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Article

Study on the Spatial Matching Between Public Service Facilities and the Distribution of Population—An Example of Shandong Province

by
Yin Feng
and
Yanjun Wang
*
College of Civil Engineering and Architecture, Shandong University of Science and Technology, Qingdao 266590, China
*
Author to whom correspondence should be addressed.
Sustainability 2025, 17(17), 7866; https://doi.org/10.3390/su17177866
Submission received: 27 July 2025 / Revised: 26 August 2025 / Accepted: 27 August 2025 / Published: 1 September 2025
(This article belongs to the Topic Architectures, Materials and Urban Design, 2nd Edition)
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Abstract

Against the backdrop of rapid new urbanisation and the ongoing integration of urban and rural areas, the evolving spatial dynamics between public service facilities and population distribution have increasingly garnered scholarly interest. The present study employs a grid-based spatial unit and a coupling coordination model as a foundation. This model integrates POI data, Baidu heat maps, and other sources of spatial and temporal information. The objective is to explore the dynamic matching pattern of public service facilities and population distribution. The study’s findings are as follows: The population within the core urban area displays a strong propensity for agglomeration during the morning and evening peak hours, thereby forming a highly coordinated public service network characterised by high-density and piecemeal distribution of public service facilities. The population residing within the transition zone between urban and rural areas is commuting in a substantial number, and the relationship between the supply of and demand for facilities demonstrates cyclical fluctuations. Local areas are subject to time-periodic pressure on the supply of and demand for facilities. In rural areas, due to the continuous population outflow and dispersed residence, the layout of service facilities is fragmented, exhibiting the island effect. The study reveals a structural contradiction between traditional homogeneous planning and the gradient difference between urban and rural areas, providing a scientific basis for Shandong Province to promote new urbanisation and rural revitalisation strategies in an integrated manner.

