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Rapid urbanization in China has led to an exponential increase in the stocks of metals used in cities. Exploring their amount and growth patterns is an important way to forecast future metal demand and identify the potential for urban mining. Here, we use a combination of bottom-up and GIS tools to estimate the amount of in-use stocks and scrap metal of steel, copper, and aluminum in 366 regions of mainland China from 2010 to 2020. We then downscaled the 2020 metal scrap volume based on a multi-source dataset of socioeconomic factors. Finally, the accessibility of the urban mining pilot base (UMPB) was calculated using the two-step floating catchment area method (2SFCA), and the spatial layout assessment analysis of the UMPB was conducted under the supply–demand balance perspective. The results showed that the total in-use stocks of steel, copper, and aluminum increased from an initial 3186 million tons to 5216 million tons, with a corresponding trend of continued growth in the amount of metal scrap. The high value of scrap metal in 2020 is concentrated in the Beijing–Tianjin–Hebei urban agglomeration, the Yangtze River Delta region, and the Chengdu–Chongqing metropolitan area. The accessibility results show that the road network distance-based accessibility covered a smaller area than the Euclidean distance-based accessibility, but when the UMPB service radius was set to 300 km, the road network distance-based accessibility could also cover most of the eastern part of China. The spatial evaluation results of UMPB show that for service radii of 200 km and 300 km, low-supply and high-demand areas account for 6.32 percent and 5.89 percent, respectively.

The spatial distribution and accessibility of urban public service facilities affect socioeconomic factors in the lives of residents, especially housing prices. Given that most previous studies focus on the accessibility of a certain, single type of facility and its impact on housing prices, this research uses improved two-step floating catchment area (2SFCA) methods by considering the differences in the service capacity of different types of public service facilities in real life to evaluate their accessibility to residential communities in Jinan city based on 3117 facilities covering 11 different kinds of facilitates. Then, we assess the spatial distribution of the impact of the accessibility of different public service facilities on housing prices in Jinan city through a local indicator of a spatial association (LISA) cluster diagram generated based on the bivariate local Moran’s index. Our objectives are to assess the accessibility of multiple public service facilities using an improved 2SFCA method and to explore the spatial correlations between the accessibility of public service facilities and housing prices. The results show that the housing prices in Jinan are clustered and that the areas with high housing prices are mainly concentrated in the Lixia District and the center of the downtown area. The accessibility of medical, shopping, educational and bus stop facilities in the Lixia District is better than that in other districts. The accessibility of shopping, medical and tourist attraction facilities has the most significant impact on housing prices, and the number of communities in which the accessibility of these public service facilities and housing prices form a positive correlation cluster accounts for 50.5%, 47.9% and 45.8% of all communities, respectively. On the other hand, educational accessibility and bus stop accessibility have nothing to do with housing prices, and the number of communities in which the accessibility of these public service facilities forms a not-significant cluster with housing prices accounting for 51.1% and 56.5% of the total, respectively. In this study, the combined 2SFCA method is used to improve the method for evaluating the accessibility of a variety of public service facilities, and its applicability is verified by practical application. By analyzing the spatial correlation between accessibility and housing prices, we expand our understanding of accessibility and show that it plays a central role in housing prices, which will help to improve the spatial pattern of urban public places in the future, provide support for decision makers and provide a reference for the government and real estate developers.

Urban vitality is a spatial phenomenon and a public service. Previous studies often did not measure the fairness of the accessibility of urban vitality. This research analyzed the spatial distribution of urban vitality in Wuhan as a case study area using big data from multiple sources. The study used the two-step floating catchment area method (2SFCA) to measure the accessibility level of each residential district to the vibrant zones (VZs). Furthermore, the inequality in the level of accessibility of residential areas with different housing prices was assessed on the basis of the Gini coefficient. The main conclusions are as follows: (1) the Gini coefficient of reaching the accessibility level of high-grade VZs is 0.426, and the corresponding sub-high-grade Gini coefficient is 0.274. This shows that the inequality in accessibility of different residential areas is more obvious as the level of vitality is higher and (2) residential areas with high housing prices have greater accessibility than those areas with low housing prices. It was also noticed that the level of accessibility and fairness in vitality is generally higher in central urban areas than in suburban areas. The Gini coefficient of high-grade vitality is generally higher than that of sub-high-grade. The results of this study provide a reference for researching the accessibility level of urban vitality, which considers the needs of population, and can also provide guidelines in urban planning regarding the allocation of services and resources.

