comparable analytical units under a unified scale and thereby provides the basis for parameter setting.

Within the hierarchical system, service radius, distance decay parameter, and supply capacity are consistently associated with facility level: service radius increases with hierarchy level to reflect the broader service range of higher-level facilities; the distance decay parameter is kept on the same scale as service radius so that service influence decreases continuously in space; and supply capacity increases with hierarchy level to represent differences in service provision among facilities. The coordinated setting of these three types of parameters enables the model to simultaneously express service range, service strength, and spatial decay mechanisms^[23].

2.5 Distance Measurement and Spatial Consistency Processing

To ensure consistency between spatial distance calculation and model parameter settings, all spatial data were projected into the same metric coordinate system before computation so that service radius (Radius_D) and distance decay parameter () would share the same unit of measurement. On this basis, Euclidean distance was used to represent the spatial relationship between demand points and facility points:

                                                                                       (1)

where denotes the spatial distance between demand point and facility point , and and are the planar coordinates of the corresponding points.

Euclidean distance was adopted mainly because it can directly reflect the spatial relationship between facilities and population under a unified spatial reference, while maintaining a balance between computational efficiency and stability. This makes it suitable for large-scale accessibility analysis involving multiple facility types. Moreover, with the introduction of the Gaussian decay function, the effect of distance on service influence is represented continuously, allowing Euclidean distance to satisfy the model’s need to characterize spatial gradient variation^[24].

2.6 MRGS2SFCA Model Implementation and Multi-Type Coupling

Based on the previously established data structures and hierarchical parameter framework, this study applies the MRGS2SFCA to quantify the accessibility of public service facilities. On the demand side, population grids are used to represent spatial demand intensity, with each demand cell characterized by its population size (), indicating potential service requirements. On the supply side, 6 categories of public service facilities are considered, with each facility unit defined by 3 core parameters: service radius (), distance decay parameter (), and supply capacity (). To ensure comparability across facility types, all facilities are mapped into a unified hierarchical system based on their service coverage and level, inheriting corresponding parameter values.

The model calculates accessibility in two steps. First, the supply-to-demand ratio for each facility is calculated as:

                                                                                    (2)

where is the supply-to-demand ratio of facility ; represents its supply capacity;  is the population of demand cell within the facility’s service radius; is the Euclidean distance between the demand cell and the facility; is the service radius; and is the distance decay parameter. This step aggregates population demand within the service radius, weighted by distance, to quantify the service pressure experienced by each facility.

Second, the accessibility for each demand point is computed as:

                                                                                      (3)

where  denotes the accessibility level of demand point , reflecting the level of service obtained after considering both facility supply capacity and spatial distance. The Gaussian distance decay function ensures that facility influence decreases continuously with distance, preventing abrupt changes that can occur when using fixed-threshold approaches.

This procedure is applied separately to each of the six facility categories—medical care, education, transportation, commercial shopping, leisure and entertainment, and life services—and the results are projected onto the same demand grid. Because all categories share a consistent hier­archical parameter system and computational framework, the resulting accessibility measures are directly comparable. This allows the analysis to reveal spatial distribution characteristics and supply disparities among different public service systems, providing a robust foundation for subsequent evaluations of service equity and spatial optimization strategies.

3 Data Results and Analysis

3.1 Spatial Distribution of Facility Coverage in Beijing

This study takes the built-up area of Beijing as the study area (Figure 2). As the capital of China and a typical megacity, Beijing has a large population and a high level of economic

Figure 2  Map of the administrative boundary and built-up area of Beijing

development, and is one of the most urbanized and functionally complex cities in China. Over the long course of urban expansion, Beijing has formed a spatial structure centered on the urban core and extending progressively outward to peripheral areas. Significant differences can be observed among different areas in terms of population distribution, land use, and the allocation of public service facilities.

The built-up area of Beijing is the area where population activities and public service demand are most concentrated, and it is also the spatial unit with the densest distribution of various public service facilities. With the continuous advancement of urbanization, public service demand in Beijing has become increasingly diverse and dynamic, while the spatial imbalance in facility supply remains prominent, as reflected in the high concentration of service resources in the central urban area and the relative undersupply in peripheral areas.