1. Introduction

Public service facilities are considered a fundamental cornerstone in supporting urban and rural society [1]. These facilities encompass basic livelihood areas, including education, healthcare, and transport [2,3,4,5]. The fairness and efficiency of their spatial allocation have been demonstrated to directly affect the quality of life of residents and the sustainable development of society [6,7,8]. In the context of global urbanisation, the phenomenon of the over-concentration of public service resources in core urban areas is prevalent [5], resulting in the intensification of urban–rural gradient differences [9,10,11]. China’s urbanisation process has undergone a substantial transformation, with the urbanisation rate rising from 18% in 1978 to 67% in 2024. This rapid change has profoundly reshaped the spatial structure of urban and rural areas [12]. Consequently, there has been a sharp increase in demand for public service facilities, resulting in a dynamic mismatch between the supply of facilities and the population distribution. The scientific quantification of the dynamic matching relationship between facility supply and population demand [13] and the construction of a precise and differentiated public service allocation system have become the core propositions that must be addressed for high-quality urban development.
The theoretical framework for allocating public service facilities has undergone a progressive transformation, evolving from the traditional spatial equity paradigm towards a more dynamic, behaviour-responsive model. Early conceptualisations, such as Harvey’s dialectical analysis of “social justice and spatial form” [14] and Talen’s “accessibility equity” [15], emphasised equal access across groups and geographic space. While these theories provided valuable critiques of spatial inequality, they were largely based on static population patterns and administrative boundaries [16], which are increasingly misaligned with contemporary urban dynamics. More recent theories integrate temporal mobility and functional heterogeneity to address the challenges posed by dynamic urbanisation. Batty’s concept of the “new science of cities” and “mobile space” [17] challenges the inflexibility of traditional planning and promotes adaptive models that align with the changing rhythms of urban populations. Meerow et al.’s “resilient city” framework [17] proposes a flexible public service network that can withstand demographic shifts. Leon Krier’s critique of modernist urbanism, meanwhile, advocates for a polycentric urban model in which distinct functional units are organised around walkable, human-scaled centres [18,19]. This vision underpins the principle of urban decentralisation and offers a theoretical basis for allocating public services in a heterogeneous manner [20]. Krier’s concept of the “traditional city” emphasises integrating living, working, and public functions within compact, legible forms, contrasting sharply with zoning-driven fragmentation. On this basis, Carlos Moreno introduced the concept of the “15 min city”—an urban model based on proximity, diversity, and density, where all essential services (healthcare, education, shopping, and recreation) can be accessed within a 15 min walk or bike ride from home [21,22]. This model challenges conventional mono-functional zoning and proposes an urban form that is functionally non-homogeneous yet spatially cohesive [23,24]. In practice, cities such as Paris and Shanghai have adopted this model to redistribute public facilities more equitably and responsively across small-scale urban areas [25,26]. In China, scholars such as Long Ying et al. have proposed spatio-temporal, behaviour-oriented planning that emphasises population mobility patterns and the temporal fluctuation of service demand [27,28,29]. These approaches recognise that urban functionality is not only spatially distributed, but also temporally differentiated, and that facility planning must move beyond “static sufficiency” to achieve “dynamic fitness.” This study is situated within the dynamic adaptation paradigm, but builds on it by introducing a non-homogeneous functional perspective. It advocates polycentric, proximity-based, and temporally responsive service layouts. This approach is consistent with the goals of Shandong Province’s urban–rural integration strategy, offering a fresh perspective on the spatial and temporal coordination of public services.
Methods for evaluating public service facilities have evolved from qualitative descriptions to multi-source data fusion [30]. Most of the early studies relied on the Gini coefficient [31,32] with the Lorenz curve to measure the fairness of the distribution of facilities [33], but it is difficult for such methods to resolve the characteristics of spatial heterogeneity. The popularity of geographic information systems (GIS) [34,35,36,37] has promoted the development of spatial accessibility models, such as the two-step moving search method (2SFCA) [38], which quantifies the pressure on facility services by calculating the ratio of supply and demand [39], but it is mostly based on static census data and ignores the impact of diurnal and nocturnal fluctuations in population density on the utilisation rate of facilities [40]. Breakthroughs in big data technology have provided new momentum for sophisticated analysis [26], such as the use of mobile phone signal data to track individual movement trajectories to invert the spatial and temporal patterns of population activity [13,41,42], and the combination of POI and social media data to accurately depict the distribution density and service capacity of facilities [43,44,45,46]. Multi-source data fusion technology also extends the evaluation dimension of matching facility supply and demand [38,47], e.g., New York’s “Fair City” strategy reshapes the network of service facilities through the 15 min life circle, and London’s “Cultural Inclusion” programme improves accessibility for disadvantaged groups through demand-responsive layout. Domestic studies have combined Baidu heat map and POI data to reveal the low utilisation of facilities due to the spatial mismatch between occupations and residences in Beijing [48], and established the coupled coordination degree model (CCDM) to quantify the synergistic degree of population aggregation and facility density, which reveals the structural contradiction in the imbalance between supply and demand [46,49,50], but most of them have adopted static weight allocation, which makes it difficult to reflect the dynamic correlation between the functional attributes of the facilities and the demand of the population.
At a practical level, the imbalance in the allocation of facilities due to the urban–rural dual structure is a common challenge in the global urbanisation process [51,52,53,54]. In developed countries, legislation and financial transfers have been used to narrow the gap between urban and rural services, such as Japan’s “Urgent. Measures for Depopulated Areas Act”, which requires public service investment to be skewed towards sparsely populated areas [55], while developing countries have explored a market-based compensation mechanism constrained by ability to pay and cultural barriers [56]. In domestic practice, Shanghai’s “15 min community living circle” achieves precise placement of facilities through fine-grained network management [25,57], but its applicability is limited in transitional zones with high population mobility; Chengdu’s “district-based” facility-sharing model improves coverage efficiency through inter-administrative resource allocation [58], but is not sufficiently responsive to new demand caused by population dynamics. These approaches indicate that achieving an equilibrium in urban and rural facilities is difficult when relying solely on administrative intervention or market mechanisms.
Shandong Province is currently at a pivotal point in its urbanisation process. The province aims to foster coordinated urban–rural development and achieve equal access to basic public services. As a densely populated region with distinct urban–rural gradients ranging from highly urbanised areas to transitional zones with ‘half urban, half rural’ characteristics, the needs of residents are diverse. In response to the urgent need for an integrated, multidimensional evaluation of facility–population matching, this study proposes a technical framework involving the integration of multi-source data, spatial heterogeneity evaluation, and dynamic matching optimisation. Using a 500 m × 500 m grid, we integrate Baidu heat map data with point of interest (POI) information to establish a temporal population density model. This model delineates the spatial–temporal distribution of public service facilities and population density and identifies areas of high aggregation with low alignment between supply and demand. We then use a coupling coordination model to convert the weighted thermal effect index into the Population–Service Matching Index (PSMI), which quantifies the difference in matching performance between multiple types of facilities, such as education, healthcare, and transport. This study makes three main contributions: (1) expanding the analytical scale to the provincial level and capturing spatial matching patterns across the full urban–rural gradient of Shandong Province; (2) adopting a dynamic temporal perspective through the use of multi-source spatio-temporal data and overcoming the reliance on static datasets that is common in previous studies; and third, introducing the PSMI as an innovative metric that enables a more nuanced, function-specific assessment than conventional coupling coordination degree models. This offers a practical tool for optimising urban–rural service networks in support of the “14th Five-Year Plan” and rural revitalisation strategies.

2. Research Area and Data Sources

In order to explore comprehensively the evolving interplay between public service facilities and population distribution in Shandong Province, this research has constructed a systematic research framework that amalgamates multi-source data collection, spatio-temporal analysis, and coupling coordination evaluation (Figure 1). This framework comprises three key phases: (1) gathering and pre-processing data from Points of Interest (POIs), Baidu heat maps and road networks; (2) conducting spatio-temporal analysis to reveal dynamic population and public service distribution patterns; (3) performing coupling coordination analysis to measure and visually represent the degree of spatial harmony between population clustering and public service facility placement. This comprehensive methodology provides a thorough understanding of spatial equity and flexibility in service delivery amidst the dynamic transformation of urban and rural landscapes.

2.1. Research Areas

As the main practice of “integrated urban–rural development” and “equalisation of basic public services”, the urban–rural development model of Shandong Province is typical and politically sensitive. The high-density population agglomeration of its core cities and the rapid expansion of its new urban areas have led to an imbalance in the distribution of resources between urban and rural areas, which has become a bottleneck restricting the high-quality development of Shandong Province. Therefore, selecting Shandong Province as the research locale offers a wealth of empirical data to investigate the spatial realignment mechanisms of public service facilities. Furthermore, it establishes a theoretical foundation for delving into the optimisation of urban–rural factor mobility and the strategic allocation of facilities.
Located on the east coast of China and downstream of the Yellow River, Shandong is an important part of the Bohai Economic Circle. The province has a land area of 158,100 square kilometres, a population of 101.23 million, and a regional GDP of 9856.6 billion yuan, of which 53.1 per cent is accounted for by the tertiary industry. It has 16 prefecture-level cities, including Jinan, Qingdao, Zibo, Zaozhuang, Dongying, Yantai, Weifang, Jining, Taian, Weihai, Rizhao, Binzhou, Dezhou, Liaocheng, Linyi, and Heze (Figure 2).

