Exploring the Spatial Patterns of Accessibility to Metro Services Considering the Locations of Station Entrances/Exits

Abstract

Accessibility to metro services is often evaluated based on the locations of stations. However, compared to the location of station itself, focusing on its entrances/exits offers a more accurate approach to assessing station supply and demand levels. Despite this, research focusing on the supply of and demand for metro services concerning metro entrances and exits remains limited. This study employed multi-source geospatial data from Xiamen, China, to examine the supply and demand dynamics of metro stations with a particular emphasis on entrances/exits. In the first phase, we treated entrances/exits as supply facilities and used land plot boundaries as the fundamental spatial units for accessibility calculations. Taking into account the layout characteristics of entrances/exits, along with the traffic generation of various land-use types, we employed the Gaussian two-step floating catchment area (G2SFCA) method to gauge the supply and demand levels of plots. Subsequently, we computed the spatial supply-and-demand relationships of station entrances/exits for both station-level and shared usage level of entrances/exits. We found that the accessibility from plots to entrances/exits diverged from previously observed spatial distribution trends, being higher in city centers, regional boundaries, and terminal stations and lower in transitional areas. Moreover, “metro accessibility” and the “imbalance index of entrances/exits” are associated with the primary functions of stations and the surrounding urban development; yet they exhibit spatial heterogeneity. The stations with a high value for “imbalanced index of entrances/exits” were always near some business parks, and “metro accessibility” seemed to be more easily affected by location factors. Based on two metrics, stations were categorized into four types, each displaying unique characteristics regarding location distributions, entrance/exit configurations, and commuting passenger sources. This research aims to identify the phenomenon of unfair transport in metro service from the perspective of their entrances, inform the optimization of metro station designs, and tailor planning recommendations, ultimately enhancing transport equity and contributing to sustainable urban built environments.

1. Introduction

Rapid global urbanization and population growth have led to numerous urban challenges, including traffic congestion, carbon emissions, and environmental pollution [1,2,3]. In this context, the metro system has been considered one of the important ways to solve urban traffic congestion and achieve energy conservation and emission reduction due to its rapid speed, high capacity, and minimal environmental impact [4,5,6]. Serving as the lifeblood of urban areas, metro systems frequently shoulder the responsibility of linking key nodes within a city, with station entrances/exits serving as vital junctures connecting the metro with the surrounding urban fabric. Properly designing the layout of metro entrances/exits is crucial for guiding people and addressing various fundamental issues [7]. Adding extra entrance/exit gates will shorten the walking distance between travelers’ origins/destinations and stations, thereby enhancing accessibility and user convenience [8]. In addition, the level of integration between station entrances and adjacent structures can yield diverse value-added benefits for the surrounding built environment [9]. Therefore, a deliberate focus on the spatial organization of entrances/exits is imperative to optimize the holistic development of metro networks.

The metro, being a public good, necessitates a judicious and equitable allocation of limited resources for its sustainable development [10]. Assessing the supply and demand levels of the metro helps guide metro construction and aids urban planners and decision-makers in optimizing metro and urban planning [11]. However, at present, many cities still have extensive planning and construction problems in the development of the metro. They do not take into account the demand for the integrated development of supporting facilities, metro stations, and entrances/exits, resulting in stations and entrances that fail to adequately meet the actual travel needs of residents [12]. Utilizing entrance/exit accessibility as a spatial unit can guide the rational allocation of more refined urban traffic resources, thus significantly enhancing the equity of metro supply and demand. However, few researchers have paid attention to the supply and demand levels of metro entrances/exits. Most of the existing supply-and-demand relationship calculations rely on broad spatial units such as traffic analysis zones (TAZs), census collector districts (CCDs), or larger-scale grid units [13,14]. However, these units lack the necessary spatial precision required for accurately assessing the supply and demand dynamics at metro entrances/exits. In addition, the varied land properties and intensities of the entrance/exit connections correspond to diverse travel volumes [15,16]. For example, according to the research of Weerasinghe and Bandara [17], residential uses, commercial uses, educational uses, health uses, private offices, and tourism, compared with other land-use types, play significant roles in improving the attraction rate of travel; in particular, the role of private offices is almost several times that of the other types. Considering these disparities in land use also has a great influence on the calculation of the spatial-level difference between metro supply and demand. Therefore, it is necessary further to refine the spatial measurement unit of the demand side and consider the impacts of land-use differences on the metro potential travel volume.

This study employed the Gaussian two-step floating catchment area (G2SFCA) method to measure accessibility. The method is recognized for its effectiveness in measuring accessibility by considering both supply and demand sides [10,18,19,20] and is suitable for measuring the supply-and-demand relationship at metro entrances/exits. Therefore, leveraging multi-source data, the G2SFCA method was optimized in two key aspects to analyze the supply and demand levels of station entrances/exits: firstly, by measuring accessibility through entrances/exits as research objects at the supply end, and secondly, by refining the calculation of land-use disparities at the demand end. The study will hopefully contribute to providing urban planners and authorities with strategies to optimize the integration of metro network layouts and urban infrastructure and ultimately, to improving the accessibility and convenience experienced by citizens.

The remaining sections are organized as follows: Section 2 reviews the existing literature. Section 3 outlines the related datasets, study methods, and study area we selected. In Section 4, the data results on accessibility and the supply and demand characteristics of stations are displayed and analyzed in detail. Finally, we discuss our work in Section 5 and present concluding remarks in Section 6.