From the perspective of spatial structure, Beijing exhibits clear functional zoning characteristics, including core functional zones represented by Dongcheng District and Xicheng District, high-density development zones represented by Chaoyang District and Haidian District, and rapidly developing areas such as Changping and Shunyi. Significant differences in economic development level, population density, and transport accessibility across these areas give rise to complex spatial heterogeneity in the supply-demand relationships of public service facilities.

Therefore, selecting the built-up area of Beijing as the study area makes it possible to reveal the intrinsic mechanisms of public service supply-demand relationships and spatial heterogeneity within the context of a typical megacity, thus providing a representative basis for subsequent multi-source spatial analysis and facility optimization.

Figure 3 presents the spatial distribution of comprehensive public service facility coverage scores at the block scale in Beijing. As shown in the figure, the spatial distributionof different coverage score levels (1–7) is highly consistent with Beijing’s urban structure and exhibits a pronounced pattern of “core concentration-peripheral decline”. High-value areas (levels 6–7) are mainly concentrated in the urban core, including Dongcheng District, Xicheng District, central Chaoyang District, and southern Haidian District, where population density is high, functions are highly concentrated, and the coverage level of public service facilities is relatively high.

As one moves outward from the urban core to peripheral areas, coverage scores gradually decline. In suburban areas such as Fengtai District, Shijingshan District, and southern Changping District, most blocks fall into medium levels (3–5). In outer suburban areas such as Shunyi District, Tongzhou District, Daxing District, and Fangshan District, coverage scores decline further, with most blocks belonging to lower levels (1–3). In addition, mountainous areas such as Yanqing District and Mentougou District generally exhibit

Figure 3  Map of the comprehensive coverage score of public service facilities in Beijing (2026)

clusters of low values and relatively low levels of public service facility coverage.

Overall, the coverage of public service facilities in Beijing shows a clear spatial gradient structure, with high-value areas concentrated in the urban core and low-value areas distributed in the urban periphery and ecological zones. This reflects the significant spatial coupling between facility allocation, population distribution, and urban functional structure.

Figure 4 shows the kernel density distribution characteristics of six types of public service facilities in Beijing. Overall, all facility types display a pronounced “core concentration- peripheral decline” pattern, although there are clear differences in the intensity of agglomeration and the extent of spatial diffusion.

Figure 4  Maps of the kernel density distribution of the six types of POIs in Beijing (2026)

For educational facilities, high-density areas are mainly concentrated in the central urban area, particularly forming obvious clusters in Dongcheng District, Xicheng District, and southern Haidian District, and then decline rapidly toward the periphery, indicating that high-quality educational resources are strongly attached to the urban core. Leisure and entertainment facilities have a relatively broader distribution range. While high-value areas are formed in the central urban area, scattered secondary hotspots also appear in some suburban areas, reflecting a certain degree of spatial diffusion in their service targets.

Medical facilities exhibit an overall distribution pattern of “multiple cores + central strengthening”. In addition to high-density agglomeration in the urban core, local high-value points are also found in areas such as Tongzhou and Changping, indicating a certain degree of balanced spatial distribution of medical resources, although the urban core still remains dominant overall. Commercial facilities have the highest kernel density and the largest agglomeration range, forming a significant high-value core in the central urban area and extending outward along major urban development axes, reflecting the strong dependence of commercial activities on population and transportation.

Life service facilities (life services) show a distribution pattern similar to that of commercial facilities, but with slightly lower agglomeration intensity, presenting a spatial pattern centered on the urban core and gradually diffusing toward suburban areas. Transportation facilities, by contrast, exhibit a strong networked distribution pattern. While high-density nodes are formed in the central urban area, they also extend outward along major transport corridors, showing strong spatial continuity and reflecting the supporting role of transport infrastructure in shaping urban spatial structure.

Overall, the six types of public service facility POIs in Beijing all exhibit obvious agglomeration characteristics in space, but differ in terms of agglomeration intensity, diffusion range, and spatial balance. Commercial and life services facilities show the most significant agglomeration, followed by educational and medical facilities, while leisure and entertainment and transportation facilities exhibit relatively stronger spatial extensibility. These differences reflect variations in the functional attributes, service targets, and location-selection mechanisms of different types of public service facilities, and also reveal the spatial heterogeneity in the allocation of public service facilities in Beijing.

