Estimating Public Transportation Accessibility in Metropolitan Areas: A Case Study and Comparative Analysis

Abstract

Accessibility-oriented public transportation planning can improve the operational efficiency of public transportation, guide orderly urban development, and alleviate issues such as traffic congestion, environmental pollution, and resource consumption in large cities. To promote the practical application and widespread adoption of public transportation accessibility estimating systems, this study proposes an improved public transport accessibility levels (PTAL) method. It innovatively incorporates residents’ preference indices for different modes of transportation and addresses the challenge of missing timetable data in the calculation process. Using actual data from Shenzhen, a case study is conducted to analyze the public transportation accessibility index and compare the results obtained through k-means clustering, the equal spacing method, the quantile method, and the application of the London PTAL method. The research findings indicate that the optimal number of clusters for public transportation accessibility index analysis in large cities is six when using clustering algorithms. Among the statistical analysis methods, the quantile method shows favorable performance. Furthermore, a comprehensive comparison of different classification methods confirms that the improved PTAL method offers better discrimination in estimating public transportation accessibility levels compared to the London PTAL method. The study concludes by providing guidance on how cities with different characteristics can reference the improved PTAL method.

1. Introduction

The construction of more transportation infrastructure remains a primary approach in mobility-oriented urban transportation planning to meet the growing transportation demands during the process of urban development. However, in the context of increasing car ownership and worsening traffic congestion, the pace of transportation demand growth has far outstripped the growth of transportation supply, resulting in a growing imbalance between supply and demand [1,2]. Transit-Oriented Development (TOD) has emerged as a new development model [3]. On the one hand, developing public transportation provides a more efficient solution for supply–demand imbalances than private cars. On the other hand, countries like China and the UK actively promote the electrification of public transportation [4], effectively reducing pollution. Furthermore, when combined with well-designed transportation policies, these efforts foster diverse innovative and sustainable solutions [5,6]. And the accessibility of public transportation services for residents in different areas of a city has become a noteworthy research topic [7]. Accessibility can be used to measure the ease of reaching destinations for urban residents [8]. Given the challenges of traffic congestion and limited land availability in many major cities [9], planning and managing cities from an accessibility perspective have become key strategies for addressing the current issues associated with mobility-oriented transportation planning [10]. Accessibility has significant applications in urban and transportation planning fields [11], with research often focusing on individual cities [12,13,14], modeling and calculating the accessibility of public transportation stations within a city, and evaluating the development of public transportation in that city [15], thereby effectively addressing problems such as traffic congestion, environmental pollution, and resource consumption.

Based on the existing literature, the most commonly used methods for measuring accessibility include the distance-based approach [16], cumulative opportunity measures [17,18,19], gravity models [20], isochrone methods [21], and utility-based metrics [22,23]. Currently, the most mature approach for evaluating public transportation accessibility is found in the London area, where Transport for London (TfL) has implemented a public transport accessibility levels (PTAL) evaluation method. The method was initially proposed by the London Borough of Hammersmith and Fulham (LBHF) and later extended for application across the Greater London area, considering the difficulty or ease with which individuals can access public transportation services from different locations. Many cities have referenced the London method and tailored it to their own characteristics to study their respective levels of public transportation accessibility. For example, Kwok et al. [24] proposed the MAG index to measure residents’ preferences for public and private transportation. Kawabata [25] observed the differences in accessibility when residents in the San Francisco and Boston metropolitan areas choose between private cars and public transportation. Salonen et al. [26] compared the accessibility differences between public transportation and private transportation choices using Helsinki as an example. Saghapour et al. [27] combined public transportation accessibility with population density to propose a measure that considers population distribution, and they conducted an empirical analysis in the Melbourne region of Australia. Moscow, Russia, conducted a comprehensive analysis of population density and public transportation accessibility levels to explore land resource utilization and allocation. Additionally, Singapore, New Zealand, New South Wales in Australia, Bangkok in Thailand, and Ahmedabad in India [28] have evaluated the public transportation accessibility levels of their respective cities based on the London method. They have conducted detailed analyses considering factors such as population density and development conditions, providing references for urban planning in their respective cities.

However, the current application of public transportation accessibility often directly applies the London PTAL method [29,30], without considering the different development conditions and geographical characteristics of each city. There is a lack of research on classification methods suitable for cities with large areas and high population densities. Furthermore, the London PTAL method has high real-time data requirements and faces challenges in data acquisition. Additionally, it does not consider the varying attractiveness of different transportation modes to residents. Given the availability of abundant transportation and urban data, it is crucial to establish an evaluation framework for public transportation accessibility that is applicable to such large cities. This framework should address issues such as parameter calibration in data-driven algorithms and the incorporation of public transportation accessibility as a scientific basis for urban planning. Comprehensive research on the application system of public transportation accessibility levels is still urgently needed.

Therefore, building upon previous research, this study innovatively establishes the “improved London PTAL Method” to construct a static accessibility evaluation model that considers residents’ access to multiple public transportation modes, from walking to accessing transit stations. The study provides a solution for calculating transit schedules at intermediate stops in the absence of detailed GPS data. The proposed method is applied to analyze real data from Shenzhen City and is compared with evaluation results from the London area to validate its effectiveness. Finally, utilizing actual data, various statistical analysis methods, including clustering algorithms, standard-deviation-based classification, percentile-based classification, and equal-interval-based classification, are employed to categorize the public transportation accessibility index at each grid point in Shenzhen City. This research establishes suitable classification methods for cities with different characteristics in estimating public transportation accessibility.