Equity of urban medical services affects human health and well-being in cities and is important in building ‘just’ cities. We carried out a quantitative analysis of the spatial accessibility of medical services considering the diverse demands of people of different ages, using outpatient appointment big data and refining the two-step floating catchment area (2SFCA) method. We used the traditional 2SFCA method to evaluate the overall spatial accessibility of medical services of 504 communities in Xiamen city, considering the total population and the supply of medical resources. Approximately half the communities had good access to medical services. The communities with high accessibility were mainly on Xiamen Island, and those with low accessibility were further from the central city. The refined 2SFCA method showed a more diverse and complex spatial distribution of accessibility to medical services. Overall, 209 communities had high accessibility to internal medicine services, 133 to surgery services, 50 to gynecology and obstetrics services, and 18 to pediatric services. The traditional method may over-evaluate or under-evaluate the accessibility of different types of medical services for most communities compared with the refined evaluation method. Our study can provide more precise information on urban medical service spatial accessibility to support just city development and design.

With the increasingly prominent phenomenon of social stratification in urban development, it is of practical significance to study the accessibility of elderly care facilities for different social groups. The study improves the mathematical model of the two-step floating catchment area method (2SFCA) as regards three aspects: the accurate demand of elderly residents, the comprehensive supply capacity of elderly care facilities, and the precision of travel costs. Taking Tianjin as an example, the study measures the accessibility of elderly care facilities from the perspective of social stratification. The results show that: (1) The improved model is more practical in evaluating the accessibility of elderly care facilities. (2) The spatial distribution of social groups in Tianjin presents a concentric structure and the social stratification in the periphery area is more obvious. (3) The accessibility scores of elderly care facilities are higher in the city center, lower in the periphery area, higher in the south, and lower in the north. (4) High- and middle-income groups have better accessibility, while the elite and low-income groups have worse accessibility.

Equal accessibility to healthcare services is essential to the achievement of health equality. Recent studies have made important progresses in leveraging GIS-based location–allocation models to optimize the equality of healthcare accessibility, but have overlooked the hierarchical nature of facilities. This study developed a hierarchical maximal accessibility equality model for optimizing hierarchical healthcare facilities. The model aims to maximize the equality of healthcare facilities, which is quantified as the variance of the accessibility to facilities at each level. It also accounts for different catchment area sizes of, and distance friction effects for hierarchical facilities. To make the optimization more realistic, it can also simultaneously consider both existing and new facilities that can be located anywhere. The model was operationalized in a case study of Shenzhen, China. Empirical results indicate that the optimal healthcare facility allocation based on the model provided more equal accessibility than the status quo. Compared to the current distribution, the accessibility equality of tertiary and secondary healthcare facilities in optimal solutions can be improved by 40% and 38%, respectively. Both newly added facilities and adjustments of existing facilities are needed to achieve equal healthcare accessibility. Furthermore, the optimization results are quite different for facilities at different levels, which highlights the feasibility and value of the proposed hierarchical maximal accessibility equality model. This study provides transferable methods for the equality-oriented optimization and planning of hierarchical facilities.