On this basis, each type of POI was mapped to a corresponding hierarchical level according to its semantic category and inherited the associated parameters, thereby completing the transformation process of “semantic classification-hierarchical mapping-parameter assign­ment”. The unified hierarchical parameter system is shown in Table 2 and Figure 5.

Table 2  Hierarchical parameter mapping scheme of the public service facility in Beijing (2026)

Figure 5  Schematic diagram of the mechanism of hierarchical parameter action

Through this hierarchical system, Figure 5 shows that differences in service capacity and spatial range among different facility types are transformed into a unified parameter expression, thereby improving the consistency and interpretability of the model.

3.2 Spatial Distribution of Accessibility for Six Types of Public Service Facilities

Based on the results calculated using the MRGS2SFCA model, the six types of public service facilities in Beijing all exhibit an overall pattern of decreasing accessibility from the central urban area toward the periphery (Figure 6). However, significant differences can be observed among facility types in terms of decay intensity and spatial continuity. Medical facilities display a typical central agglomeration structure, with high-value areas mainly concentrated in the urban core and accessibility declining rapidly in peripheral areas, indicating that their service supply is constrained by both hierarchical systems and resource concentration. Educational facilities show an overall pattern similar to that of medical facilities, but local secondary high-value areas are formed in some sub-centers and cluster areas, suggesting that educational resources exhibit a certain degree of spatial diffusion, although balanced coverage has not yet been achieved. Transportation facilities present a high-value network structure with stronger continuity, where areas of high accessibility extend along major transport corridors and nodes, and the spatial transition is relatively smooth, indicating that the connectivity function of transport facilities within the network structure can effectively reduce spatial impedance. Commercial shopping facilities exhibit a multi-center distribution pattern, with high-value areas appearing not only in the urban

core but also in several regional commercial nodes, suggesting that their spatial layout depends more strongly on market forces and the distribution of consumption demand. Leisure and entertainment facilities are distributed in a relatively scattered manner, with high-value areas appearing as isolated points or patches and lacking continuous coverage, indicating that their supply is more strongly influenced by specific resource endowments and functional positioning. Life service facilities, by contrast, show the most even spatial. distribution pattern, with high-value areas covering a wide range and spatial decay being relatively moderate, indicating that under the drive of daily life needs, this type of facility has formed a relatively dense and stable grassroots service network

Overall, although all six facility types exhibit a core-periphery gradient structure, their formation mechanisms are not identical. Medical care and education rely more heavily on hierarchical systems and administrative allocation; Transportation reflects the continuity of network structure; Commercial shopping reflects market-oriented nodal agglomeration; Leisure and entertainment facility shows dispersed distribution under the constraints of resources and function; and life services are characterized by high density and broad coverage. These differences indicate that different types of public services do not expand homogeneously within the same urban space, but rather jointly shape the urban service pattern through different mechanisms.

3.3 Comprehensive Comparison and Structural Differences in the Accessibility of the Six Types of Facilities

On the basis of spatial distribution analysis, a statistical comparison of the accessibility of the six types of facilities can more clearly reveal the differences between their overall levels and distribution characteristics (Figure 7). In terms of average accessibility, life services and transportation facilities are significantly higher than the other types, with life service facilities having the highest average value, followed by transportation facilities. This indicates that these two types have stronger universality and availability in spatial supply. Commercial shopping facilities are at a medium level. Medical care and education facilities are generally

Figure 6  Distribution maps of accessibility to six types of public service facilities
in Beijing based on the MRGS2SFCA model (2026)

lower, reflecting a stronger selectivity in their spatial service supply. Leisure and entertainment facilities are also at a relatively low level, indicating that their coverage range and service continuity are relatively limited.

In terms of distribution patterns, significant differences exist in the degree of dispersion among facility types. The boxplot ranges of transportation and life service facilities are relatively concentrated, indicating that their accessibility varies less across regions and reflects a relatively high degree of spatial balance. The distributions of medical and educational facilities show more obvious long-tail characteristics, with high-value areas concentrated but low-value areas widely distributed, indicating a high degree of spatial imbalance. Commercial shopping and leisure and entertainment facilities fall between these two extremes, with their distributions containing both a certain range of medium- accessibility areas and local coexistence of high and low values. Combined with Figure 6, these statistical differences can be further understood as resulting precisely from the different spatial organization patterns of the various facility types: network-based and high-density facilities are more likely to form balanced distributions, whereas hierarchical and resource-dependent facilities are more likely to generate spatial disparities.