2. Materials and Methods

A list of symbols used in the manuscript is given in

Table 1. List of symbols used in the manuscript.

Group	Symbol	Parameter
Traffic accessibility index parameters	TW	Walking time from the POI to the public transport station
	TAW	Average waiting time
	TTA	Total average time from the POI to access public transport services
	d	Distance from the POI to the public transport station
	v	Walk speed
	p	Public transport accessibility estimating period
	f	Frequency of a public transportation arrival during the period
	F	Equivalent doorstep frequency
	αi	Equivalent frequency weight for the i-th route
	AImode_i	Accessibility index of the i-th public transportation mode
	AIPOI	Total accessibility index of the POI
	βi	Accessibility index weight for the i-th public transportation mode
Classification parameters	SSE	Sum of the squared errors
	k	The number of clustering
	Ci	The set of elements of the cluster i
	s	Sample point
	mi	The mass center of the cluster i
	Si	The profile coefficient of sample i
	ai	The average distance from sample i to other points in the same category
	bi	The average distance from sample i to the nearest sample in different categories

.

Accessibility indicates the potential interaction between travelers and the spatial distribution of opportunities [31,32], which is jointly determined by travelers’ travel characteristics and the ease of reaching destinations [33,34]. Therefore, there are three essential elements in measuring accessibility: origin, mode of travel, and destination.

• The origin refers to the location where accessibility is measured.
• Modes of travel include walking, cycling, public transportation, private vehicles, as well as mixed modes involving multiple forms of transportation.
• The destination is determined by the traveler’s interests and is commonly referred to as a Point of Interest (POI) in accessibility studies [35].

In this study, the attractiveness of public transportation services is measured by calculating the number of public transportation opportunities in the vicinity of specific locations. The accessibility level of the location is then estimated by reducing the value of each public transportation opportunity based on walking time impedance. The calculation method for the public transportation accessibility index involves the following steps:

• Walk time from the POI (Point of Interest) to the public transport station, ${\mathrm{T}}_{\mathrm{W}}$, was calculated as:

$${\mathrm{T}}_{\mathrm{W}}=\frac{\mathrm{d}}{\mathrm{v}}$$

(1)

where d is the distance from the POI to the public transport station and v is the walking speed of the traveler.

2.

The average waiting time, ${\mathrm{T}}_{\mathrm{AW}}$, was calculated as:

$${\mathrm{T}}_{\mathrm{AW}}=\frac{1}{2}\times \frac{\mathrm{p}}{\mathrm{f}}$$

(2)

where p is the public transport accessibility estimating period and f is the frequency of a public transportation arrival during the period.

3.

The total average time from the POI to access public transport services, ${\mathrm{T}}_{\mathrm{TA}}$, was obtained by summing the walking time and the average waiting time.

$${\mathrm{T}}_{\mathrm{TA}}={ \mathrm{T}}_{\mathrm{W}}+{ \mathrm{T}}_{\mathrm{AW}}=\frac{\mathrm{d}}{\mathrm{v}}+\frac{1}{2}\times \frac{\mathrm{p}}{\mathrm{f}}$$

(3)

4.

The equivalent doorstep frequency of POI, F, was calculated as:

$$\mathrm{F} =\frac{1}{2}\times \frac{60}{{\mathrm{T}}_{\mathrm{TA}}}$$

(4)

F converts the total arrival time, ${\mathrm{T}}_{\mathrm{TA}}$, into a measure in terms of frequency, ensuring a negative correlation between the calculation result and the total arrival time, i.e., if the public transportation service obtained from the evaluated point after walking through to the public transportation stop and waiting for a certain time is equivalent to the public transportation service obtained directly at that point without walking at a certain frequency, taking into account the walking time, then the frequency is called the equivalent frequency.

5.

The accessibility index of the i-th public transportation mode, ${\mathrm{AI}}_{\mathrm{mode}}$, was calculated as:

$${\mathrm{AI}}_{\mathrm{mode}}={\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathsf{\alpha }}_{\mathrm{i}}\times { \mathrm{F}}_{\mathrm{route}\_\mathrm{i}}$$

(5)

where ${\mathrm{AI}}_{\mathrm{mode}}$ is the equivalent frequency weight for the i-th route, e.g., the bus accessibility index, the metro accessibility index, etc.; ${\mathrm{F}}_{\mathrm{route}\_\mathrm{i}}$ is the equivalent frequency of a particular route of that public transport mode; and ${\mathsf{\alpha }}_{\mathrm{i}}$ is the average distance from sample i to other points in the same category.

6.