2. Literature Review

2.1. Entrance Space

The entrance and exit spaces of the stations, serving as the link between the metro and the urban surface, play a crucial role in enhancing urban connectivity. Previous studies have indicated that a reasonable layout of entrances/exits is essential for effectively directing and managing passenger flow. For instance, Wang et al. [6] showed that, compared to metro stations, the distance between the locations of entrances/exits and departure points aligns more in line with individuals’ perceived feeder distance. This is mainly due to underground spaces lacking traffic obstacles like traffic lights, which facilitates smoother travel. Research suggests that strategically placing entrances and exits can significantly enhance convenience and improve travel efficiency [6]. Furthermore, Du and He [9] found a positive correlation between commercial real estate prices and the integration level of entrances/exits, with properties demonstrating seamless integration commanding premiums of over 40%. This finding underscores how the convenience of entrances/exits impacts individuals’ travel preferences. Additionally, Xu et al. [21] suggest that an equidistant insertion entrance layout along strip-style metro commercial streets enhances evacuation efficiency.

However, there are few studies on entrances/exits, while there are many studies on stations. Most of them treat entrances/exits solely as independent variables to assess the influence on dependent variables, such as subway ridership, which does not adequately address the actual needs. For instance, Li et al. [4] and Gan et al. [22] explored the relationship between the number of entrances/exits and subway ridership, finding a positive correlation between them. Similarly, Lin et al. [5] investigated the bicycle catchment area (BCA) of subway stations and confirmed that the number of entrances/exits is positively correlated with these areas. Shen et al. [23] examined the influence mechanism of the transfer rates between shared bicycles and subways, proving that an increased number of entrances/exits can significantly increase the transfer rate. Additionally, Li et al. [24] suggested that a greater number of entrances/exits would reduce the travel time of shared bicycles connecting to the subway in suburban area. While these studies highlight the key role of subway entrances in improving station ridership and traffic efficiency, they also reveal a lack of sufficient attention to the entrance as the research object. Therefore, this paper positions entrances/exits as the research focus, aiming to enhance accuracy and better meet practical needs.

2.2. Metro Supply-and-Demand Relationship

2.2.1. The Calculation of Supply and Demand

With the rapid development of metro systems, they are also confronted with challenges such as dense passenger flow and severe crowd congestion during the peak hours [25]. Hence, an analysis of metro resource allocation based on the supply-and-demand relationship is imperative. Research on transportation equity primarily involves equity performance evaluation and accessibility metrics. For the former, most research methods employ the Gini coefficient and Lorenz curve for evaluation [26,27,28]. For example, Delbosc and Currie [28] utilized the Gini coefficient combined with the Lorenz curve to conduct a system-wide assessment of the overall transport supply of the Melbourne population in Australia. Similarly, Peungnumsai et al. [27] proposed a performance evaluation index system for public transportation, employing supply indices to gauge service levels, demand indices to estimate travel needs, and the Lorenz curve and Gini coefficient to assess fairness. However, most of these works of research tended to aggregate data at larger spatial units such as TAZs, CCDs, or larger-scale grid units [13,14], which can obscure spatial nuances crucial for precise ingress and egress evaluations. This limitation hampers the ability to depict spatial disparities in supply and demand accurately.

For the latter, accessibility serves as a pivotal measure for assessing the disparities between supply and demand in public services by revealing spatial interactions [13,29]. Recent research has examined regional disparities in accessibility from the perspectives of efficiency and equity, and continues to evolve and refine accessibility measurement methodologies. These advancements include transitioning from the potential models and weighted average travel time models to incorporating parameters that account for time or distance impedance-decay, as well as various travel modes [18]. Accessibility measurement methods can achieve a variety of target-based accessibility measurements by adding different indicators to the measurement [30]. However, with regard to “metro accessibility”, most previous studies have lacked an analysis from the demand side, which is widely believed to correlate significantly with geographical location. For instance, Wu et al. [11] utilized space syntax to demonstrate that stations located centrally or near central business districts exhibit higher accessibility, while those situated at terminal points experience lower accessibility. Similar conclusions were drawn by Li et al. [31] and Yuan et al. [19], although they used different methodologies; this discrepancy may stem from the insufficient measurement of demand-side factors. From the perspective of supply and demand, metro accessibility is closely related to passenger demand and the supply of facilities [32]. Whether accessibility demonstrates a spatial gradient that decreases uniformly from the city center to the periphery remains a topic warranting further investigation. Therefore, it is necessary to further optimize the demand-side measurements to obtain more accurate assessments of subway accessibility.

2.2.2. Metro Accessibility Measurement

From the perspective of research methods, the measurement of metro accessibility has primarily relied on space syntax [11,31], the gravity model [33,34], and the 2SFCA method [10,19,35] (

Table 1. Comparison of different metro accessibility calculation methods.

Method	Basic Principle	Application Scope	Advantages and Limitations	References
Space Syntax	Analyzes the geometric and topological relationships of spatial structures to evaluate accessibility and fluidity.	Mainly used to analyze how building interiors or urban-level spatial design affects accessibility.	It analyzes the multi-level impacts of spatial layout on accessibility in depth, primarily focusing on geometric characteristics while neglecting socio-economic factors.	Wu et al. [11], Li et al. [31]
The Gravity Model	Based on Newton’s law of gravity, considers the distance decay effect and the service capacity of facilities.	Widely used in geographical research, particularly suitable for evaluating the attractiveness of services and regional accessibility.	It can quantify the distance decay effect and has a wide range of applications, but it mainly relies on the accuracy of assumptions and requires substantial data.	Wu et al. [33], Song et al. [34]
The 2SFCA Method	Calculates accessibility in two steps: first, service providers search for demanders within their service area; and, second, demanders search for service providers.	Suitable for evaluating the accessibility of public services such as healthcare and educational institutions.	It balances service supply and demand well, providing a relatively precise accessibility assessment.	Guo et al. [10], Yuan et al. [19], Liu et al. [35]
Cumulative Opportunities Model	Based on the number of service facilities that individuals can reach within a certain distance or time frame.	Suitable for evaluating the distribution of public transport facilities within walking distance.	It is simple and intuitive, and easy to understand and implement, but it focuses mainly on quantity rather than quality and ignores the differences in services.	Zhai et al. [38]
Spatial Barrier Model	Considers the impact of physical barriers (e.g., rivers and mountains) in geographical space on accessibility.	Suitable for evaluating service accessibility in complex terrain areas.	It quantifies the impeding effect of physical barriers but only considers physical factors and ignores socio-economic factors.	Weng et al. [39]

). The 2SFCA method was first proposed by Radke in 2000 [36] and was further improved by Luo and Qi [37] in 2009. This method introduces the concept of the “spatial threshold” to measure the influence of spatial impedance by a dichotomous approach. It can consider both the scale of supply and demand facilities and deal with the issue of distance decay, making it particularly suitable for analyzing the accessibility of metro stations and similar facilities [29]. Moreover, in the context of metro systems, passenger flows at station entrances/exits are intricately linked to the functions of surrounding areas [7]. Varied land-use types and development intensities correspond to differing travel volumes [16]. Therefore, to effectively measure the demand for metro entrances/exits, it is necessary to consider the potential travel volumes associated with various land-use types in the vicinity of metro stations.