Overall, the statistical results reflected in Figure 7 do not merely replicate the spatial distribution maps but provide a quantitative expression of the accessibility differences among six types of public service facilities. Different facility types exhibit distinct patterns in terms of average accessibility, interquartile range, and whisker length, indicating that public service provision in Beijing is not homogeneously distributed but displays pronounced type- specific differentiation. Transportation and life service facilities show relatively high average accessibility, and their boxes and whiskers are also comparatively long, suggesting that while their overall coverage is extensive, there remain noticeable spatial gradients and regional variations; accessibility across different areas is not uniform but exhibits a continuous decline from high to low. In contrast, commercial shopping and leisure facilities are at moderate levels, with spatial patterns situated between those of transportation/life services and medical/educational facilities, indicating that their spatial organization relies on a limited number of support nodes, showing a certain degree of clustering and unevenness. Medical and educational facilities have relatively low average accessibility, with lower-end values extending more prominently, reflecting that their service provision is spatially concentrated and that some areas still experience substantial accessibility deficits. Therefore, the overall structure of Beijing’s public service system can be characterized by broadly distributed basic services with internal gradients, while specialized services are more concentrated and exhibit greater spatial disparity. These findings provide a foundation for subsequent analyses focusing on supply mechanisms and spatial optimization.

4 Discussion and Conclusion

Public service facilities in Beijing as a whole exhibit is a pronounced pattern of “core concentration-peripheral decline” in space. Areas of high coverage and high accessibility are mainly concentrated in the core urban districts, including Dongcheng District, Xicheng District, central Chaoyang District, and southern Haidian District, whereas peripheral areas such as Shunyi, Tongzhou, Daxing, Fangshan, Yanqing, and Mentougou experience varying degrees of service insufficiency. This pattern is highly consistent with the long-established core-periphery urban structure of Beijing and reflects the significant coupling between public service facility allocation, population density, land development intensity, and functional zoning. Further analysis shows that although all six facility types follow the overall gradient structure, their spatial organization patterns and formation mechanisms differ significantly: medical and educational facilities exhibit strong hierarchical and central agglomeration characteristics; transportation facilities show strong network continuity; commercial facilities display a multi-centered nodal expansion pattern; leisure and entertainment facilities are relatively dispersed; and life service facilities are characterized by high density, broad coverage, and strong grassroots-level balance. This indicates that Beijing’s public service system is not a single homogeneous system, but rather a composite structure jointly shaped by different service scales, supply mechanisms, and functional attributes. On this basis, this study argues that the traditional Two-Step Floating Catchment Area method, under fixed thresholds and uniform service radii, cannot accurately capture differences among multiple facility types in terms of service range, spatial attractiveness, and supply capacity. By contrast, MRGS2SFCA introduces continuous distance decay, multi-scale service ranges, and hierarchical weights, thereby achieving comparable representation of different facilities within the same analytical framework and more realistically reflecting the spatial heterogeneity of public service supply and the supply-demand mismatch within megacities. Overall, Beijing’s public service system exhibits a structural feature in which “high-frequency basic services tend to be balanced, whereas professional and hierarchical services show significant disparities”. The analytical framework constructed in this study not only helps reveal the spatial differentiation patterns of public service supply within megacities, but also provides methodological support and empirical evidence for the optimization of public service facility allocation, the development of living circles, and refined urban governance in Beijing.

Author Contributions

Tian, H. Z. was responsible for data collection and manuscript writing. Jiang, X. H. and Alimujiang, A. were responsible for data verification and methodology design. Zhang, N. processed the data and contributed to part of the manuscript writing. Wang, S. H. reviewed, supervised, revised, and improved the paper.

Acknowledgements

We would like to thank the Key Laboratory of Historical and Cultural Heritage Monitoring, Ministry of Housing and Urban-Rural Development for its data and technical support for this study.

Conflicts of Interest

The authors declare no conflicts of interest.

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