The total accessibility index of the POI, ${\mathrm{AI}}_{\mathrm{POI}}$, was calculated as:

$${\mathrm{AI}}_{\mathrm{POI}}={\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathsf{\beta }}_{\mathrm{i}}\times { \mathrm{AI}}_{\mathrm{mode}\_\mathrm{i}}$$

(6)

where ${\mathrm{AI}}_{\mathrm{POI}}$ is obtained by weighting the accessibility index, ${\mathrm{AI}}_{\mathrm{mode}\_\mathrm{i}}$, of different public transportation modes and ${\mathsf{\beta }}_{\mathrm{i}}$ is the accessibility index weight for the i-th public transportation mode.

7.

Aggregation of accessibility estimating indices.

The model adopts the grid-based approach in the direct representation method for aggregation. The evaluation points are represented by the center points of the grids, as shown in Figure 1. The accessibility index of each grid is computed based on the accessibility index of the corresponding center point.

8.

Classification of Public Transportation Accessibility Index

After obtaining the accessibility indices for all grid points, the accessibility levels of the study area can be determined by classifying them according to certain criteria. Classification methods for one-dimensional data can be divided into two categories: clustering algorithms and statistical classification methods. In this study, the k-means clustering algorithm was employed to classify the accessibility indices of public transportation and determine the accessibility levels of the city. The choice of the number of clusters (k) is a crucial parameter in the k-means clustering process. Common methods for selecting the value of k include the elbow method and the silhouette coefficient method.

• The elbow method, also known as the sum of squared errors (SSE) method, is used to determine the optimal number of clusters by identifying the point of inflection where the loss value decreases steadily. The SSE is a widely used measure to quantify the total variability within each cluster. It is calculated as the sum of the squared Euclidean distances between each data point and its centroid within a cluster. The number of clusters is chosen based on the point at which the SSE begins to level off, indicating diminishing returns in terms of clustering improvement. The SSE calculation is given by the following formula:

$$\mathrm{SSE} ={\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{k}}{\displaystyle \sum }_{\mathrm{c}\in {\mathrm{C}}_{\mathrm{i}}}{\left|\mathrm{s}-{\mathrm{m}}_{\mathrm{i}}\right|}^2$$

(7)

where k is the number of clustering, ${\mathrm{C}}_{\mathrm{i}}$ is the set of elements of the cluster i, s is the sample point, and ${\mathrm{m}}_{\mathrm{i}}$ is the mass center of the cluster i.

• The silhouette coefficient method involves computing the maximum value of the silhouette coefficient to calculate the optimal number of clusters. The calculation method for the silhouette coefficient is as follows:

$${\mathrm{S}}_{\mathrm{i}}=\frac{{\mathrm{b}}_{\mathrm{i}}-{ \mathrm{a}}_{\mathrm{i}}}{\max \left({\mathrm{a}}_{\mathrm{i}} ,{ \mathrm{b}}_{\mathrm{i}}\right)}$$

(8)

where ${\mathrm{S}}_{\mathrm{i}}$ is the profile coefficient of sample i, ${\mathrm{a}}_{\mathrm{i}}$ is the average distance from sample i to other points in the same category, and ${\mathrm{b}}_{\mathrm{i}}$ is the average distance from sample i to the nearest sample in different categories.

3. Results

3.1. Shenzhen Public Transportation Accessibility Evaluation Model

3.1.1. Parameter Selection

The parameter values involved in the Shenzhen Public Transportation Accessibility Evaluation Model established in this study are as follows:

• The evaluation scope covers the entire area of Shenzhen City (excluding the Shenshan Special Cooperation Zone).
• The considered public transportation modes are buses and metro.
• The service range of bus stops is set to 500 m (approximately a 7 min walk), while the service range of metro stations is set to 1000 m (approximately a 15 min walk). According to the Urban Road Traffic Planning and Design Specification in China, the service range for bus stops is typically 300 or 500 m, and for metro it is 800 m. Additionally, 800 m is a critical threshold for evaluating the layout of bus stops, and a 10 min walk is considered the service range for rail commuting. The average pedestrian walking speed was determined based on measured data in Shanghai, where the average walking speed was calculated to be 1.24 m per second or 74.4 m per minute. Another study conducted in Beijing using video recording to observe the walking speeds of 1882 individuals found the average walking speed in Beijing to be 1.22 m per second.
• The grid method is used for the estimation of public transportation accessibility in Shenzhen. The grid spacing is set at 150 m, and the accessibility index at the center of each grid is considered as the public transportation accessibility index for that grid.
• The research period focuses on the morning peak hours from 7:00 am to 9:00 am Beijing time.
• The weight assigned to the metro accessibility index is 0.6, while the weight assigned to the bus accessibility index is 0.4. Based on the 2021 Shenzhen metro operating data, the total annual passenger volume of the entire metro network reached 2.17 billion, and the public transportation modal share in the city is 60.4%.
• The public transportation accessibility evaluation method employed in this study does not take into consideration factors such as the passenger capacity and congestion level of public transportation vehicles.