For differences in travel rates associated with different land-use types or demographic groups, many scholars have incorporated POI weights from different categories within buffer zones to adjust these weights [40,41]. For instance, Li et al. [40] distinguished six POI types and developed a method to calculate the demand intensity at crosswalks. However, this approach often lacks the granularity necessary for effectively distinguishing between different land-use types, leading to inaccuracies in estimating the potential travel volume. In practice, the technical methods commonly used to estimate the traffic impact assessments of different construction projects can achieve this goal well. By calculating the “peak hour travel volume” index, these methods facilitate the estimation of potential demand scales for different land-use types [42]. Therefore, this study will use this method to measure the potential travel volume based on the traffic occurrence rates associated with various land-use types.

In response to the aforementioned issues, this study uses multi-source data to calculate the potential travel volumes based on the traffic occurrence rates of different land-use types. Based on the distribution characteristics of the entrances/exits, the traditional G2SFCA method is improved to measure the accessibility from the plots to the entrances/exits of the metro stations in Xiamen, China. Furthermore, the accessibility level of the stations and the imbalance of the entrances/exits are measured, and the stations are further classified and analyzed based on different supply-and-demand relationships.

3. Methods and Data

3.1. Study Data

Five datasets were used in this study: Amap job-housing data, current land-use data, building outline data, metro basic data, and POI data. Amap job-housing data encompass records in the city within half a year at least 20 days of IDs as the final IDs, combined with GPS positioning timestamps and locations to determine the residential and employment clusters, finally forming a 100 m × 100 m grid. This dataset was used to screen the metro-related land plot. The current land-use data in 2020, were checked by combining the construction situation in 2021. The building outline data were sourced from the Baidu Map open platform, including the building contour and the number of floors. By integrating these data with satellite imagery and street view images, we checked the data within the metro catchment area (MCA), resulting in approximately 47,000 individual building outlines. This dataset was mainly used to calculate the total construction area and estimate potential travel volume. The metro basic data include attributes of metro lines and stations, including 256 entrances/exits of 65 metro stations across 3 lines in Xiamen. The POI data were derived from the Amap open platform (https://lbs.amap.com/ accessed on 26 June 2023), including 14 major categories. For this research, the categories of “shopping consumption, hotel accommodation, and company enterprise” were primarily utilized to identify the specific attributes of commercial land.

3.2. Methods

Firstly, the MCA was delineated by integrating the Amap job-housing data with the Amap path-planning application programming interface (API), which facilitated the identification of station-related land plots. Utilizing multi-source data, including current land-use data, POI data, and building outline data, the peak travel volume was calculated according to the peak travel rates of different land-use types. The distances from the plot to the entrance/exit were calculated through Amap path-planning API. Subsequently, the G2SFCA method was employed to measure the accessibility from the plots to the entrances/exits. Secondly, a spatial difference analysis was performed to examine the distribution of entrance/exit supply and potential demand volume. We compared the spatial heterogeneity in supply-and-demand relationship based on the results of accessibility measurement. Based on the station as a unit, the “metro accessibility” and “the imbalance index of the entrances and exits” were calculated by synthesizing the results of the accessibility. Using these two indicators, we conducted cross-analysis and classification of stations, further analyzing the stations’ locations, entrance/exit distributions, and commuter flow distributions across different stations. Finally, the optimization suggestions for various types of stations were proposed (Figure 1).

3.2.1. Land-Use Data-Processing Process

The specific data calculation process is as follows:

Step 1: Delineation of the metro lines catchment area. With the help of Amap job-housing data, the catchment area around the station was defined. Previous studies have frequently employed a threshold of 1500 m to delineate the core MCA [43,44]. Given the widespread use of dockless bike-sharing (DBS), which extends the MCA, the 1.5 km radius can encompass most pedestrian connections and non-motor vehicle connections. Therefore, this study adopts a 1500 m threshold. Firstly, a buffer zone was used to identify the entrances/exits within this range for grid point matching. Subsequently, the Amap walking path-planning API was utilized to screen the data within the 1500 m radius. The 100 × 100 m grid cells covering within the 1500 m buffer around the entrances/exits were designated as the metro lines catchment area.

Step 2: The screening of metro-related land plots. The metro lines catchment area, filtered in the previous step, was intersected with land-use data to identify metro-related land plots. These plots encompass diverse terrain types such as mountainous areas, water bodies, and large village zones. To locate specific plots within these areas, large-scale plots were segmented using a 4 hm² criterion. This criterion is based on the “Standard for Urban Residential Area Planning and Design” issued by the Ministry of Housing and Urban-Rural Development of China, which rules that residential units should generally range from 2 hm² to 4 hm² [45]. Hence, the upper limit of this range was selected, and a 200 × 200 m grid was employed to segment plots larger than 4 hm².

Step 3: Calculation of potential travel volume of plots. By integrating POI data, the category of each metro-related land plot was identified. Combined with the travel rate of different land-use types, the potential travel volume of each plot were then calculated based on the total construction area or site area of each plot.