Background Poor spatial accessibility to hospital services is associated with higher morbidity and mortality rates among people living with disability. Improved methods to evaluate spatial accessibility are needed. This study measured the potential spatial accessibility of people living with disability by applying four configurations of the two-step floating catchment area (2SFCA) method to recommend the best model for use in health services research. Methods 2SFCA and an enhanced version (E2SFCA) were used to measure hospital accessibility for people living with disability. We also developed and embedded a non-spatial severity index into the two 2SFCA models. We used 16,186 records of people living with disability experience to evaluate the methodological performance across 68 neighbourhoods of the city of Ahvaz, located in south-western Iran. The models’ performance were measured through correlation of the four accessibility scores with the distance to closest hospital for each neighbourhood centroid. Results Among the four models used to measure spatial accessibility, the E2SFCA integrated with the severity index displayed the best performance. Most people with disabilities lived in neighbourhoods located in the South-western and central areas of the city. Interestingly, south-western neighbourhoods had poor hospital accessibility score and were identified as unmet need areas for access to health services. Conclusions Inclusion of the severity factor in the E2SFCA improved access measurements. Identifying areas with poor levels of hospital accessibility can help policymakers design tailored interventions and improve accessibility to hospital-based care in urban settings for people living with disability.

In recent decades, access to primary health care has become a crucial issue for health policy planners and researchers. One of the fundamental problems is inequitable access to health care due to imbalanced resource distributions between health care providers and population location. Accordingly, this study aims to examine the spatial access to Community Health Centers (CHC) in the Asmat district, one of the most isolated regions in Papua, Indonesia. We conducted the study using a two-step floating catchment area (2SFCA) method to quantify accessibility value to primary health care of each village in the district of Asmat. By taking five distance thresholds ranging from 5 to 25 km with an increment of 5 km, the results indicate that distance has a varying impact on each village. For example, within a 5-km distance threshold, 74% of villages have a zero score or have no access to CHCs, 22% have a score 100 or meet the minimum score recommended by World Health Organization (WHO). Two major related factors of these geographic disparities are the unequal distribution of CHCs and the high population dispersion. As an attempt to provide equal access to health care services, these results suggest that spatial access should be conscientiously considered by health planners and policy makers.

With the growing challenge of aging populations around the world, the study of the care services for older adults is an essential initiative to accommodate the particular needs of the disadvantaged communities and promote social equity. Based on open-source data and the geographic information system (GIS), this paper quantifies and visualizes the imbalance in the spatial distribution of elderly care facilities in 14,578 neighborhoods in downtown (seven districts) Shanghai, China. Eight types of elderly care facilities were obtained from Shanghai elderly care service platform, divided into two categories according to their service scale. With the introduction of the improved Gaussian 2-step floating catchment area method, the accessibility of two category facilities was calculated. Through the global autocorrelation analysis, it is found that the accessibility of elderly care facilities has the characteristics of spatial agglomeration. Local autocorrelation analysis indicates the cold and hot spots in the accessibility agglomeration state of the two types of facilities, by which we summarized the characteristics of their spatial heterogeneity. It is found that for Category−I, there is a large range of hot spots in Huangpu District. For Category−II, the hot-spot and cold-spot areas show staggered distribution, and the two categories of hot spot distribution show a negative correlation. We conclude that the two categories are not evenly distributed in the urban area, which will lead to the low efficiency of resource allocation of elderly care facilities and have a negative impact on social fairness. This research offers a systematic method to study urban access to care services for older adults as well as a new perspective on improving social fairness.

Parks are an important component of the green infrastructure in cities. They provide multiple benefits for residents’ life. Due to the uneven spatial distribution of parks, it is necessary to evaluate the spatial disparity about residents’ access to parks. The two-step floating catchment area method is suitable for measuring the accessibility of urban parks. However, few studies have noticed the representative of entrances of parks, especially adding them into the process of accessibility measurements. The floating catchment area is often determined by road speed and empirical travel time. In this article, the impact of multi-entrances of the park will be considered and real-time travel time is used in calculating accessibility. In a case of multi-entrance parks in Beijing, the average travel time of the sub-district is calculated, and with the support of the modified method, the spatial accessibilities of car driving, public transport and car-public transport mixed travel modes are obtained. The results show that the time–space compression effect of car driving is more obvious and the mixed travel mode presents the advantage of high accessibility index. This study has a theoretical and practical value for urban planning, such as advising urban planners on the siting of green park space.