Therefore, in this paper, the total average time from the POI to access public transport services, ${\mathrm{T}}_{\mathrm{TA}}$, was calculated as:

$${\mathrm{T}}_{\mathrm{TA}}={ \mathrm{T}}_{\mathrm{W}}+{ \mathrm{T}}_{\mathrm{AW}}=\frac{\mathrm{d}}{73.2}+\frac{1}{2}\times \frac{120}{\mathrm{f}}$$

(9)

The total accessibility index of the POI, ${\mathrm{AI}}_{\mathrm{POI}}$, in Shenzhen was calculated as:

$${\mathrm{AI}}_{\mathrm{POI}}=0.6\times { \mathrm{AI}}_{\mathrm{metro}}+0.4\times { \mathrm{AI}}_{\mathrm{bus}}$$

(10)

3.1.2. Sample Point Selection

To ensure both sampling accuracy and comprehensive coverage, this study adopted a square grid with dimensions of 150 m by 150 m to partition the entire area of Shenzhen City. The grid spacing, denoted as x, was determined to be 150 m. Subsequently, the latitude increment for each raster, $\Delta \mathrm{lat}$, was calculated as:

$$\Delta \mathrm{lat}=\frac{\mathrm{x} \times 360}{2\times \mathsf{\pi } \times { \mathrm{R}}_{\mathrm{e}}}$$

(11)

where ${\mathrm{R}}_{\mathrm{e}}$ is the radius of the Earth. The longitude increment for each raster, $\Delta \mathrm{lon}$, was calculated as:

$$\Delta \mathrm{lon}=\frac{\mathrm{x} \times 360}{2\times \mathsf{\pi } \times { \mathrm{R}}_{\mathrm{e}}\times \cos \frac{\Delta \mathrm{lat} \times \mathsf{\pi }}{360}}$$

(12)

As shown in Figure 2, after gridification, all the grids were tightly connected, ensuring comprehensive coverage during the estimation of public transportation accessibility in Shenzhen City.

In this study, the coordinates of the WGS-84 coordinate system were transformed into GCJ-02 coordinate system (China Geodetic Coordinate System 2000) coordinates, and the grids were uniformly encoded with a unique ID assigned to each grid point. After processing, the data samples of grid points are shown in Figure 3, with a total of 96,983 grid points.

3.1.3. Data Preprocessing

The transportation data required as input for the model include the following: public bus and metro station location data, bus route direction data, bus and metro route station data, and bus and metro departure interval data. Specifically:

• Bus route station data: Obtained on 15 December 2021, with a total of 55,729 records, including route direction, route number, unique station ID, station name, and location coordinates.
• Bus departure interval and operation status data: Obtained on 31 December 2021, with a total of 2228 records. The data fields include the operating mode of each bus route, operation date, and departure intervals at different time periods.
• Shenzhen City bus route overview: Obtained on 27 February 2022, with a total of 888 records. The data fields include route number, starting station, ending station, stations passed in the up direction, and stations passed in the down direction. The data source is the Shenzhen Municipal Transportation Bureau, and the Shenzhen Metro line map is shown in Figure 4.
• Metro route station and departure interval data: Obtained on 22 March 2022, with a total of 290 records, including route direction, route number, unique station ID, station name, and location coordinates.

After data acquisition, cleaning, and preprocessing, the calculation of the public transportation accessibility index for each grid point was performed following the steps illustrated in Figure 5.

Specifically:

• The steps for obtaining walking distance and time are as follows:

• Obtain the location information of each public transportation station through data cleaning.
• Establish a buffer zone for public bus and metro stations, with radii of 500 m and 1000 m, respectively.
• Select grid points located within the buffer zones of each station as starting points for walking navigation.
• Set each station as the destination for walking navigation.
• Utilize the walking navigation interface provided by the Amap Web API to crawl the walking information from each grid point to the corresponding station.

In the entire area of Shenzhen, a total of 207,130 “grid point—bus station” data and 92,256 “grid point—metro station” data were obtained. After filtering the data to include only walking distances within the station’s service range, 94,220 samples of “grid point—bus station” walking data and 17,932 samples of “grid point—metro station” walking data were obtained. The walking time (T_W) was obtained through the Amap Web API.

2.

Steps for calculating the bus accessibility index are as follows:

• Obtain the departure time for each route from its starting station. To obtain the arrival frequency of buses at each station during the study period, process the data of 107,360 bus departure times.
• For each station, calculate the arrival time of each route at that station. By adding the departure time of each route from its starting station to the travel time from the starting station to the specific station, the departure time of each route at that station can be obtained.
• For each station, filter the arrival frequencies of each route during the study period (from 7:00 am to 9:00 am).
• For each route at each station, calculate the average waiting time based on the departure frequency.
• For each station, filter the grid points within its service range and obtain the walking distance and time from the grid points to the public transportation stations.
• For each grid point–bus station pair, calculate the equivalent frequency using the walking time and average waiting time.
• For each grid point, sum up the equivalent frequencies of all bus stations to obtain the bus accessibility index for that grid point.

3.

Steps for calculating the metro accessibility index are as follows:

• Obtain the departure interval for each route during the morning peak hours.
• For each station on each route, calculate the average waiting time based on the departure interval.
• For each station, filter the grid points within the service range and obtain the walking time.
• For each grid point–metro station pair, calculate the equivalent frequency using the walking time and average waiting time.
• For each grid point, sum up the equivalent frequencies of all metro stations to obtain the metro accessibility index.