Step 4: Origin–Destination (OD) identification of matching entrances/exits and accessibility calculation. The centroid of each land plot was identified, and the entrances/exits data were combined to call the Amap path-planning API for distance calculation. The behavior of selecting entrances/exits is flexible only within a certain range, necessitating the selection of a distance threshold to define this range. According to China’s metro construction standards, the distance between entrance/exit channels should generally not exceed 100 m [46]. Therefore, this study adopted 100 m as the standard value for the distance selected for the entrances/exits, considering that it is possible to replace the same plot within 100 m of multiple entrances/exits. The OD data of the nearest entrance/exit from each grid and the OD data of the distance difference between the nearest entrance/exit within 100 m were screened (Figure 2), and the OD data of the matching entrance/exit were obtained. Finally, the G2SFCA method was used to measure the accessibility from the plot to the entrance/exit, as shown in Figure 3.

3.2.2. Demand Scale Calculation

This study uses the “peak hour travel rate” estimation method from the “traffic impact assessment” to replace the traditional method, thereby optimizing the accuracy of demand calculation. This method typically considers each construction project as a unit, taking into account their specific characteristics and distinguishing travel units to measure travel volumes. To unify the calculation standard, we converted most land-use types to units of “person/building area” or “person/site area”. However, for facilities that occupy a large site area, such as stadiums or green spaces, the building area is not the dominant factor in determining traffic volume, and, thus, calculation must be based on “person/site area”. The calculation process is as follows:

Firstly, the peak travel rate of different land-use types is determined by referring to the “Technical Standards of Traffic Impact Analysis of Construction Projects” [47] and the peak travel rate provided by the “Xiamen Land Space and Transportation Research Center”, integrating and selecting values according to the land-use type (

Table 2. Trip rate reference table for different types of construction projects.

ID	Major Category	Category	Peak Travel Rate	Unit of Calculation	Land-Use Type	Formulae
1	Dwelling	Common residential	2.5	Person/100 m2 building area	R2, R3	(1)
2		Village	2	Person/100 m2 building area	R4, H14
3		Villa	1.5	Person/100 m2 building area	R1
4	Office institutions	Governmental agency	3	Person/100 m2 building area	A1, U, A8, H4
5		Scientific research institution	4	Person/100 m2 building area	A35, B29
6		Office	3.5	Person/100 m2 building area	B1, B11, B2	(3) (1)
7	Commercial facility	Service nodes	4	Person/100 m2 building area	B41, B4, B9	(1)
8		Wholesale market	3.5	Person/100 m2 building area	B1, B11	(3) (1)
9		Trade market	7.5	Person/100 m2 building area	B1, B11
10		Comprehensive business	5.5	Person/100 m2 building area	B1, B11
11		Hotel	2	Person/100 m2 building area	B14, B3, B1, B11
12	Recreational facility	Park	0.5	Person/100 m2 site area	G1, G3, A9, A7	(2)
13		Woodland	0	Person/100 m2 site area	G2, G22	(2)
14		Waters	0	Person/100 m2 site area	E1, E11, E13	(2)
15		Theatre	5	Person/100 m2 building area	B3, B31	(1)
16		Stadiums and gymnasiums	2.7	Person/100 m2 site area	A4, A41, A42	(2)
17		Library and exhibition hall	2.8	Person/100 m2 building area	A2, A21, A22	(1)
18	Hospital	Comprehensive hospital	8	Person/100 m2 building area	A5, A51, A52, A53, A59	(1)
19		Welfare institutions	1	Person/100 m2 building area	A6	(1)
20	School	Elementary and high (school)	5	Person/100 m2 building area	A33, A3	(1)
21		University	2	Person/100 m2 building area	A31	(1)
22		Secondary specialized school	2	Person/100 m2 building area	A32, A34	(1)
23	Industry and warehousing	Industry	1.1	Person/100 m2 building area	M	(1)
24		Warehousing	0.3	Person/100 m2 building area	W, H23, H2	(1)
25	Traffic facilities	Railway and aviation hubs	1–2	10,000 Person/station	H2	&
26		Traffic station	1.1	Person/100 m2 building area	S3, S4, S41, S42, S9	(1)
27		Hub port	0.2–0.4	10,000 Person/station	H3	&
28		Buildings over the metro	2.5	Person/100 m2 building area	S2	(1)
29	Other non-construction land		0.1	Person/100 m2 site area	-	(2)
30	Vacant land		0.1	Person/100 m2 building area	Vacant land	(1)

Notes: Formula (1) is applied to calculate the potential travel volume based on building area; Formulas (3) and (1) are applied to first determine the land-use attribute through POI, and then calculate the potential travel volume through the construction area; Formula (2) is applied to calculate the potential travel volume based on site area; and “&” means taking the station as the unit, and the integral calculation is carried out for the traffic facilities.

). The land-use type criteria are based on China’s land-use classification standards [48]. For other countries/districts, it may be possible to refer to the “Travel Generation Manual” and local actual travel rate conditions to determine the specific travel rate values for each land-use type. Secondly, the current land-use data and building outline data are superimposed, and the total area of the building on the plot is calculated. The product of the specific peak travel rate and the total construction area on the plot yields the potential travel volume of the plot.

The formula for calculating the travel volume of the matching land-use type is as follows:

$$D_i^{buiding}=S_i{\mu }_i$$

(1)

$$D_i^{land}=C_i{\mu }_i$$

(2)

where $D_i$ is the potential travel volume of $i$ plot. In Formula (1), for the land-use type using the construction area to calculate the travel volume, $S_i$ is the construction area of the plot $i$, and ${\mu }_i$ is the peak hour travel rate of the plot. In Formula (2), for the site area used to calculate the potential travel volume, $C_i$ is the site area of the $i$ plot.