2.2. Data Source

2.2.1. Point of Interest (POI) Datasets

Based on relevant standards and adapted for the conditions in Shandong Province, point of interest (POI) data were categorised into nine main types: accommodation and catering; government and community organisations; housing services; healthcare; education; finance and banking; transportation; recreational activities; and tourist attractions. These data were sourced from the Amap (Gaode Map) Open Platform (https://lbs.amap.com/, accessed on 24 November 2024). After thorough filtering and classification, 2,349,285 valid POIs were retained for analysis (Table 1).

2.2.2. Baidu Heat Map

To guarantee the data’s reliability and minimise any potential disruptions caused by extraordinary circumstances like severe weather, national holidays, or significant events, the Baidu heat map data were gathered during standard conditions. Specifically, the collection took place on a weekend day (Sunday, 15 December 2024) and a weekday (Monday, 16 December 2024). Data were recorded at three-hourly intervals between 07:00 and 24:00, resulting in 14 heatmap snapshots over time. The fourth round of data was processed using ArcGIS Pro (version number 3.3), and the natural breaks classification method was applied to reclassify and assign values according to heat intensity levels.

3. Methodology

3.1. Kernel Density Analysis

Initially proposed by Rosenblatt and Parzen, kernel density estimation is a non-parametric statistical technique used to estimate the probability density function of a variable based on a set of known sample points. This technique clarifies the spatial distribution patterns of the variable under investigation by applying a smoothing function to the observed data. In spatial analysis, the kernel density estimation method is frequently employed to assess the concentration of point or linear features within a defined area, thereby generating a seamless surface that captures and illustrates patterns of spatial intensity [59,60].
f ( x ) = ∑ i = 1 n 1 h 2 k x − c i h
In the formula, f ( x ) is the kernel density calculation function at the spatial location x ; h is the distance decay threshold; n is the number of feature points less than or equal to h from position x ; k is the spatial weight function. The density value is maximum at each kernel element c i , and as the distance from c i increases, the density value decreases until the distance from c i reaches the threshold value h , and the kernel density value decreases to 0. In this study, the values of h are 20,000 m, 25,000 m, and 30,000 m, and the results obtained under the search radius of 20,000 m can accurately characterise the overall spatial features of the POI points.

3.2. Data Grid Overlay

In order to reduce spatial uniformity and redundant information, this study adopted a grid framework with a basic unit of 500 m × 500 m, moving beyond conventional administrative divisions such as streets and townships [61]. To investigate the patterns of population concentration at distinct time intervals and uncover spatial discrepancies among diverse categories of points of interest (POI), both the Baidu heat map data and the kernel density results of POIs were converted into a raster format aligned with this grid system. Heat map layers from the same time period were superimposed and clustered to depict population activity intensity and distribution during that timeframe [47], as calculated by the following expression.
H = ∑ H n N
In the formula, H denotes the mean value calculated over a specific time period; H n represents the value corresponding to the n th time interval within a day; and N indicates the total number of heat maps generated for that time period.