3.1.4. Analysis of Public Transportation Accessibility in Shenzhen City

Among the 96,983 grid points in Shenzhen City, there are 38,141 grid points with a positive bus accessibility index, accounting for approximately 39.33% of the total. This means that the coverage of bus stations in Shenzhen City represents around 40% of the city’s total area. As shown in Figure 6, Shenzhen has nine administrative districts under the jurisdiction of Futian, Luohu, Nanshan, Yantian, Bao’an, Longgang, Longhua, Pingshan and Guangming. According to the China Urban Construction Statistical Yearbook—2020, the total area of Shenzhen City is 1986.4 square kilometers, with a built-up area of 955.68 square kilometers. Therefore, the proportion of the built-up area to the total area of Shenzhen City is approximately 48.11%. Since the majority of bus station coverage is concentrated in the built-up area, it can be inferred that the coverage area of bus stations within a 500 m walking distance can be calculated as the ratio of the coverage area of bus stations to the built-up area, which yields approximately 83.14% or can be approximated as 85%.

Moreover, there are 8766 grid points with a positive metro accessibility index, accounting for approximately 9.04% of the total. This indicates that the coverage of metro stations in Shenzhen City represents around 9% of the city’s total area. Considering that the proportion of the built-up area to the urban area in Shenzhen City is 48.11% and that the coverage of metro stations is concentrated in the built-up area, it can be inferred that the coverage area of subway stations within a 1000 m walking distance can be calculated as the ratio of the coverage area of subway stations to the built-up area, which yields approximately 18.71% or can be approximated as 20%.

After calculating the bus accessibility and metro accessibility for each grid point and conducting weighted calculations, the results of the public transportation accessibility index for each grid point are presented in Figure 7, where the field PTAI represents the public transportation accessibility index for each grid point.

Among the 96,983 grid points in Shenzhen City, there are 40,391 grid points with a public transportation accessibility index greater than 0, accounting for approximately 41.65% of the total. This means that the coverage of public transportation stations in Shenzhen City represents around 42% of the city’s total area. Considering that the proportion of the built-up area to the urban area in Shenzhen City is 48.11% and that the majority of the coverage of public transportation stations is concentrated in the built-up area, it can be inferred that the coverage of public transportation stations in Shenzhen City represents approximately 90% of the built-up area.

3.2. Grading Method for the Public Transportation Accessibility Index in Shenzhen City

To evaluate the level of public transportation accessibility in Shenzhen City, the computed public transportation accessibility index for each grid point is classified into different levels.

3.2.1. Classification Method Based on a Clustering Algorithm

The k-means clustering algorithm was applied to classify the public transportation accessibility index in Shenzhen City into 2 to 20 clusters. The sums of squared errors and silhouette coefficients were computed for each clustering solution, as shown in Figure 8.

The silhouette coefficient exhibits a decreasing trend during the clustering process of public transportation accessibility, indicating that it is not meaningful to identify the maximum value of the silhouette coefficient as the number of clusters. However, a distinct elbow point can be observed in the sum of squared errors when the number of clusters is six. Therefore, according to the elbow method, six clusters was selected as the optimal number of clusters.

By setting the number of clusters to six and applying the k-means clustering algorithm, the classification results and the corresponding evaluation of public transportation accessibility levels in Shenzhen City are presented in Figure 9. Notably, for visualization purposes, only areas where the public transportation accessibility index is greater than 0 are displayed.

It can be observed that, under this classification result, areas with the highest level of public transportation accessibility are mainly concentrated in the central regions of Luohu, Futian, Nanshan, Bao’an, Longhua, and Longgang. The public transportation accessibility level in the northern parts of the Bao’an, Guangming, Yantian, and Kuichong areas is relatively lower. Most of the areas with a public transportation accessibility index of 0 are mountain peaks, reservoirs, and other regions that are difficult to reach and lack public transportation coverage, which is consistent with the development situation in Shenzhen City.

In summary, the classification results obtained by applying the k-means clustering method with six clusters align well with the actual conditions of Shenzhen City.

3.2.2. Classification Method Based on Statistical Analysis

In addition to clustering algorithms, commonly used classification methods also include statistical-analysis-based methods, such as standard deviation classification, quantile classification, and equal interval classification. To ensure the comparability of the classification results, this study also divided the public transportation accessibility index into six levels (excluding level 0) when using statistical-analysis-based classification methods, maintaining the same number of categories. Before performing the classification, statistical analysis was conducted on the data. Due to the significant number of areas with a public transportation accessibility index of 0, to ensure the accuracy of the statistical analysis, only data with a public transportation accessibility index greater than 0 were considered. The key statistical parameters are presented in

Table 2. Values of public transport accessibility index (non-zero value) statistics for Shenzhen.

Statistics	Value
Count	40,391
Mean	18.0193
Median	10.82
Overall standard deviation	19.7182
Sample standard deviation	19.7184
Min	0.18
Max	184.28
Q1	4.19
Q3	24.935

. Among the 40,391 non-zero grid points, the average public transportation accessibility index was 18.0193, the median was 10.82, the overall standard deviation was 19.7182, and the maximum value was 184.28.

The histogram of the data distribution is shown in Figure 10. It can be observed that the standard deviation is too large, indicating that the standard deviation classification method is not suitable for classifying the public transportation accessibility indices in Shenzhen.

