## 4 Results  
### Coefficient Test of the MM-G2 SFCA Method  
We chose a series of search radii and distance decay coefficients for experimentation to verify the roles of these two coefficients in the MM-G2 SFCA method. Unless otherwise specified, the MM-G2 SFCA method discussed in the following section uses the standardized gravity model by default. Fixed-duration isochrones, such as 10 min community life circles and 30 min travel time circles, are crucial tools for assessing accessibility. They are commonly used for tasks related to accessibility analysis. Isochrones with 10 to 30 min search radii are often chosen for community-wide accessibility analysis [23], while city-wide search radii may extend to hours [22]. To test the performance of the MM-G2 SFCA method with different search radii, 10 to 60 min intervals at 10 min increments, along with supplementary 90 and 120 min intervals, are selected in our experiments. Figure 5 shows the accessibility of the study area as the search radius increases from 10 min to 60 min, as well as at 90 min and 120 min, with the distance decay coefficient set at 1. Figure 4: Technical workflow for the research. The search radius represents two interrelated concepts: the range within which medical facilities provide services and the maximum time that residents are willing to spend (cost) to access these facilities. At a very low search radius, the accessibility values are concentrated in a few areas with a high density of medical facilities, leaving vast regions with an accessibility value of zero. As the search radius expands, the spatial distribution of accessibility results across the region becomes more uniform, leading to a more rational representation of the service capacity of the facilities. Figure 5: Accessibility of the study area calculated by the MM-G2 SFCA method under a range of search radii. Unlike common public facilities such as parks, dining, and shopping, medical service facilities are irreplaceable, leading residents to generally accept higher time costs. Therefore, taking into account the typical time cost, the search radius for the experiment in the following section is set at 60 min. The distance decay coefficient regulates the degree to which distance (cost) influences the supply-demand ratio and accessibility. The selection of distance decay coefficients is guided by the existing literature and empirical observations. For individual movement at the urban scale, distance decay coefficients typically ranges from 1.0 to 2.0 [25]. In accessibility studies using the gravity model, distance decay coefficients typically range from 0.9 to 2.29 [7; 8; 9]. These values, derived from empirical studies analyzing travel behavior and accessibility patterns in various urban settings, serve as a benchmark for understanding the sensitivity of accessibility measures to distance. Additionally, the modifications to the supply-demand relationship in the MM-G2 SFCA method (Equation (6)) on the distance decay coefficient can be regarded as \(2\beta\). Considering the aforementioned points, an initial distance decay coefficient range of 0.5 to 2.0 is selected for the experiment. However, upon analyzing the experimental results, it is evident that the relatively gradual distance decay curve of the standardized gravity model suggests that an increase in the distance decay coefficient has a relatively minor impact on accessibility. Consequently, a distance decay coefficient range of 0.5 to 4.0 is selected, as illustrated in Figure 6.  
Figure 6: \(Cont.\)  
It can be observed that only significant changes in the distance decay coefficient result in noticeable differences in accessibility. The experiment demonstrates that the distance decay coefficient can control the distance decay effect in the MM-G2 SFCA method using the standardized gravity model and is relatively insensitive.