3.3. Matching Index of Population Aggregation and Service Facilities

The coupling coordination degree model is utilised to evaluate the degree of interactive harmony between the concentration of urban populations and the spatial layout of service facility densities. By taking cues from the capacity coupling theory in the field of physics, a coupling model is developed to measure and quantify the mutual reliance and interconnectedness of these two systems [62,63]. The specific formula is given below.
C = 2 u 1 × u 2 u 1 + u 2 2
In the formula, the variable C denotes the coupling degree, with its value ranging from 0 to 1. A higher value of C indicates a stronger coupling between the intensity of population concentration and the spatial distribution pattern of service facilities. Meanwhile, u 1 represents the normalised population concentration, and u 2 signifies the normalised density of service facilities. While the coupling degree serves as an indicator of the intensity of interaction between systems, it fails to incorporate considerations regarding the comparative developmental stages of each individual system. Therefore, a model that considers both consistency and coordination is required to capture their combined performance.
D = C × T
T = a u 1 + b u 2
In the formula, the variable D denotes the coupling coordination degree between the concentration of urban population and the spatial distribution of service facilities. Concurrently, the variable T represents the comprehensive coordination index, which captures the holistic synergistic relationship between population concentration and the allocation pattern of service facilities. In Equation (5), the weights “a” and “b” are set to 0.5, reflecting the assumption that population agglomeration and facility supply contribute equally to overall matching performance. This balanced weighting is a common approach in coupling coordination studies when there is no strong empirical basis for prioritising one subsystem over the other. The rationale is to avoid biasing the results towards either population or facilities in the absence of context-specific evidence. However, we acknowledge that, in certain contexts such as emergency healthcare provision or tourism-driven economies, the relative importance of supply and demand factors may differ. Future work could incorporate expert elicitation, the analytic hierarchy process (AHP), or entropy weighting to assign context-specific weights, thereby improving the model’s adaptability [64]. Furthermore, the coupling coordination degree is divided into four levels for analysis (Table 2) [65].
We acknowledge that the CCD indicator is not a pure correlation coefficient and does not always correspond perfectly to the extremes of intuitive agreement or disagreement. In this study, the CCD is used as an intermediate construct to capture the joint interaction strength of population and facility systems. This is then transformed via the PSMI into a relative-deviation index that more directly reflects disparities in spatial matching.
The Population–Service Match Index (PSMI), which draws upon and modifies the weighted thermal effect index introduced by Wang et al. [66], serves as a quantitative metric to assess the degree of spatial congruence between population distribution patterns and the arrangement of service facilities. Unlike the direct use of the coupling coordination degree (D), which provides an absolute measure of the harmony between population density and facility distribution, the PSMI focuses on the relative deviation from the overall average matching level across the study area. Setting the mean PSMI to zero means that positive values indicate above-average matching performance for a given facility type, while negative values signify below-average performance. This normalisation enables disparities between different facility types to be compared directly, facilitating the identification of structural imbalances that could be obscured by an analysis of absolute D values. Therefore, the PSMI is particularly well-suited to diagnosing uneven service provision and guiding type-specific optimisation strategies. The index uses the overall average matching level across the study area as a benchmark, ensuring that the total sum of all matching values is zero, which indicates a balance between positive and negative deviations around the mean. The Population–Service Matching Index (PSMI) effectively quantifies the extent of coordination and spatial alignment between various categories of service facilities and population density within urban settings. Given an ensemble of I service facilities, P S M I = P S M I | I = 1 … I , it is calculated as follows:
P S M I i = ∑ j = 1 n D ¯ i j − D ¯ A i j D ¯ A × 100 %
In the formula, A denotes the overall area of the geographical region under consideration, A i j represents the area occupied by the distribution of service facility type i at the specified coupling coordination level j , D ¯ signifies the mean coupling coordination value for the entire region, and D ¯ i j indicates the average coupling coordination value specifically for service facility type i at the coupling coordination level j .

4. Results

4.1. Population Density and Spatial and Temporal Characteristics of Service Facilities

4.1.1. Spatial and Temporal Trends in Population Density

Natural breakpoint classification (Jenks optimisation) was applied to the Baidu heat map values to identify clusters in the data distribution. This method minimises intra-class variance and maximises inter-class variance, resulting in statistically optimal class boundaries. The results revealed distinct value groupings, with heat map values of 6–7 constituting the top cluster and values of 4–5 forming the second-highest cluster. Consequently, zones with values of 6 and 7 were categorised as high agglomeration areas, and zones with values of 4 and 5 were categorised as sub-agglomeration areas. This classification was therefore data-driven rather than arbitrary, ensuring consistency with the underlying population density patterns. The distribution of population activity across seven distinct time intervals was computed separately for weekdays and weekends, and significant temporal and spatial differences in activity were observed between core urban areas, sub-agglomeration areas, and low agglomeration areas (Table 3). The heat values of the core city on weekdays show a typical “bimodal” pattern: the morning peak (7:00–12:00) is characterised by a rapid build-up of population towards employment centres and the highest intensity of activity, with a slight decrease at lunchtime (12:00–18:00) and an increase in intensity at the evening peak (18:00–24:00) with the return of commuters and night-time consumption. On rest days, there is a pattern of “polycentric diffusion”, with a significant increase in activity in commercial areas and scenic areas at midday and a slight fluctuation in the evening peak, reflecting a shift in the focus of residents’ activities from productive demand on weekdays to leisure consumption; the intensity of population aggregation on weekdays in sub-aggregation areas is relatively low and fluctuates slowly, while the intensity of activity increases in the middle of the day on rest days, indicating that short-distance leisure activities have become the driving force of population aggregation. In the remaining areas, the activity intensity of the population is consistently lower, highlighting structural differences in activity intensity between urban and rural areas. The weekend ratios are noticeably higher in core urban zones, mainly due to the concentration of leisure, retail, and tourism activities attracting additional inflows of people. In transitional and peripheral zones, the weekend increase is smaller, reflecting a more stable population distribution throughout the week. This pattern indicates that weekend activities in the core are a significant driver of short-term fluctuations in population–facility matching.
Figure 3 shows that urban core areas such as Lixia District in Jinan and Shinan District in Qingdao are densely populated, forming a “double core radiation” pattern. These districts have high-intensity economic activities, and the phenomenon of “separation of work and residence” has led to significant differences in daytime and night-time population densities. Lanshan District in Linyi and Quiwen District in Weifang show a typical “tidal” flow of population density. During the morning peak, the population moves rapidly from residential areas to the urban core, while the evening peak shows a reverse flow. Although the number of public service facilities in these areas is close to urban standards, the actual service pressure fluctuates over time due to the high mobility of the population.