The non-zero values of the public transportation accessibility index in Shenzhen were classified into six levels using the equal interval method and the quantile method. The histograms of the data distributions are shown in Figure 11a,b, respectively. The evaluation results of public transportation accessibility levels in Shenzhen are presented in Figure 12 and Figure 13.

As shown in Figure 12, due to the large range, the equal interval method resulted in the highest level of public transportation accessibility having the fewest number of observations, while the majority of areas fell into the two lowest levels. Therefore, the equal interval method does not provide sufficient discrimination for areas with lower levels of public transportation accessibility, making it unsuitable for classifying the public transportation accessibility indices in Shenzhen.

As shown in Figure 13, when using the quantile method for classification, areas with the highest public transportation accessibility levels were predominantly located in the original Special Economic Zone, as well as the central areas of the Bao’an and Longhua districts. Additionally, regions along Songbai Road in Guangming District, the Buji area in Longgang District, Longgang Avenue, and Shenshan Road in Pingshan District also exhibit high levels of public transportation accessibility. Conversely, the areas with the lowest public transportation accessibility are relatively fewer in number and mainly concentrated in the peripheral areas of Dapeng New District and other districts. It can be observed that the classification results of the quantile method effectively identify areas with the highest public transportation accessibility index, demonstrating reasonable differentiation and aligning well with the actual situation in Shenzhen. The classification performance of the quantile method is superior to that of the equal spacing method. Therefore, among the statistical-analysis-based classification methods, adopting the quantile method yields better results.

3.2.3. Summary of Grading Methodology

A comprehensive comparison of the classification results obtained from the quantile method and k-means clustering revealed that the quantile method classifies more regions as having higher public transportation accessibility, while the k-means clustering method yields fewer regions with high accessibility. However, the classification results of the quantile method lack sufficient differentiation for areas with a higher public transportation accessibility index. To ensure better differentiation and consider the expected future development of public transportation, which will lead to an increase in the accessibility index, it is more suitable to choose a classification method that provides better differentiation for areas with a higher public transportation accessibility index. This allows room for future development.

A summary of the various classification methods for the public transportation accessibility index in Shenzhen and their suitability is presented in

Table 3. Comparison of different classification methods for the public transport accessibility index in Shenzhen.

Classification Method	Appropriateness	Description
k-means clustering	Suitable	The classification results can effectively reflect the differences in accessibility indices of different regions, and the differentiation degree is good
Jenks natural discontinuity method	Suitable	Since the public transportation accessibility indices are one-dimensional data, the classification result is the same as k-means clustering
Quantile classification	Unsuitable	Most of the regions are classified as the lowest class, and the distinction is poor
Standard deviation classification	Unsuitable	The standard deviation is too large to use standard deviation classification
Equal spacing classification	Somewhat suitable	It can distinguish the public transportation accessibility indices of different areas, but there are too many areas with a high accessibility index, and the differentiation is average

.

Therefore, in the current stage, it is most suitable to adopt the k-means clustering method to classify the public transportation accessibility indices into six categories in Shenzhen. Additionally, to facilitate the classification of the accessibility indices and make it more user-friendly, this study fine-tuned the classification thresholds based on the results of k-means clustering. The nearest integer values were selected as the threshold values for classification. The final determined classification ranges are presented in

Table 4. Range of public transport accessibility classification in Shenzhen.

Public Transportation Accessibility Level Rating	Range of Values before Adjustment	Range of Values after Adjustment	Map Color
0 (lowest level)	0	0
1	(0, 6.68]	(0, 5]
2	(6.68, 18.53]	(5, 20]
3	(18.53, 34]	(20, 35]
4	(34, 54.47]	(35, 55]
5	(54.47, 86.78]	(55, 85]
6 (highest level)	(86.78, +∞)	(85, +∞)

, and the classification results based on these ranges are illustrated in Figure 14.

3.2.4. Proposals for Estimating the PTAL

Based on considerations of distinguishability and future development space, this study conducted cluster analysis using the k-means clustering method and established a classification method based on the clustering results to create an accessibility estimating model suitable for evaluating public transportation accessibility levels in Shenzhen. However, the choice of classification method should be flexible in practical applications, considering the evaluation objectives and relevant factors of public transportation accessibility levels. The selection of the classification method should be based on the specific purpose of using public transportation accessibility levels to better serve the estimation of public transportation accessibility. For instance, in this study, considering the potential continuous improvement of the public transportation accessibility index with the future development of public transportation, a clustering method with a smaller proportion of higher-level regions, such as the k-means clustering method, was chosen. However, if the goal is to intuitively understand the public transportation development status across different percentiles in Shenzhen based on the results of public transportation accessibility level estimation, the quantile method would be more suitable.

Therefore, when other cities refer to the estimation of public transportation accessibility levels in Shenzhen, appropriate adjustments should be made based on the specific characteristics of each city. The Shenzhen public transportation accessibility estimating method can serve as a reference, and potential adjustments based on the city’s characteristics are presented in

Table 5. Different types of cities refer to the Shenzhen method for public transport accessibility estimation.