Background Spatial accessibility to healthcare facilities has drawn much attention in health geography. In China, central and local governments have aimed to develop a well-organized hierarchical system of healthcare facilities in recent years. However, few studies have focused on the measurement of healthcare accessibility in a hierarchical service delivery system, which is crucial for the assessment and implementation of such strategies. Methods Based on recent improvements in 2SFCA (two-step floating catchment area) method, this study aims to propose a Hierarchical 2SFCA (H2SFCA) method for measuring spatial accessibility to hierarchical facilities. The method considers the varied catchment area sizes, distance decay effects, and transport modes for facilities at various levels. Moreover, both the relative and absolute distance effects are incorporated into the accessibility measurement. Results The method is applied and tested in a case study of hierarchical healthcare facilities in Shenzhen, China. The results reveal that the general spatial accessibility to hierarchical healthcare facilities in Shenzhen is unevenly distributed and concentrated. The disparity of general accessibility is largely caused by the concentrated distribution of tertiary hospitals. For facilities at higher levels, average accessibility of demanders is higher, but there are also larger disparities in spatial accessibility. The comparison between H2SFCA and traditional methods reveals that traditional methods underestimate the spatial disparity of accessibility, which may lead to biased suggestions for policy making. Conclusions The results suggest that the supply of healthcare resources at primary facilities is far from sufficient. To improve the spatial equity in spatial accessibility to hierarchical healthcare facilities, various actions are needed at different levels. The proposed H2SFCA method contributes to the modelling of spatial accessibility to hierarchical healthcare facilities in China and similar environments where the referral system has not been well designed. It can also act as the foundation for developing more comprehensive measures in future studies.

The layout of public service facilities and their accessibility are important factors affecting spatial justice. Previous studies have verified the positive influence of public facilities accessibility on house prices; however, the spatial scale of the impact of various public facilities accessibility on house prices is not yet clear. This study takes transportation analysis zone of Wuhan city as the spatial unit, measure the public facilities accessibility of schools, hospitals, green space, and public transit stations with four kinds of accessibility models such as the nearest distance, real time travel cost, kernel density, and two step floating catchment area (2SFCA), and explores the multiscale effect of public services accessibility on house prices with multiscale geographically weighted regression model. The results show that the differentiated scale effect not only exists among different public facility accessibilities, but also exists in different accessibility models of the same sort of facility. The article also suggests that different facilities should adopt its appropriate accessibility model. This study provides insights into spatial heterogeneity of urban public service facilities accessibility, which will benefit decision making in equal accessibility planning and policy formulation for the layout of urban service facilities.

China's rapid economic development has led to inequality in terms of property, education, and health. Equal access to basic public facilities has become a key concern of inclusive development policies. However, previous studies have paid little attention to the effects of different travel modes on the accessibility of basic public facilities. The present research fills this gap. Taking Xiamen city as a case study, it explores the degrees of horizontal and vertical equity by examining the accessibility of various basic public facilities, paying attention to different travel modes and travel times. The results for Xiamen city show that disadvantaged groups experience a greater level of inequity. By taking these aspects into account, one is better equipped to identify areas in the city where access to basic public facilities is in need of substantial improvement.

The hierarchical healthcare system is widely considered to be a desirable mode of the delivery of healthcare services. It is expected that the establishment of a hierarchical healthcare system can help provide better and more equal healthcare accessibility. However, limited evidence has been provided on the impacts of a hierarchical healthcare system on healthcare accessibility. This study develops an improved Hierarchical two-step floating catchment area (2SFCA) method, which incorporates variable catchment area sizes, distance friction effects and utilization efficiency for facilities at different levels. Leveraging the Hierarchical 2SFCA method, various scenarios are set up to assess the accessibility impacts of a hierarchical healthcare system. The methods are applied in a case study of Shenzhen. The results reveal significant disparity and inequality in healthcare accessibility and also differences between various facility levels in Shenzhen. The overall healthcare accessibility and its equality can be significantly improved by fully utilizing existing facilities. It is also demonstrated that allocating additional supply to lower-level facilities can generate larger accessibility gains. Furthermore, allocating new supply to primary facilities would mitigate the inequality in healthcare accessibility, whereas inequality tends to be aggravated with new supply allocated to tertiary facilities. These impacts cannot be captured by traditional accessibility measures. This study demonstrates the pivotal role of primary facilities in the hierarchical healthcare system. It can contribute to the literature by providing transferable methods and procedures for measuring hierarchical healthcare accessibility and assessing accessibility impacts of a hierarchical healthcare system in developing countries.