4.1.2. Features Relating to the Spatial Configuration of Service Provision

The spatial distribution of public service facilities in Shandong Province shows significant hierarchical characteristics, the overall spatial pattern of the two core urban areas of Jinan and Qingdao as a high-density radiation pole, the urban–rural transition zone and the rural hinterland as scattered small aggregation points, the density of public service facilities from the centre to the periphery of the circular diffusion and the gradient of decline, along the traffic arteries or townships were scattered distribution, forming a typical “core diffusion” spatial structure (Figure 4).
Drawing upon the distinctive features of the nuclear density distribution exhibited by diverse categories of service facilities, their spatial configurations are categorised into two primary types: the dual-core dispersed pattern and the axial point pattern (Figure 5 and Figure 6). (1) The spatial distribution of public service facilities, such as accommodation and food services, government offices and social organisations, medical services, education services, banking and financial services, and housing and recreation services, is in the form of a dual-core scatter pattern. The urban part of the city takes Jinan and Qingdao as the dual-core pole centre, forming a continuous high-density agglomeration along the city’s main roads and commercial axes. Among them, administrative resource-driven facilities such as medical services and education services are densely distributed along the government axis (Figure 5c,e), and market-driven facilities such as accommodation and catering services and residential and recreational services form multi-hotspot clusters around the commercial centre; The urban–rural transition zone forms sub-nodes that rely on hotspots of population relocation, such as Lanshan District in Linyi and Kuifang District in Weifang, and the density of facilities decreases in a gradient with increasing distance from the urban core; the rural areas are manifested in the form of The rural areas have an isolated and sporadic distribution that relies on townships and villages, and the service radius is significantly limited. (2) Axis point type: Transport services are extended along highways and railway lines in the form of belts, with high-density nodes formed by core transport hubs, insufficient radiation capacity of main roads in rural areas, and difficulty in forming an effective connection of secondary roads, resulting in fragmentation of service coverage. Scenic facilities are concentrated in natural and humanistic scenic spots, and their spatial distribution is in the form of discrete points away from densely populated areas, and service coverage shows seasonal fluctuations.

4.2. Spatial Linkages Between Population Density and Services

4.2.1. Spatial Matching Patterns

The match between public service facilities and population density in Shandong Province shows a significant “core–periphery” pattern (Figure 7). The core urban areas (Lixia District in Jinan, Shinan District in Qingdao, etc.) are highly coordinated, and the supply of facilities is highly compatible with the demand of the population, forming a continuous high-density service network; Intermediate coordinated areas are distributed around the periphery of advanced coordinated areas (West Coast New District in Qingdao, Huayin District in Jinan, etc.), and serve as a transition zone between the core area and the suburbs, where the layout of facilities is basically appropriate for the population density, but there is local pressure on the time of day. The urban–rural transition zone (Lanshan District in Linyi, Kuiwen District in Weifang, etc.) is mainly intermediate coordinated, mostly point or ring-shaped, with limited coverage of facilities, relying on the radiation of the urban core; the rural hinterland is generally in a low-coordinated state, with sparse facilities and population loss forming a vicious circle.
Based on the analysis of the spatial coupling between service facilities and population density, the spatial matching pattern is grouped into three categories (Figure 8): (1) High-continuity matching facilities: represented by educational services and banking and financial services, a continuous high-density service network is formed along the main roads and commercial axes in the core urban areas of Jinan and Qingdao, which are deeply coupled with the hotspots of population activities. These facilities form local nodes in the centre of the county, but the coverage is limited, and the rural areas show sporadic distribution due to population outflow, and the overall performance is the spatial differentiation characteristic of “strong radiation in the core—gradient attenuation in the periphery”; (2) Dynamic fluctuation matching facilities: for example, transportation services and catering services. The degree of matching is significantly influenced by population flows and the timing of activities. The morning peak of the core urban transport hub forms a matching hotspot, and the evening peak leads to a mismatch between supply and demand due to commuter pressure; the transition zone between urban and rural areas manifests itself as a discrete matching node, with congestion in the core urban area at midday on weekdays and short-term matching in the county recreation areas at evening on weekends; the rural areas are inefficient due to dispersed demand over a long period and the overall formation of a composite spatial structure of “multi-peak fluctuation-transitional discrete-low-value in the countryside” is formed; (3) Fragmented and inefficient facilities: Medical services and scenic spots are typical examples, and there is a mismatch between their distribution and the population’s demand. Medical services in urban core areas are locally excessive, while the rural hinterland relies only on townships to form isolated service points; scenic facilities are concentrated in natural scenic spots away from densely populated areas, and service coverage shows seasonal fluctuations. The spatial structure shows a fractured pattern of “congested core-isolated islands on the fringes”, highlighting the delayed response of the traditional planning model to dynamic demand.
In summary, the core urban area functions as a service highland in the region through the processes of resource agglomeration and function superposition. The transition zone between urban and rural areas gives rise to regional service nodes through the inflow of industry and population, demonstrating dynamic adaptation and local pressure. The rural hinterland inhibits the scale effect of facilities, due to the low-density population and dispersed living pattern. Furthermore, the traditional “coverage by establishment” [67,68] planning mode is difficult to adapt to actual demand.

4.2.2. Space Matching Index

The present study measured the spatio-temporal coupling status of public service facilities and population density in Shandong Province through the PSMI method. The study found that the matching degree of different service facilities showed significant differences (Table 4). The high degree of coordination exhibited by banking and financial services is indicative of their compatibility with population density in core urban areas, particularly in financial agglomeration areas, where they form a stable match; transport services are subject to limitations due to local congestion during evening peak hours and the absence of coverage for rural feeder routes; medical and education services have a high level of compatibility in the morning of the day off, which is related to commuter demand and the concentration of government activities, but their compatibility decreases in the afternoon of weekdays due to the time lag in the scheduling of resources; living services have a low degree of matching in weekday afternoons and evenings, with a mismatch between supply and demand due to dispersed demand and insufficient supply response; accommodation and food services show significant temporal variation, with weekday lunchtime saturation in the urban core and short-lived matching in the county recreation area on weekday evenings, highlighting the spatial and temporal mismatch between commercial activities and population movements; recreational services, government institutions and social organisations exhibit a high degree of stability, with no discernible temporal fluctuations, indicating that their supply is weakly correlated with population activities. The results show that the coupling relationship between public services and population density is multidimensional and complex, and needs to be precisely optimised by combining functional attributes and spatial and temporal demands.

