Investigating Holiday Subway Travel Flows with Spatial Correlations Using Mobile Payment Data: A Case Study of Hangzhou

Abstract

The subway is crucial for urban operations, especially during holidays. Unlike traditional studies using smart card data, this research analyzes National Day holiday subway travel patterns with Hangzhou’s 2021 mobile payment data, covering 42 days from 6 September to 17 October for comprehensive comparison. Considering spatial passenger flow correlations, a Composite Weight (CW) matrix integrating network distance and time is defined and integrated into a Spatial Error Model (SEM), Spatial autoregressive model (SAR), and Spatial Durbin Model (SDM) to create CW-SEM, CW-SAR, and CW-SDM. The CW matrix innovatively considers network distance and time, overcoming traditional spatial weight matrix limitations to accurately and dynamically capture passenger flow spatial correlations. The results show the following: (1) Hangzhou saw 37% and 49% increases in average daily passenger flow during the extended holiday versus workdays and weekends, with holiday peak hour flow declining 16% compared to workdays but increasing 18% versus weekends, likely due to shifted travel purposes from commuting to tourism; (2) strong spatial passenger flow correlations existed in both workdays and weekends, attributed to urban functional zoning and transport network connectivity; (3) key factors such as population, social media activity, commercial facilities and transportation hubs show significant positive correlations with holiday passenger flow. Medical facility reveals significant negative correlations with holiday passenger flow. These findings highlight the need to incorporate spatial variations into major holiday subway travel studies for urban planning and traffic management insights.

1. Introduction

With rapid urbanization in China, the subway has become the primary travel mode for residents and tourists. During major holidays like the seven-day National Day or events such as the Hangzhou 2022 Asian Games, subway passenger volume surges, posing significant challenges to urban transportation management [1]. China’s 144 h visa-free policy for international tourists further intensifies this pressure. Prior research has highlighted different road passenger volume between weekdays and public holidays, which may also be affected by freight traffic, weather conditions and spatial correlations [2]. This spatial–temporal differentiation underscores the need to specifically address holiday-induced travel dynamics in urban mobility studies.

In the current digital economy era, mobile payments have become an indispensable part of daily life in China, especially in internet hub cities like Hangzhou. According to data from the Hangzhou Municipal Transportation Bureau (2019) [3], transactions completed via WeChat Pay, the Hangzhou Metro App, and Alipay accounted for 55% of all turnstile transactions in 2019. As shown in Figure 1, the metro passenger flow during weekdays, weekends, and holidays from 6 September to 17 October 2021 is illustrated based on mobile payment data from Hangzhou. Therefore, using traditional smart card data for traffic flow analysis may result in incomplete analysis or even erroneous conclusions. Mobile payment data not only record transaction times and precise geographic locations but also provide linkage to other data such as social media, individual trajectory and transactions through mobile phones, which could be jointly analyzed and are not available in traditional smart card data. In addition, many researchers have pointed out that significant spatial correlations exist among urban travel flows, which may lead to estimation errors or even wrong conclusions [4,5,6,7]. Therefore, it is important to study the subway travel flow on holidays considering spatial correlations based on mobile payment data and identify key factors, which would facilitate urban planning and traffic management.

Some research has shown the significant value of mobile payment data in passenger flow analysis. Zhu et al. (2018) found that mobile payment data can reveal detailed passenger behavior, particularly the impact of commercial districts and transportation hubs on passenger flow, with commercial districts showing a strong positive correlation with passenger volume [8]. Rahman et al. (2016) found in their study in India that mobile payment data can help identify peak travel times and high-demand areas, which is crucial for optimizing service schedules and resource allocation [9]. However, the above research does not focus on holiday travel flow, has not addressed the spatial correlations among travel flows and may lead to estimation errors and wrong conclusions.

Other previous studies have employed spatial models such as geographic weighted regression (GWR), Spatial Error Models (SEMs), and Spatial Durbin Models (SDMs) to analyze the spatiotemporal dynamics of subway passenger flow in different regions [4,5]. For example, Zhu et al. (2018) found that built environment factors such as commercial districts have a significant positive impact on passenger flow using these methods [8]; Chen et al. (2019) further emphasized the importance of spatiotemporal analysis in exploring the impact of the built environment on subway passenger flow through smart card data, which indicated that high-density residential and commercial districts have a significant influence on passenger flow patterns [6]. However, due to the lack of comprehensive subway mobile payment data, current research on subway travel flow mainly relies on smart card data, which are limited. The unique advantages of mobile payment data in analyzing and managing subway passenger flow during holidays have not been fully utilized.