To ensure adequate access to urban facilities, it is important for urban planners to achieve equity in the geographical arrangement of such facilities. For the evaluation of vertical spatial equity in the geographical organization of urban facilities, there is a requirement to examine whether and to what degree the variation in spatial accessibility to urban facilities corresponds to the variation in aspatial accessibility for such facilities. While no studies so far measure vertical spatial equity in accordance with ‘need’ and ‘demand’ based approaches of equity with a focus on both spatial and aspatial accessibility. Therefore, this paper attempts to measure an integrated spatial accessibility index for the evaluation of geographic variation in spatial accessibility to urban facilities, and then, seeks to integrate spatial accessibility and aspatial accessibility in one framework to evaluate vertical spatial equity in the geographical arrangement of urban facilities. This paper measures integrated spatial accessibility index for urban facilities following the concept of 2SFCA method incorporating supply and demand for urban facilities, the travel distance or time that users are willing to cover to reach such facilities, and the interaction of residents across geographic boundaries. Aspatial accessibility to urban facilities is defined through demographic-demand index and social-need index for those facilities. Spearmen correlation coefficient, spatial analysis models (local spatial autocorrelation in this case), and overlay are used to assess the association between spatial accessibility and aspatial accessibility to urban facilities. The results indicate there exists a variation (inequality) in spatial accessibility to urban facilities in the case study area (DCC). Urban facilities are inequitably distributed within DCC, as high-social-need areas and high-demographic-demand areas have low spatial accessibility to such facilities. These areas should be prioritized in distributing urban facilities in the future, and thus, it can help urban planners to achieve an equitable distribution of urban facilities. Keywords: Spatial accessibility, Aspatial accessibility, Spatial equity, Urban facilities, 2SFCA

While great progress in the development of a methodological approach to measure the accessibility of healthcare services has been made, the exclusion of the complex multi-mode travel behavior of urban residents and a rough calculation of travel costs from the origin to the destination limit its potential for making a detailed assessment, especially in urban areas. In this paper, we aim to describe and implement an enhanced method that enables the integration of multiple transportation modes into a two-step floating catchment area (2SFCA) method to estimate accessibility. We used a travel-mode choice survey, based on distance sections, to determine the complex multi-mode travel behavior of urban residents. Taking Nanjing as a study area, we proposed complete door-to-door approaches to determine every aspect of basic transportation modes. Additionally, we processed open data to implement an accurate computing of the origin-destination (OD) time cost. We applied the enhanced method to estimate the accessibility of residents to hospitals and compared it with three single-mode 2SFCA methods. The results showed that the proposed method effectively identified more accessibility details and provided more realistic accessibility values.

Limited studies focus on educational equity from the spatial accessibility perspective. This study combines survey data and big data and proposes a multi-mode Huff two-step floating catchment area (MMH2SFCA) method to calculate accessibility while considering multiple travel modes and school attractiveness. This method can also calculate education quality by extending the accessibility in each community. Results show that our proposed method can reliably identify the accessibility differences of schools across communities. The case study indicates an inequitable distribution of educational accessibility and quality. The communities with high accessibility are concentrated in the urban center and exurban zones surrounding schools, whereas high-quality areas are mainly concentrated in the urban center. Correlation analysis suggests that the educational quality of communities with high accessibility is not always high. The findings of this study can provide improvement for accessibility measurements and help explore a new research perspective for educational equity research.