Among them, for commercial land-use types, construction projects with different functions may belong to the same type of land use. It is necessary to further combine with POI data to determine the actual attributes of the land plots. By implementing Formula (3), the ratio of the number of such POIs in the plot to the number of such POIs in the study area is calculated to determine the dominant function of the plot:

$$F_k={\displaystyle \frac{n_k}{N_k}}(k=1,2,3)$$

(3)

In the formula, $k$ represents the type of POI, and $n_k$ represents the number of the $k$th type of POI in the calculation range; $N_k$ represents the total number of POIs of type $k$; and $F_k$ represents the frequency density of the $k$th type of POI in the total number of POIs of that type.

Some plots of land-use types, whose actual travel situation is determined by the site area rather than the construction area, are calculated separately. In addition, the travel situation of some construction projects, such as railway stations, ports, airports, etc., is set according to survey data or related special indicators. Based on the passenger flow peak data during the tourism period of Xiamen City [49], combining with conversion coefficient of peak hour passenger flow in passenger transport hub, the Xiamen Station is estimated to 10,000 persons, the Xiamen North Station is set to 20,000 persons, and the passenger port to 2000–4000 persons. Moreover, special sports venues are calculated separately, with the Xiamen Stadium set to accommodate 15,000 persons. Other stadiums in the research areas are calculated according to the site area of 2.7 persons/100 m².

It should be noted that, when a plot is cut, if the plot is large but the main building is prominent, it is necessary to identify the main building of the station land first for calculation. Taking the land plot of a high-speed rail (HSR) station as an example, the plot boundary may include not only the location of the station hall but also the area covered by the HSR tracks, resulting in an overall shape that is narrow and irregular. However, the main building and main travel volume of the HSR station plot mainly come from the station hall. The calculation method involves cutting the plot individually according to the scope of the station hall and assigning it according to the peak hour travel volume, while the other areas are cut according to the 200 × 200 m grid and calculated according to the assignment method of “(26) traffic station” land-use type.

3.2.3. Accessibility Measurement Methodology

The Gaussian function is often used as a distance attenuation function because it is consistent with the distance sensitivity change of people visiting the metro station [50]. Based on the 2SFCA method, this study improves and measures accessibility. The specific operations are as follows:

The first step is to calculate the service capacity of the entrance/exit:

$$R_j={\displaystyle \frac{C_j}{\sum _{i\in \left\{d_{ij}\le d_0\right\}}^k{D}_i\times G\left(d_{ij}\right)}}$$

(4)

where $R_j$ is the service capacity of the entrance/exit. The larger the value is, the less the demand for the service of the entrance/exit is, and the higher the saturation degree of supply and demand is. $i$ is the land plot; $j$ is the supply point; and $C_j$ is the service capacity of the supply point. This paper only discusses the number and layout of entrances/exits. It is considered that the supply capacity of all entrances/exits is the same. Therefore, $C_j$ is calculated as a constant 10,000 to facilitate calculation and data display. $D_i$ has the same meaning as Formulas (1) and (2); $k$ is the number of plots in the MCA; $d_{ij}$ is the distance between the centroid of plot $i$ and the supply point $j$; $d_0$ is the search radius; and $G\left(d_{ij}\right)$ is a Gaussian distance attenuation function, and its calculation formula is as follows:

$$G\left(d_{ij}\right)=\left\{\begin{array}{c}{\displaystyle \frac{e^{{-\left(1/2\right)\times \left(d_{ij}/d_0\right)}^2}-e^{-\left(1/2\right)}}{1-e^{-\left(1/2\right)}}},d_{ij}\le d_0\\ 0,d_{ij}>d_0\end{array}\right.$$

(5)

In the formula, $d_0$ is set as the farthest distance obtained after the high-step path-planning calculation of all plots, which is 2663 m after calculation.

The second step is to calculate accessibility:

$$A_i={\sum }_{j\in \left\{d_{ij}\le d_0\right\}}G\left(d_{ij}\right)\times R_j$$

(6)

where $A_i$ is the accessibility value of each plot; $R_j$ is the supply–demand ratio calculated in the first step; and $G\left(d_{ij}\right)$ is obtained by Formula (5).

3.2.4. Imbalance Index of Entrance and Exit

To determine whether the service level among the station entrances/exits is balanced, the imbalance among the entrances/exits needs to be assessed at the station level to reflect the service gap among each entrance/exit within the station. In this study, the spatial distribution imbalance index is used to describe the unbalanced relationship between the development of a geographical system and that of another to reveal the characteristics of spatial distribution [51,52]. This method can reflect the differences between different small spatial units within a large spatial unit. The calculation formula is as follows:

$$B=\sqrt{{\displaystyle \frac{\sum _{j=1}^m\left[\frac{\sqrt{2}}{2}{\left(\frac{1}{m}-\frac{R_j}{\sum _{j=1}^m{R}_j}\right)}^2\right]}{m}}}$$

(7)

In the formula, $B$ is the service imbalance index of the entrances/exits of the station. The greater the value, the greater the service imbalance of the entrance/exit, and the greater the service difference of each entrance/exit; and $m$ is the total number of entrances/exits of the station. $R_j$ means the same as Formula (4).

3.3. Study Area

Xiamen is a sub-provincial city located on the southeast coast of China. The current city is composed of Xiamen Island (including Siming District and Huli District) and four districts outside the island (including Jimei District, Haicang District, Tong’an District, and Xiang’an District). The scope of spatial research is that, as of June 2021, Xiamen Metro has opened three operating lines, including Line 1, Line 2, and Line 3. It includes 65 stations, covering Xiamen Island and of Jimei District, Haicang District, and Xiang’an District outside the island (Figure 4). Xiamen is a typical island city, with the island itself representing the initial area of development and the most mature area of urbanization. Among the districts outside the island, the regions proximate to the island within Jimei District and Haicang District exhibit relatively advanced urban maturity. Given Xiamen’s embryonic metro network, the city’s TOD needs to be further explored and improved. In addition, Xiamen’s unique geographical traits and urban morphology dictate the distribution and configuration of its metro network. This gives Xiamen’s metro system unique spatial supply–demand characteristics compared to other cities, as well as an even more pressing need to relieve traffic on the island.