4.2.3. Coupled Coordination Characteristics

The correlation between public service facilities and population distribution in Shandong Province exhibits a pronounced spatial differentiation pattern characterised by “core polarisation–transition fluctuation–edge fragmentation”. From the perspective of spatial and temporal characteristics of population density, the core urban areas exhibit a “double-peak” agglomeration pattern in the morning and evening peaks, and the high-intensity population activities are deeply matched with the supply of facilities, which is shown as a “well-coordinated” grade; the emerging urban areas demonstrate temporal fluctuations in the matching degree of facilities due to the “tidal wave” population flow of population. The pressure of local supply and demand is highlighted during the midday and evening peaks. Rural hinterlands exhibit fragmented and isolated coverage of facilities due to the low-density distribution of the population and the continuous outflow, resulting in an overall “low-coordination” state. The spatial distribution of public service facilities is hierarchical. Core urban areas rely on high-density POI networks to form a continuous service pole core, with a gradient that decreases along the traffic arteries to the periphery; urban–rural transition zones present secondary nodes and local hotspots, with a limited scope of coverage; rural areas are dominated by dispersed point facilities, which are out of touch with the residential pattern.
This coupling is in structural contradiction to Shandong’s strategy of “integrated urban–rural development”. The efficient coordination of core urban areas is attributable to the tilting of policy resources and the population concentration effect, which follows the requirements of intensive development. The absence of dynamic adaptation in urban–rural transition zones and the structural imbalance in rural areas reflect the deep-seated contradiction between the traditional one-size-fits-all planning model and the urban–rural gradient differences. The current distribution pattern of facilities does not yet fully align with the policy direction of “equalisation of basic services between urban and rural areas”. While the “double-core radiation” of the core urban areas has strengthened regional competitiveness, it has exacerbated the resource siphoning effect of the peripheral areas. The “isolated” layout of facilities in the countryside poses significant challenges in supporting the fundamental services enshrined in the goal of common prosperity. This situation creates a discernible gap between this objective and the innovative approach of “piecemeal synergistic development”.

5. Discussion

This study reveals a fundamental mismatch between the traditional, homogeneous planning paradigm and the emerging demand for public services that are both spatially and temporally differentiated. In the context of Shandong Province’s rapid urbanisation and complex urban–rural transition dynamics, over-reliance on static spatial equity frameworks has resulted in the over-concentration of facilities in core urban areas, insufficient services in transitional zones, and functional fragmentation in rural hinterlands. Addressing these spatial disparities requires adopting a more robust theoretical framework that incorporates functional heterogeneity, temporal elasticity, and proximity-based accessibility.
In this regard, Leon Krier’s theory of polycentric urbanism offers a fundamental perspective. He critiques the monofunctional zoning of the modernist city and instead advocates a structure comprising multiple self-sufficient centres, each integrating living, working, and service functions, to form a balanced, human-scaled urban fabric [18,19,69]. The high coordination zones identified in Qingdao and Jinan demonstrate the characteristics of such polycentric systems, with multiple urban centres functioning as regional service hubs. This is particularly evident in the dual-core agglomeration of public facilities along transport and commercial corridors. However, these supporting sub-centres are lacking in the periphery and transitional areas, resulting in mismatches and inefficient service distribution. Carlos Moreno’s “15 min city” concept further enriches this discussion. His model proposes the spatial organisation of urban functions so that all essential services are accessible within a 15 min walk or bike ride [22,70,71]. This proximity-based planning paradigm not only addresses spatial equity but also temporal responsiveness, offering a strategy for integrating service delivery with residents’ daily activity rhythms [72,73,74]. The empirical results of this study, such as the “bimodal” population aggregation pattern in core cities, “tidal” commuting in transitional zones, and “seasonal sparsity” of rural scenic services, underscore the need for planning models that are both spatially decentralised and temporally adaptive. Moreno’s chrono-urbanism closely aligns with the necessity of configuring “tidal service nodes” in urban fringes and deploying “mobile or on-demand services” in low-density rural areas.
The “core–periphery” pattern observed in Shandong Province is consistent with spatial equity theory, whereby the concentration of resources in urban centres perpetuates service disparities in peripheral areas. This spatial inequality is exacerbated by temporal discrepancies, as revealed by our PSMI results. These results challenge traditional static models and emphasise the need for dynamic adaptation in facility planning. In urban–rural transition zones, observed “tidal” population flows generate fluctuating demand peaks, highlighting the need for planning frameworks that can allocate resources flexibly and build resilience. Contrary to the 15 min community living circle in Shanghai, which focuses on proximity-based equity, our findings reveal that proximity alone is insufficient when temporal demand surges are ignored. Similarly, while Chengdu’s district-based sharing model improves spatial coverage, it does not fully address the need for time-sensitive facility deployment in areas of high mobility. This study contributes a new perspective by integrating multi-source big data with a relative deviation-matching index. This approach bridges the gap between spatial equity theory and dynamic adaptation principles, informing the development of more resilient, temporally responsive service networks.
At the policy level, this study suggests that the spatial coordination of public services should transition from a “coverage-first” model to a demand-responsive, polycentric governance structure. Urban cores should prioritise functional compounding and saturation management, while transitional zones should develop semi-autonomous sub-centres with temporal elasticity. Rural hinterlands, meanwhile, should pursue clustered multifunctional hubs embedded within township frameworks. Administrative barriers can be reduced by establishing inter-jurisdictional planning alliances, standardising facility provision targets, and enabling cross-boundary data sharing. Integrated digital platforms combining AI-based forecasting, IoT-enabled service monitoring, and digital twin simulations can facilitate the real-time scheduling and adjustment of facilities in response to population needs. Integrating spatio-temporal big data enables the continuous identification of mobility patterns and demand peaks. This provides empirical support for dynamic adaptation models that are aligned with the emerging “spatio-temporal behaviour-oriented planning” approach in Chinese urban studies. To facilitate inter-regional resource compensation, a differentiated fiscal transfer mechanism could be introduced that links subsidy levels to measurable service shortfall indicators derived from the PSMI. Resource-rich core cities could provide targeted financial or facility support to underserved peripheral and transitional zones. Pilot programmes, such as mobile healthcare units or modular educational facilities, could test the feasibility of behaviour-responsive service allocation. As this study has demonstrated, different types of services (e.g., education, catering, and healthcare) exhibit different temporal coupling patterns with population density. This highlights the need for planning mechanisms that adapt dynamically to behavioural demand, rather than relying on rigid administrative allocations.
Using Baidu heat map data offers clear advantages over conventional census datasets in terms of temporal resolution and dynamic monitoring capability. By providing population distribution data in near real time at a fine spatial scale, it enables the detection of short-term fluctuations, such as commuting peaks, weekend surges and seasonal variations, which static census data cannot capture. This dynamic granularity is particularly valuable for analysing the match between facilities and population in rapidly changing urban–rural contexts. However, several limitations must be acknowledged. Firstly, Baidu heat map data reflects the activity of mobile users accessing Baidu services, which may result in the underrepresentation of certain demographic groups, such as the elderly, children, and residents without smartphones. Secondly, the data may be biased towards areas with higher smartphone penetration, which could affect its representativeness in remote rural regions. Thirdly, unlike census data, Baidu heat maps do not distinguish between permanent residents and transient visitors, which can affect the interpretation of short-term surges. These limitations should be considered when generalising the findings. Future research could integrate Baidu data with census statistics and other location-based service datasets to combine the advantages of dynamic monitoring with the demographic comprehensiveness of traditional sources.
In summary, the misalignment between the supply of facilities and the demand for them in Shandong Province is not just a technical issue of spatial layout; it is also a deeper theoretical and institutional problem rooted in outdated planning logic. Incorporating the principles of polycentricity, proximity, temporal efficiency, and data-driven dynamic adaptation into future urban–rural facility networks can help to achieve a state of ‘differentiated equilibrium’, balancing efficiency, equity, and sustainability within an integrated spatial system.