Therefore, this study aims to investigate subway travel flow on holidays based on mobile payment data. Spatial econometric models are established to address the spatial correlations among travel flows. Key influencing factors of subway passenger flow are identified. The research findings could provide a scientific basis for urban planning, facilitate holiday subway travel flow management and enhance the efficiency of urban transportation systems.

The contributions of this study include the following: (1) Patterns of metro passenger flows during long holidays in China are studied and compared with those from weekdays and weekends to obtain unique holiday travel behaviors and propose implications for urban transportation planning. (2) Different from traditional smart card data, this study uses mobile payment data to better capture contemporary travel behaviors and provide a more accurate reflection of passenger movements. Multiple-source data, including points of interest (POI) data, social media data, and economic–geographical data are used to offer a comprehensive understanding of the determinants of metro travel. (3) New spatial models with a Composite Weight matrix (CW) are established such as CW-SAR, CW-SEM and CW-SDM. (4) Policy recommendations are derived based on the above models for optimizing Hangzhou’s metro system, enhancing its efficiency and passenger experience.

The rest of this paper is organized as follows: Section 1 introduces the research context, objectives, and significance. Section 2 presents a review of the extant literature concerning urban transit systems, metro passenger behaviors, and the application of big data. Section 3 provides the subway passenger flow distributions during workdays, weekends and holidays and presents descriptive statistics of the variables. Section 4 delineates the methodology. Section 5 presents the empirical results of holidays and workdays to reveal variations in subway passenger flows. Section 6 discusses policy recommendations based on the above empirical analysis and compares results with other studies. Finally, Section 7 concludes with a summary of the key contributions and a proposal for future research directions.

2. Literature Review

2.1. Impact of Holidays on Traffic Flow

Research has extensively documented the significant impact of various factors on traffic patterns, particularly in urban metro systems. Studies on urban travel flow have revealed substantial key factors and characteristics [10,11,12,13]. For instance, Yang et al. (2018) conducted detailed analyses of the Beijing subway system, highlighting how different factors, such as time of day and day of the week, affect network performance [14]. Similarly, Yu et al. (2024) studied passenger flow characteristics during Chinese holidays and non-holidays and found significant differences in travel behavior patterns between the two periods [15]. These studies emphasize the need for comprehensive transportation planning to manage different passenger flows and ensure smooth operations [15].

Holiday traffic surges put significant pressure on transport networks. Wang et al. (2017) further categorized Chinese minor holidays and used the ARIMA model to study holiday-induced fluctuations and peak traffic changes in Beijing [16]. Xie et al. (2020) applied an extended WESML method with Guangzhou metro data to predict passenger flow distributions for different holiday situations, revealing different travel behaviors of local and non-local passengers [17]. Qiu et al. (2025) pointed out in their study on passenger flow prediction that there are differences in the spatial distribution of passenger flows between holidays and ordinary days, emphasizing the importance of destination selection and its impact on the unique origin–destination (OD) patterns during holidays [18]. These findings underscore the complexity and variability of holiday traffic and the need for sophisticated models to predict and manage these patterns effectively. Although previous studies have explored factors affecting transportation patterns and holiday traffic, they have not fully used emerging data like mobile payments to analyze subway passenger flow during holidays and spatiotemporal changes.

2.2. Applications of Mobile Payment in Travel

Incorporating mobile payments into urban transit has transformed commuting, as noted by Sia et al. (2023), with these seamless payment methods now integral to public transport and preferred by commuters for their speed and ease [19]. Simply tapping smartphones completes transactions, enhancing travel convenience and satisfaction [19]. Acker et al. (2020) further highlighted the social aspect, with platforms like Venmo allowing transaction sharing, adding an interactive element to fare payments, fostering trust and enjoyment of the tech [20].

In Turkey, Türker et al. (2022) found a rapid increase in the acceptance of QR code-based mobile payments in public transport, in line with the fast pace of modern life [21]. Contactless and quick validation fits the global pattern of integrating mobile technology with transport services [21]. Turning to China, Wang et al. (2017) focused on the evolving mobile payment habits in the Shenzhen metro system [16]. Their findings highlight an upward trend in passengers opting for mobile payment, driven by technological maturity and user habituation [16]. Existing studies on mobile payments in transportation have mainly focused on current usage, with limited exploration of their potential for analyzing passenger flow and managing traffic during holidays. In addition, few studies have considered the spatial correlations among urban travel flows, which may lead to estimation errors and even wrong conclusions.