4. Results

4.1. Supply Space and Demand Space

For the supply of entrances/exits (Figure 5a), a higher supply of entrances/exits is mainly concentrated in the cross-line area, and Jimei District which is the most maturely developed area outside the island; in contrast, other districts exhibit limited facilities. When examining the potential travel volume (Figure 5b), it is evident that high values are primarily found in the old town (Region 1, 2). In addition, a certain population is also gathered in the east of the island (Region 6), where the relevant data showed that only the office function area of the Software park phase Ⅱ recently had an industrial population of about 67,000 [53]. Conversely, the potential travel volume outside the island appears scattered, with notable aggregation in the regions adjacent to the island (Region 3, 4, and 5). By summarizing the supply–demand ratios of the stations (Figure 5c), it becomes apparent that, the larger the circle, the more pronounced the degree of supply exceeding demand, thereby indicating an improved overall supply–demand situation. The map reveals that stations with a better supply–demand balance are mainly distributed within the cross-line area of the island and at the ends of the lines.

4.2. Spatial Heterogeneity of Accessibility

By using the G2SFCA method to analyze the spatial distribution of accessibility, as shown in Figure 6, it is found that the spatial distribution of accessibility and the station supply–demand ratio exhibit substantial similarities, with accessibility displaying a “strong core agglomeration, strong multi-terminal dispersion” pattern across the entire region. Accessibility is higher in the city center, located at the island’s midsection. Overall, the accessibility diminishes progressively with increasing distance from the station, which confirms the rationality of most previous assessments of station accessibility [11,19]. However, in contrast to prior findings, the stations at the line termini exhibit higher accessibility, which is due to the lower demand at these locations. Specifically, the cross-line area (Region 1) shows relatively high accessibility. Although there are many potential trips, the transfer stations have more entrances/exits, resulting in high accessibility levels and forming an obvious aggregation core. Accessibility remains high in Regions 2, 3, 4, 5, and 6, which are mainly located at the “edge” positions of the regional space and metro line terminals. This indicates that stations located on the non-old-town regional edge maintain a relatively sufficient spatial relationship between supply and demand, likely due to relatively lower potential travel demand in these areas.

4.3. Supply and Demand Characteristics of the Station

The metro accessibility and the imbalance index of the entrance/exit serve as indicators that reflect the supply-and-demand relationship for both station-level and shared usage level of entrances/exits, respectively. In the past, the calculation of “metro accessibility” lacked the consideration of the demand side. Therefore, this study regards “metro accessibility” as the equilibrium between all supply (i.e., entrances and exits) and the travel demand within the MCA. By synthesizing the demand-side measurement results, the accessibility from the plots to the entrances/exits is divided into five levels according to the G2SFCA method. Specifically, the lowest level is denoted by “−2”, the second lowest by “−1”, the mid-level by “0”, the second highest by “1”, and the highest by “2”. The distribution of the land plots’ proportions at different levels within each MCA of each station is summarized in Figure 7a, with the categorization anchored by the station. The average accessibility assignment value across plots within each MCA is counted as the “metro accessibility” of this station (Figure 7c). In addition, the imbalance index is calculated to reflect the service gap among various entrances/exits of each station, with the distribution shown in Figure 7b. The larger the circle, the greater the service differentiation among the entrances of the stations. The main high values of the imbalance index are distributed in the eastern coastal area of the island and Haicang District. In addition, we found the metro accessibility and imbalance index are mostly correlated with the predominant function of the station. Stations with low accessibility are circled by the purple rectangles in Figure 7c, most of which are large residential and commercial hubs. In contrast, several stations with a high imbalance index, marked by black rectangles in the figure, mainly serve business office functions.

The mean statistics of the metro lines presented in Figure 8 indicate that the mean value of the imbalance index is relatively consistent across different lines. However, significant differences are observed in the mean metro accessibility values among different lines. Generally, the imbalance index and metro accessibility outside the island are higher than those within the island, with the exception of the relative average value for Line 2. This observation shows that the maturity of land development may exert a noticeable impact on these two indicators. Specifically, Line 2 exhibits the highest imbalance index, a phenomenon we attribute to its extensive passage through coastal areas. In contrast, the metro accessibility of Line 3 demonstrates considerable variation between the inside and outside the island, likely due to the significant disparity in development levels between Xiang’an District and the island. Furthermore, our analysis reveals that there is no significant correspondence between the indicators for the stations. This leads us to conclude that metro accessibility cannot effectively substitute for the measurement of entrance/exit shared usage in evaluating the supply-and-demand relationship for stations.

4.4. Station Classification and Characteristics

The “metro accessibility” metric provides an overview of the overall supply and demand situation of the stations, and the “imbalance index” reflects the equilibrium of entrances/exits of each station. Both indicators reflect the supply-and-demand relationship of entrances/exits at different levels. Therefore, to explore the spatial layout of stations under different supply-and-demand relationship, we conducted a binary cross-analysis of the two indicators. The numerical boundaries formed by the natural breakpoint method are used as the coordinate axes. Consequently, the stations are divided into four quadrants, high accessible—balanced (HB), high accessible—unbalanced (HU), low accessible—unbalanced (LU), and low accessible—balanced (LB), along with their corresponding types (Figure 9).

According to the previous research conclusions, this paper summarizes the built environment, entrance/exit settings, and distribution of commuter passenger flow. The distribution characteristics of commuter passenger flow are derived from the commuter OD data provided by Amap Software Co., Ltd. in Beijing, China. The data are based on the Amap LBS data returned by the client using the Amap positioning service. Based on the Amap LBS data, the travel links are constructed from GPS dynamic points captured during the travel period, and the travel mode for each individual trip is determined according to the identified travel characteristics. The IDs of taking the metro have been selected as the main mode of transportation, given their highest occurrences in half a year. Consequently, the travel chains delineated as “origin–arrival station–leave station–destination” are established. We integrated these data with actual stations’ information (see

Table 3. The distribution characteristics of entrances/exits and tourist sources of some stations.