Spatial accessibility is an important factor for planning healthcare services to maintain a quality life for the metropolitan area. The metropolitan suburb is a special area for its location and rapidly changing population during urbanization. Taking Qingpu district, a suburb of Shanghai as a case, this study evaluated the spatial accessibility to healthcare services of 203 villages and neighborhoods based on the Two-Step Floating Catchment Area (2SFCA) method by ArcGIS software. The result shows that the spatial accessibility in the whole district is quite uneven under lower thresholds, and the spatial differences are beyond the traditional zoning of East Qingpu, New City and West Qingpu. The worst accessibility was mainly distributed at the edges of Jinze, Liantang and Zhujiajiao, while the best accessibility was mainly distributed in the New City and the region close around it. The average value of the spatial accessibility in Qingpu is 2.84, with a reach equal under 90 min threshold by bus index of 2.85, or an under 60 min threshold by self-driving index of 2.70. Secondly, the difference shows a new pattern, that is the spatial accessibility could be affected by both the New City and the Central City. Thirdly, the transportation mode, urbanization, the density of road network and bus lines, as well as the number of doctors in each healthcare service would directly affect the spatial accessibility. Lastly, in order to improve the spatial accessibility in metropolitan suburbs, greater effort is needed in increasing the numbers of bus stations and doctors, especially the areas which are farthest from the New City or the Central City, such as Jinze, and Lian Tang town in Qingpu. We acknowledge that the public transportation is vital to the accessibility to healthcare services. We also emphasize that healthcare services should be planned based on the anticipated future trends of population agglomeration. Our results for Shanghai are applicable to other big cities that are experiencing similar rapid urbanization in China, or other developing countries in Southeast Asia, South Asia, South America and Africa.

Two-step floating catchment area (2SFCA) methods that account for multiple transportation modes provide more realistic accessibility representation than single-mode methods. However, the use of the impedance coefficient in an impedance function (e.g., Gaussian function) introduces uncertainty to 2SFCA results. This paper proposes an enhancement to the multi-modal 2SFCA methods through incorporating the concept of a spatial access ratio (SPAR) for spatial access measurement. SPAR is the ratio of a given place’s access score to the mean of all access scores in the study area. An empirical study on spatial access to primary care physicians (PCPs) in the city of Albuquerque, NM, USA was conducted to evaluate the effectiveness of SPAR in addressing uncertainty introduced by the choice of the impedance coefficient in the classic Gaussian impedance function. We used ESRI StreetMap Premium and General Transit Specification Feed (GTFS) data to calculate the travel time to PCPs by car and bus. We first generated two spatial access scores—using different catchment sizes for car and bus, respectively—for each demanding population location: an accessibility score for car drivers and an accessibility score for bus riders. We then computed three corresponding spatial access ratios of the above scores for each population location. Sensitivity analysis results suggest that the spatial access scores vary significantly when using different impedance coefficients (p

Background Shenzhen has rapidly grown into a megacity in the recent decades. It is a challenging task for the Shenzhen government to provide sufficient healthcare services. The spatial configuration of healthcare services can influence the convenience for the consumers to obtain healthcare services. Spatial accessibility has been widely adopted as a scientific measurement for evaluating the rationality of the spatial configuration of healthcare services. Methods The multi-modal two-step floating catchment area (2SFCA) method is an important advance in the field of healthcare accessibility modelling, which enables the simultaneous assessment of spatial accessibility via multiple transport modes. This study further develops the multi-modal 2SFCA method by introducing online map APIs to improve the estimation of travel time by public transit or by car respectively. Results As the results show, the distribution of healthcare accessibility by multi-modal 2SFCA shows significant spatial disparity. Moreover, by dividing the multi-modal accessibility into car-mode and transit-mode accessibility, this study discovers that the transit-mode subgroup is disadvantaged in the competition for healthcare services with the car-mode subgroup. The disparity in transit-mode accessibility is the main reason of the uneven pattern of healthcare accessibility in Shenzhen. Conclusions The findings suggest improving the public transit conditions for accessing healthcare services to reduce the disparity of healthcare accessibility. More healthcare services should be allocated in the eastern and western Shenzhen, especially sub-districts in Dapeng District and western Bao’an District. As these findings cannot be drawn by the traditional single-modal 2SFCA method, the advantage of the multi-modal 2SFCA method is significant to both healthcare studies and healthcare system planning.