6. Conclusions

Through multi-source data integration and spatial econometric analysis, this paper identifies the coupling patterns between public service facilities and population distribution in Shandong Province. The results show that: (1) the “dual core polarisation” effect in urban core areas is due to policy-driven resource agglomeration and market-induced economies of scale, both of which enhance the efficiency of facility services; (2) fluctuations in supply and demand in urban–rural transition zones are closely related to the spatial and temporal heterogeneity of industrial and demographic mobility as well as the planning response lag; (3) the siloing of facilities in rural areas is not only limited by gradient differences in financial inputs, but also forms a vicious circle with the lack of economies of scale due to decentralised settlement patterns. This hierarchical model of adaptation suggests that the dynamic balance between efficiency and equity in the allocation of facilities needs to break through the rigid constraints of traditional administrative boundaries and move towards a more flexible spatial governance framework.
Although this paper constructs an analytical framework for dynamic matching of public service facilities based on multi-source data, the following limitations remain: (1) data timeliness and refinement are insufficient, relying on static POIs and heat maps of discrete periods, which makes it difficult to accurately capture the instantaneous dynamic response characteristics of the supply and demand of facilities; (2) the model is limited in its applicability, and the existing PSMI focuses on evaluating spatial equilibrium, and lacks in-depth coupling of the prediction of population mobility and the flexible mobilisation mechanism of facilities. In the future, we can deepen the fusion of multi-source data, introduce high-frequency mobile phone signals, IoT devices and other real-time data streams, build an integrated digital twin platform, achieve the second-level response of facility supply and demand, develop AI-driven dynamic optimisation models, and enhance learning to simulate the effect of facility allocation under different policy scenarios, to provide scientific support for accurate decision-making, promote the transformation of urban and rural public services from “scale and coverage” to “precise and balanced”, and help Shandong Province’s urban–rural integration strategy to be realised.

Author Contributions

Conceptualization, Y.W. and Y.F.; Data curation, Y.F.; Methodology, Y.F.; Resources: Y.F.; Software, Y.F.; Supervision, Y.W.; Visualisation, Y.F.; Writing—original draft, Y.F.; Writing—review and editing, Y.W. All authors have read and agreed to the published version of the manuscript.

Funding

This research is funded by the National Natural Science Foundation of China (Grant No. 51408344) and the Qingdao Philosophy and Social Science Planning Project (QDSKL2101111, QDSKL2401104).