Legend
Type	The LU stations
Name	Software Park Phase II	Jimei Software Park
Example diagram
Station accessibility	−1.014	−0.799
Imbalance of entrance/exit	0.141	0.317
Number of entrances/exits	3/4	2/5
Similar feature stations	Haicang Business Center, Talent Center, Guluo	Haicang Bay Park, Cruise Center, Cross-Strait Financial Center, Wuyuan Bay
Type	The LB stations
Name	Wushipu	Houpu
Example diagram
Station accessibility	0.087	−0.449
Imbalance of entrance/exit	0.042	0.100
Number of entrances/exits	7/7	4/4
Similar feature stations	Xinyang Avenue, Wengjiao Road, Jianye Road, Jiangtou, Xiamen Railway Station	Luozhen Road, Xinglin Village, Xingjin Road, Lingdou, Hecuo, Wetland Park, Huli Park, Huarong Road, Huli Innovation Park
Type	The HU stations
Name	Haicang Administrative Center	Sport Center
Example diagram
Station accessibility	0.406	1.655
Imbalance of entrance/exit	0.145	0.145
Number of entrances/exits	5/5	6/6
Similar feature stations	Yuxiu East Road, Garden Expo Park
Type	The HB stations
Name	Lu Cuo	Guanren
Example diagram
Station accessibility	0.272	0.374
Imbalance of entrance/exit	0.084	0.069
Number of entrances/exits	8/9	4/6
Similar feature stations	Hubin East Road, Lianban, Torch Garden, Jimei Avenue, Maqing Road

) to summarize the characteristics of different types of stations, as follows:

(i)

The LU stations are mainly office function stations with special location environments, and the passenger aggregation at these stations shows a clear direction.

In terms of the built environment, LU stations are mainly distributed in areas along both coastal and mountainous regions (Figure 10). The accessibility on one side of these stations is compromised, leading to significant disparities in the service conditions of entrances/exits in different directions. This results in an overall low level of supply and demand equilibrium at these stations. In addition, most of the stations serve office functions. This is primarily due to the land-use on one side of the station, leading to a concentrated passenger flow with a pronounced direction, which, in turn, causes an uneven distribution of passenger sources on either side of the station. Regarding the entrances/exits, most of these stations have not fully open all their entrances, such as Jimei Software Park Station, etc. The surrounding land development often precedes the full opening of station entrances/exits of the station, resulting in a substantial mismatch between supply and demand.

(ii)

The entrance density of LB stations is insufficient.

In terms of the built environment, stations located in the LB quadrant are mainly distributed in the non-line crossing areas within the island. This distribution pattern may be due to the short distances between the stations on the same line and the lack of vertical line stations, resulting in forming a narrow MCA and many low-accessibility plots at both sides. From the perspective of entrances/exits, the density of entrances/exits is relatively low, with limited coverage, which leads to less choice of entrances/exits for passengers within MCA, resulting in a strong overall supply and demand imbalance. In terms of commuting passenger flow distribution, compared to LU stations, this type of station often exhibits no significant aggregation phenomenon in the direction of passenger sources. This contrast is notably evident when comparing Jimei Software Park Station (LU) and Wushipu Station (LB).

(iii)

The HU stations mainly serve public functions, and the connection between the passenger flow channels and entrances/exits of these stations is inadequate.

From the perspective of the built environment, HU stations are mainly located around public service facilities situated in mountainous and coastal areas. During peak travel times, these public service facilities do not attract significant commuter passenger flow compared to office and residential areas, resulting in a less pronounced total potential travel demand. In addition, public service facilities are often located in favorable environments that showcase the cityscape, such as areas with views of mountains or seas. This geographic orientation leads to an eccentric MCA, leading to different supply and demand levels for entrances/exits in different directions. Regarding entrances/exits, while the number is relatively high, their distribution tends to be scattered. In terms of the distribution of commuter source, there is often a poor connection between the entrances and the main passenger flow channels in the vicinity, causing some passenger flow to redirect to other entrances. For instance, at Haicang Administrative Center Station (HU), the entrance/exit of the station is located on a main road, while the residential area’s exit is located on a branch road, resulting in a weak linkage between the main passenger flow channel and the entrance. Consequently, the main passenger flow is concentrated at the northern and western entrances.

(iv)

The HB stations are associated with a higher level of development, and the potential demand at these stations corresponds well with their entrance/exit settings.

From the perspective of the built environment, HB stations are mainly located along Jimei District and along Line 1 within the island. Line 1 is the earliest established metro line, traversing the most developed areas of Xiamen. This correlation shows that the supply and demand dynamics of HB stations are closely linked to the level of development in their surrounding areas. In terms of the entrance/exit layout, compared with the LB stations, the HB stations exhibit a broader coverage and higher density of entrances compared to LB stations. For example, while both Wushipu Station (LB) and Lu Cuo Station (HU) attract significant passenger volumes, Lu Cuo Station features a significantly more dispersed and numerous entrance layout, which enable a larger coverage area and facilitate service to more passengers. Regarding commuter flow distribution, HB stations demonstrate a more homogeneous passenger distribution compared to HU stations, meaning an absence of pronounced directional aggregation in demand.

5. Discussion

5.1. The Land-Use Difference Should Be Considered in Metro Service Accessibility

In the past, measurements of demand for transportation facilities have predominantly relied on the number of the residential population as the demand points [19,20], or involved aggregate calculations at the TAZs [13]. However, these approaches often overlook the travel demand from office land or result in significant discrepancies between the calculated and actual travel patterns due to the large size of the analysis units. This study addresses these limitations by enhancing the traditional G2SFCA method using multi-source data, incorporating characteristics of station entrances/exits and travel rates associated with different land-use types. The results demonstrate that this updated method effectively captures the demand side, as well as the supply and demand disparities across different land-use types. Moreover, it can reflect the supply-and-demand relationship of different types of stations and their surrounding spatial layout patterns. In comparison to other studies employing the G2SFCA method to measure the “to-metro accessibility” [11,19], our findings yield different insights. The accessibility results on the demand side do not completely exhibit a simple decline from the urban center to the periphery. Instead, an oversupply of transportation resources may also be observed in suburban areas. This research not only provides a more accurate method for calculating metro supply and demand but also provides useful ideas for alleviating transportation inequities and achieving high-quality urban development.