City Characteristics	Reference Method
Higher public transportation coverage, fewer railroads and streetcars undertaking intra-city transportation, rail transportation network basically taking shape, but still a large amount of public transportation infrastructure planned or under construction.	Similar to the case of Shenzhen, the calculation steps in this paper can be referred to, but the parameters need to be adjusted according to the actual situation.
High degree of public transportation coverage, public transportation network basically formed, public transportation development tends to be mature, less public transportation infrastructure planned or under construction.	Due to the maturity of the development area, the quartile can be used for grading, in order to effectively differentiate the development situation of different regions.
High degree of public transportation coverage, intercity railroads, commuter railroads, etc., with a large amount of intra-regional transportation also undertaken.	Include railroad operation data in the calculation and determine the weighting according to the passenger flow sharing ratio.
There is no rail transit, or the scale of rail transit is small, but rail transit construction has been planned or is under construction.	The weight of rail transit is determined according to the actual passenger flow or the projected passenger flow of planning.
Low public transportation coverage, no rail transit planning, in other words, low proportion of public transportation for all modes of travel.	Public transportation accessibility estimation is of little significance.

.

3.3. Similarities and Differences in PTAL between Shenzhen and London

3.3.1. Improvements of the Improved PTAL Method

The public transportation accessibility level studied in this paper can be applied in various fields, such as urban planning, urban development, and comparative analysis. Internationally, the most well-established mechanism for applying public transportation accessibility levels is found in Greater London. In Greater London, public transportation accessibility levels are utilized in areas such as parking allocation and planning analysis, and they are incorporated into the city’s urban planning.

By utilizing public transportation operation data from Shenzhen and adopting the same public transportation accessibility estimating method and parameters as in Greater London, it is possible to obtain an evaluation of Shenzhen’s public transportation accessibility levels based on the same evaluation criteria as in Greater London. By comparing the evaluation results of Shenzhen with those of Greater London, it is possible to analyze the similarities and differences in the development of public transportation between the two areas. The main differences between the PTAL method used in Greater London and the improved PTAL evaluation method established in this paper for Shenzhen are summarized in

Table 6. Similarities and differences in public transportation accessibility levels between Shenzhen and London regions.

Project Object	London PTAL Model	The Improved PTAL Model
Evaluation time	8:15 a.m.–9:15 a.m.	7:00 a.m.–9:00 a.m.
Walking speed	80 m/min	72.2 m/min
Bus stop service area	Walking distance 640 m (8 min)	Walking distance 500 m (7 min)
Subway station service area	Walking distance 960 m (12 min)	Walking distance 1000 m (15 min)
Bidirectional line frequency calculation method	Take the direction with a higher frequency as the frequency of the line	Bidirectional calculation separately
Equivalent frequency weights of different routes	Equivalent frequency of the line with the highest frequency is weighted at 1; the other routes are weighted at 0.5	Equivalent weights
Weights of different public transportation modes	Equal weights	Metro accessibility index weight: 0.6 Bus accessibility index weight: 0.4

.

It can be observed that the main differences between the London PTAL evaluation method and this paper lie in the evaluation time, service scope, total waiting time, and calculation method for bidirectional route frequency.

The improved PTAL method exhibits several notable advantages over the London PTAL method. Firstly, it addresses the issue of data accessibility by requiring lower real-time data demands for urban public transportation, thus reducing the difficulty in data acquisition. This improvement is particularly significant for cities with limited data availability.

Moreover, the simulation performance of the improved PTAL method is enhanced in two key aspects. To begin with, recognizing that different transportation modes attract varying levels of passenger flow, the method replaces the equal weighting of all transportation modes with weights determined based on actual passenger flows. This refinement allows for a more accurate representation of the attractiveness of different transportation options to residents. Additionally, the calculation of equivalent frequencies for bidirectional routes has been enhanced by evaluating each direction separately instead of simply choosing the direction with the higher frequency. This adjustment results in better simulation accuracy for the improved model, especially when considering complex urban transport networks.

By incorporating these improvements, the proposed improved PTAL method addresses some of the limitations of the London PTAL method and enhances the model’s applicability, performance, and interpretability in the context of Shenzhen’s public transport system.

3.3.2. Comparative Analysis of the Results

By applying the London PTAL evaluation model to calculate the public transportation operational data of Shenzhen and conducting the classification, the final evaluation results are shown in Figure 15.

It can be seen that according to the London PTAL evaluation method, areas in Shenzhen with a public transportation accessibility level of 6 (including 6a and 6b) are widely distributed in the districts of Futian, Luohu, Nanshan, Bao’an, and Longhua. There are also some areas along Longgang Avenue, Shiyan, Guangming, and Yantian that have a public transportation accessibility level of 6.

The public transportation accessibility levels in Greater London are shown in Figure 16. It can be observed that areas in Greater London with a public transportation accessibility level of 6 are mainly concentrated in the central city area of London and scattered in the centers of various towns. A comparison reveals that the proportion of areas in Shenzhen with a public transportation accessibility level of 6 is significantly higher than that in Greater London, indicating that, under the same standard, a higher proportion of areas in Shenzhen have better public transportation development compared to Greater London.

The proportion of areas in Greater London with no public transportation coverage (i.e., a public transportation accessibility level of 0) is significantly smaller than in Shenzhen, and most areas in Greater London have a public transportation accessibility level of 1 (including 1a and 1b). In contrast, nearly half of the area in Shenzhen lacks public transportation coverage.