Data Availability Statement

The raw data supporting the conclusions of this article will be made available by the authors on request.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. A comprehensive research framework designed for the analysis of spatial alignment between public service facilities and population distribution patterns.
Figure 1. A comprehensive research framework designed for the analysis of spatial alignment between public service facilities and population distribution patterns.
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Figure 2. Research areas.
Figure 2. Research areas.
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Figure 3. Degree of aggregation at different times.
Figure 3. Degree of aggregation at different times.
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Figure 4. Total service factor Kernel density.
Figure 4. Total service factor Kernel density.
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Figure 5. Nuclear density analysis charts for each type of facility.
Figure 5. Nuclear density analysis charts for each type of facility.
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Figure 6. Topology of facilities by category.
Figure 6. Topology of facilities by category.
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Figure 7. Overall service factor coupled to population density and spatial structure diagram.
Figure 7. Overall service factor coupled to population density and spatial structure diagram.
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Figure 8. Coupling of various service factors with population density.
Figure 8. Coupling of various service factors with population density.
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Table 1. Categorization and quantitative analysis of public service facility-related POI data within Shandong Province.
Table 1. Categorization and quantitative analysis of public service facility-related POI data within Shandong Province.
Primary IndicatorSecondary IndicatorNumber of POIs
Accommodation and food servicesChinese and Western eateries, fast food outlets, cafés, teahouses, cold beverage stores, patisseries and dessert parlours, casual dining establishments, as well as hotels, inns, and other accommodation-related services628,139
Government institutions and social organisationsGovernment offices, social organisations, industrial, commercial and fiscal institutions305,087
Living servicesConvenience stores, supermarkets, shopping malls, household appliance retailers, electronics shops, hardware outlets, sporting goods stores, stationery suppliers, specialty boutiques, general markets, business offices, beauty salons, spas, automotive and motorcycle repair garages, office service centres, household goods and appliance repair workshops, laundromats, wedding and funeral service providers, and housekeeping services708,079
Medical servicesHospitals, clinics, emergency centres, disease prevention centres, health management centres, physiotherapy, pharmacies165,327
Educational servicesKindergartens, elementary schools, middle schools, universities, training centres, adult education programmes and vocational and technical training institutions117,688
Banking and financial servicesBanks, securities firms, insurance providers, finance companies, futures trading companies, and automated teller machines (ATMs)47,466
Transport servicesBus terminals, railway stations, airports, ticket counters, postal service centres, logistics and parcel delivery stations, seaports, metro systems, buses, and parking lots279,417
Recreational servicesScientific and technological museums, general museums, libraries, archives, periodical publications, sports venues, recreational and leisure amenities, holiday retreats, movie theatres, cultural/activity hubs, exhibition spaces, and cultural palaces73,352
Scenic spotsParks and squares, scenic spots24,730
Table 2. Criteria for assessing coupling coordination.
Table 2. Criteria for assessing coupling coordination.
Coupling Coordination LevelCoordination LevelType
0 < D ≤ 0.3 Serious disturbancesSerious disturbances in recession
0.3 < D ≤ 0.5 Slightly out of tunePrimary Coupled Coordination
0.5 < D ≤ 0.7 Moderate CoordinationIntermediate Coupled Coordination
0.7 < D ≤ 1 Good CoordinationAdvanced Coupled Coordination
Table 3. Percentage of regions characterised by high aggregation and sub-aggregation patterns (%).
Table 3. Percentage of regions characterised by high aggregation and sub-aggregation patterns (%).
TimeHigh Aggregation AreasSub-Aggregation Areas
RestdayWorkdayRestdayWorkday
7:000.8960.5964.3094.137
9:000.7170.6314.0663.963
12:000.5670.6133.5183.879
15:000.5820.6133.7603.879
18:000.6410.6623.9134.064
21:000.6980.6804.2601.794
24:000.5740.6093.9253.758
Table 4. The PSMI.
Table 4. The PSMI.
POI TypesMorningAfternoonEvening
RestdayWorkdayRestdayWorkdayRestdayWorkday
Accommodation and food services0.0160.0130.014−0.4140.0160.013
Government institutions and social organisations0.0650.0600.0610.0590.0650.060
Housing services0.0190.0150.0150.0140.0170.014
Medical services0.4530.4500.4490.4480.4530.448
Educational services0.5230.5190.5200.5190.5240.519
Banking and financial services0.690−0.0260.6860.6850.6900.686
Transport services0.017−0.030.0130.0120.0150.012
Recreational services0.3820.3770.3780.370.3810.377
Scenic spots0.2140.2120.2130.2110.2160.212
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Feng, Y.; Wang, Y. Study on the Spatial Matching Between Public Service Facilities and the Distribution of Population—An Example of Shandong Province. Sustainability 2025, 17, 7866. https://doi.org/10.3390/su17177866

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Feng Y, Wang Y. Study on the Spatial Matching Between Public Service Facilities and the Distribution of Population—An Example of Shandong Province. Sustainability. 2025; 17(17):7866. https://doi.org/10.3390/su17177866

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Feng, Yin, and Yanjun Wang. 2025. "Study on the Spatial Matching Between Public Service Facilities and the Distribution of Population—An Example of Shandong Province" Sustainability 17, no. 17: 7866. https://doi.org/10.3390/su17177866

APA Style

Feng, Y., & Wang, Y. (2025). Study on the Spatial Matching Between Public Service Facilities and the Distribution of Population—An Example of Shandong Province. Sustainability, 17(17), 7866. https://doi.org/10.3390/su17177866

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