5.2. The Application Potential of Taking Entrances/Exits as the Research Object

Previous studies have always focused on the accessibility and supply–demand dynamics of metro stations [10,11,19,20], ignoring the important role of entrances/exits. In this study, we took the entrances/exits as the research object, and accurately studied the spatial units of the supply-and-demand relationship at metro stations. This approach enables us to evaluate supply-and-demand relationship for both station-level and shared usage level of entrances/exits. Our findings indicate that the two indicators, “metro accessibility” and the “imbalance index of entrances/exits”, do not show clear corresponding characteristics. Consequently, the supply–demand level of the station cannot be simply calculated in place of the shared usage level of entrances/exits. Instead, for stations with different index characteristics, it is essential to tailor the focus on specific supply and demand characteristics for optimization and improvement. In contrast to the traditional methods that rely solely on station-level calculations, our method offers a more nuanced analysis of public usage patterns and the supply–demand level of metro facilities. Specifically, by conducting a detailed analysis of the supply-and-demand relationships of entrances/exits, urban planners can more effectively identify locations where additional or optimized access points are necessary, thereby enhancing the overall accessibility and convenience of subway services. For instance, at metro stations located within transition zones, the overall supply and demand may be balanced or even excessive; however, individual entrances may still experience congestion or uneven utilization. This analysis offers a novel perspective for the planning and optimization of metro systems, contributing to efforts aimed at mitigating transportation inequities and promoting sustainable urban development.

6. Conclusions and Suggestion

6.1. Conclusions

With the rapid development of urban space and the rapid renewal of metro systems and the surrounding land, it is difficult to avoid the imbalance between supply and demand. The measurement of the supply-and-demand relationship of metro station entrances/exits, considering differences in land-use types, holds significant theoretical and practical value for improving transportation equity. The conclusions are summarized as follows:

Firstly, the G2SFCA method can clearly reflect the demand side and the disparities in the supply and demand. Accessibility from plots to the entrances/exits reveals that overall accessibility is higher in the city center, at regional boundaries, and at terminal stations, but lower in transition areas. This pattern mirrors the spatial distribution of the supply–demand ratio at stations, underscoring the need for the layout optimization of entrances/exits in transition areas.

Secondly, the indicators both station-level and shared usage level of entrances/exits do not reflect consistent trends, indicating that transportation equity cannot be solely assessed by the station-level accessibility. Moreover, both indicators suggest that they are related to the dominant functions of stations and the development of the surrounding land. For example, stations with a high value for the “imbalance index” are always near some business parks. Statistically, the difference in two indicators between lines inside and outside the island reflects that “metro accessibility” is more susceptible to location factors.

Thirdly, categorizing stations into four types—LU, LB, HU, and HB—based on the “metro accessibility” and “imbalance index of entrance/exit” reveals distinct spatial distribution characteristics, entrance/exit configurations, and actual passenger source characteristics for each type. LU stations are mainly office function stations with special location environments, and the passenger aggregation at these stations shows a clear direction. LB stations have insufficient entrance density. HU stations mainly serve public functions, and the connection between the passenger flow channels and entrances/exits of these stations is inadequate. HB stations are associated with a higher level of development, and the potential demand at these stations corresponds well with their entrance/exit settings.

This study, however, has certain limitations. Firstly, while selecting 9 categories and 30 sub-categories of land-use types based on the study area’s characteristics, the further segmentation of land-use types could be beneficial. Drawing insights from the relevant research [54,55], we could better understand the differences in the traffic incidence of different land-use types in different locations, thereby accurately estimating the potential travel volumes. Secondly, our selection of entrances/exits mainly considered distance as a factor; yet, practical choices are influenced by multiple factors. Further work could incorporate findings on entrance/exit selection determinants [56] to more accurately measure the proportion of passenger flow shared by entrances/exits, enhancing the method’s application efficacy and feasibility.

6.2. Suggestion

According to the analysis of the supply-and-demand relationship concerning the entrance/exit spaces of the abovementioned stations, the study identifies a notable degree of “supply and demand imbalance” among the three categories: LU, LB, and HU stations. Therefore, planning adjustments should prioritize the development of these stations and their surrounding areas. From the perspective of refined urban design, the following suggestions are put forth to optimize metro station spaces and improve the supply-and-demand relationship:

For LU stations, it is recommended to improve the entrance/exit settings in alignment with passenger source aggregation. This should involve increasing the entrances/exits and expanding their overall coverage, as well as augmenting the station density and available connectivity facilities in these directions. Furthermore, attention should be given to improving the layout of entrances/exits at intersections and ensuring effective connections between the entrances/exits with lower passenger flow and the pedestrian pathways of adjacent plots. In the case of LB stations, it is essential to add entrances/exits to expand the coverage, particularly focusing on the inclusion of entrances/exits that are perpendicular to the line. For HU stations, consideration should be given to increasing the entrances/exits in line with the direction of passenger source aggregation. Additionally, increasing the conversion layers to connect new entrances/exits can strengthen the connectivity measures for areas with high passenger flow. It is also important to reinforce the spatial connection between the main passenger flow channels and entrances/exits.

To further advance this research, we advocate for the integration of artificial intelligence (AI) interventions. Specifically, the implementation of facilities for ridership identification and interactive tools for passengers at metro station entrances/exits can provide planners with valuable insights into actual ridership dynamics and user feedback. This approach facilitates the optimization of entrance/exit locations, thereby enabling metro stations to respond more effectively to changing demand and addressing supply–demand imbalances.