The main reason for this difference is that Shenzhen is located in a hilly area with a large number of natural features, such as mountains and reservoirs. As the built-up area of Shenzhen accounts for only 48.11% of the city area, this indicates that over half of the area in Shenzhen is undeveloped. These areas mainly consist of mountains and bodies of water within the city, making it difficult for public transportation to reach them and not necessary to provide public transportation coverage. In contrast, London spans both sides of the River Thames and is predominantly flat with lower terrain. Therefore, public transportation in Greater London can conveniently cover most areas of London.

In conclusion, due to the topography, the proportion of Shenzhen’s area covered by public transportation is smaller than in Greater London. However, under the same standard, the proportion of areas in Shenzhen with a higher public transportation accessibility level is significantly higher than in Greater London. This indicates that, under the same standard, the public transportation development in the built-up area of Shenzhen is better than in Greater London.

Furthermore, as depicted in Figure 17, the comparative analysis reveals that Shenzhen’s more advanced public transportation development results in an excessively large proportion of areas being classified as having higher public transportation accessibility levels, according to the London PTAL classification method. Consequently, there is a lack of differentiation for areas with higher public transportation accessibility indices. In contrast, considering the ongoing advancements in public transportation infrastructure, the improved PTAL evaluation method demonstrates better differentiation for the public transportation accessibility index in comparison to the London PTAL method.

This comparative analysis, along with the visual representations, offers a comprehensive understanding of the effectiveness of the improved PTAL method and highlights its advantages over the London PTAL method in assessing public transportation accessibility in the context of Shenzhen. It provides valuable insights into the unique characteristics of Shenzhen’s public transportation system and aids in refining the assessment methodology for public transportation planning and management.

4. Discussion and Conclusions

4.1. Conclusions

This study proposes a method to analyze the static accessibility of public transportation services to residents using pedestrian data, public transportation station data, and departure data. Taking Shenzhen as an example, the study calculated the public transportation accessibility index for nearly 100,000 grid points in the entire city and provides an overview of the public transportation accessibility in Shenzhen. By studying the performance and results of different classification methods for the public transportation accessibility index in Shenzhen, the study identified a suitable classification method for assessing the public transportation accessibility levels in the city. The evaluation results of Shenzhen’s public transportation accessibility levels were analyzed and compared with those of other cities, providing a reference for the application of public transportation accessibility levels.

Based on the calculation and classification of the public transportation accessibility indices in Shenzhen, the study established an evaluation framework for the public transportation accessibility levels in the city and drew the following conclusions:

• When clustering the public transportation accessibility index using clustering algorithms, selecting six clusters is more appropriate. After comprehensive comparison, the use of k-means clustering with six clusters is recommended, but adjustments to the classification method should be made based on the specific application scenarios.
• When using statistical analysis methods to classify the public transportation accessibility indices in Shenzhen, the quantile method shows better performance.
• The proposed evaluation method for public transportation accessibility levels in this study requires fewer data and can be quickly applied to compare the development of public transportation in different areas and predict the impact of major transportation infrastructure construction on surrounding areas.
• The proposed method for assessing public transportation accessibility in this study can provide theoretical guidance for the policy formulation of future new public transportation lines in Shenzhen. The operation of new subway lines in the Longgang, Pingshan, Nanshan, and Bao’an districts can significantly improve their public transportation conditions. However, in the Futian and Luohu districts, where the surrounding public transportation facilities are relatively mature, the improvement effect on the surrounding areas’ public transportation conditions after the subway lines are put into operation may be limited. Additionally, the public transportation coverage in the Shenshan Special Cooperation Zone area exhibits a scattered linear distribution, and the majority of areas covered by public transportation only achieve level 1 accessibility. This indicates that the public transportation accessibility level is low in this area, and efforts are needed to enrich its public transportation resources.

4.2. Limitations and Suggestions

There are limitations to this study due to factors such as data sources. The main limitations are as follows:

• The use of grid method in evaluating public transportation accessibility levels may result in differences from the actual distribution of travel points.
• Due to data limitations, the study treats same-named bus stops on both sides of the road as the same stop. However, in reality, there may be differences in walking time to bus stops on either side of the road, especially for stops along main roads or expressways, where the differences in walking time are more pronounced.
• A more comprehensive and reliable urban public transportation accessibility measurement model could be developed by integrating city taxi GPS trajectory data and bicycle data.

Therefore, future improvements can be made in the following aspects:

• Utilize building and community data to define the research scope as individual buildings or communities, rather than analyzing based on grid points, to make the research findings more realistic and applicable.
• Further divide bus stops to capture walking distances and times, such as separately calculating bus stops on each side of the road, to improve the accuracy of public transportation accessibility evaluation results.
• Incorporate real-time public transportation operational data, mobile signaling data, and other data sources to expand the study of static public transportation accessibility to dynamic public transportation accessibility.
• The proposed improved PTAL method in this study can be applied in various fields, including urban planning and comparative analysis. Additionally, as the method does not require real-time data, it can also incorporate expected future public transportation operational data for calculating the improvement level, providing a quantitative reference for anticipated operational plans.