Emergency Medical Services form the backbone of the prehospital emergency medical care system in the United States. Prompt treatment and transport to a definitive care facility provide the greatest chance for reduced morbidity and mortality. People’s ability to use this public service can be a determinant of their wellbeing, as well as a measure of community disaster preparedness. The objective of this study is to measure spatial access to Emergency Medical Service (EMS) systems, and to quantify local demand for these services. EMS facilities and population location data are mapped across Utah. Spatial access is measured using an enhanced two-step floating catchment area method (E2SFCA) that incorporates both travel time and EMS ground transport capacity. Demand is estimated from the EMS spatial access metric and local population count. Results are evaluated using actual response times and patient death rates. The study finds that the 2SFCA method adequately measures relative access across large areas that encompass multiple service regions. In conclusion, additional improvements and future research potential are discussed.

Background The two-step floating catchment area (2SFCA) method, which is one of the most widely used methods for measuring healthcare spatial accessibility, defines the catchment area of each facility as the area within a certain distance from the facility. However, in some cases, the service utilization behavior is constrained by administrative boundaries, therefore the definition of catchment area within a certain distance may be inappropriate. Methods In this study, we aim to propose a modification of the 2SFCA method for measuring spatial accessibility to healthcare services in a system constrained by administrative boundaries. The proposed method defines the catchment areas of healthcare facilities within certain administrative units. The method is applied in a case study of the healthcare services in Yanqing District of Beijing, China. Three types of healthcare facilities, including general hospitals, community healthcare centers and stations, are included. Results Based on the sensitivity analysis of the distance-decay parameter β, result of the β = 1 scenario is relatively appropriate and is utilized for further analysis. The difference between spatial accessibility with or without constraint of administrative boundary is relatively significant. The results of the proposed model show that the village-level spatial accessibility to healthcare services shows a significant disparity, and the uneven distribution of general hospitals is the main cause. Conclusions The constraint of administrative boundary has a significant impact on healthcare accessibility, which verifies the validity of the modification proposed by this study in empirical studies. The empirical results also lead to policy recommendations to improve healthcare equity in the study area. At the town-level, the improvement of equity in healthcare accessibility could be achieved in two ways. First, the sizes of community healthcare centers in towns with small accessibility scores should be expanded. Second, new general hospitals can be built in the eastern part of Yanqing District. Within each town, to improve the equity in healthcare accessibility, community healthcare stations should be expanded or newly built in the periphery villages.

Assessing the access to fire service at an urban scale involves accounting for geographical impedance, demand, and supply, thus both spatial and non-spatial dimensions must be taken into account. Therefore, in this paper, an optimized two-step floating catchment area (F-2SFCA) method is proposed for measuring urban fire service access, which incorporates the effects of both spatial and non-spatial factors into fire service access. The proposed model is conducted in a case study to assess the fire service accessibility of Nanjing City, China, and then compares its differences and strengths to the existing 2SFCA (two-step floating catchment area) methods. The experimental results demonstrate that the proposed method effectively quantifies the actual fire service needs and reflects a more realistic spatial pattern of accessibility (i.e., high accessibility level corresponded to a low fire service needs). In addition, we teste the relationship between service accessibility and the facility busyness using the inverted 2SFCA method. The empirical findings indicate that the weighted average accessibility obtained by F-2SFCA is reciprocal to facility busyness across the study area (based on a 5-min catchment), and fits an obvious nonlinear correlation with the high R-square values. The above results further prove the effectiveness and accuracy of the proposed method in characterizing the accessibility of fire services.