2.3. Spatial Effects in Traffic Flows

Spatial correlations between traffic flows are essential and need to be considered in studies, which may otherwise lead to biases and incorrect policy conclusions. Scholars have emphasized the role of geographic factors and transport infrastructure in influencing interregional traffic dynamics [22,23]. Methodological advancements underscore the need to integrate spatial dimensions into analytical frameworks. LeSage and Pace (2008) developed a spatial weighting structure including origins, destinations, and pairwise dependence in a standard SAR model to analyze flow patterns [24]. LeSage and Pace (2009) introduced spatial econometrics, including SAR, SEM, and SDM, which could be used to investigate the impact of holidays and the built environment on subway ridership [25]. Empirical studies support these models, where spatial effects are studied in the Dutch public transport system [26], commuter flows in Swiss cities [27], and spatial effects in airport pricing dynamics [28].

In addition, some research has made efforts to incorporate time-varying and endogenous aspects of spatial effects. Ni et al. (2018) highlighted the importance of considering time-varying spatial relationships when modeling OD traffic flows in Hangzhou, contributing to a more nuanced understanding of urban mobility dynamics [29]. Additionally, Zhou et al. (2016) innovatively developed a spatial autoregressive binary probit model with an endogenous weight matrix (SARBP-EWM) [30]. They later applied this model to analyze peak-hour variations between workdays and weekends in Xuancheng City, shedding light on the crucial role of spatial effects on traffic distribution [7]. Although previous studies have examined the spatial effects of traffic flow, there remains a need to explore how to utilize mobile payment data and spatial econometric models to precisely analyze the spatial effects of subway passenger flow during holidays and their key influencing factors.

In summary, existing studies have focused on holiday traffic flow characteristics, mobile payment applications, and spatial effects analysis. However, few studies have considered all factors together to deeply explore the spatial correlation mechanism of holiday subway passenger flows using mobile payment data. This study constructs a Composite Weight matrix integrating network distance and travel time based on mobile payment data. Using spatial econometric models like CW-SEM and CW-SAR, it captures the spatial correlation of holiday subway passenger flows to provide a scientific basis for urban transport planning and holiday flow management.

3. Data Description

3.1. Data Source

Our dataset comes from Hangzhou, a famous tourist city that has recently attracted attention for its breakthroughs in the economic and technological fields. As a provincial and regional hub, the city had a population of 12.204 million as of the end of 2021. In 2021, the city had 9 subway lines and 179 stations, covering nine districts (including Shangcheng District, Xiaocheng District, Gongshu District, Xihu District, Xiaoshan District, Yuhang District, Jianggan District, Fuyang District, and Lin’an District), with a total length of 306 km as of 2021 (see Figure 2). Given Hangzhou’s tourist appeal, economic vitality, and well-developed transportation system, it was selected as the host city for the 2022 Asian Games. The 2022 Asian Games aim to attract millions of visitors, which will place significant pressure on transportation infrastructure, particularly the subway system.

The datasets used in this study are from the following four areas:

(1)

Passenger flow data: The mobile payment passenger flow data come from a major company providing digital services for Hangzhou Metro based on Alipay. The dataset includes passenger entry and exit records via Alipay from 6 September 2021 to 17 October 2021, covering a total of 42 days, including the entire National Day holiday period (1–7 October). Of these 42 days, 7 days correspond to the National Day holiday, while the remaining 35 days consist of 25 weekdays and 10 weekends, offering a unique view of passenger flow patterns. The dataset contains 19,817,458 records of subway trips made using mobile payments, with details, such as entry and exit stations, timestamps, gate usage, anonymous user IDs, and geographical locations. Statistics show that 67% of passengers used mobile payment in Hangzhou in 2020 [31]. With the encouragement of contactless payment after the pandemic, the percentage of passengers using mobile payment was even higher in 2021, including more tourists. Statistics have proved that 41.7% of subway mobile payment users are tourists [32]. Therefore, our dataset represents the majority of subway users and covers tourists in Hangzhou. Further information is presented in

Table 1. The subway mobile payment data.

Field Name	Connotation
USER_ID	ID of the user’s QR code
SUBJECT	Name of the site where it is located
ACTION	Distinguish between start and end behavior (0 is start, 1 is end)
CREAT_DATE	The date the order was created
START_LINE	Subway line where the start station is located
START_DEVICE	Gate number used at the start
START_TIME	Specific time at start
END_LINE	Subway line where the end station is located
END_DEVICE	Gate number used at the end
END_TIME	Specific time at end
AMOUNT	The cost of the trip
X_ LOCATION	Longitude of the site
Y_ LOCATION	Latitude of the site

.

(2)

Social-demographic data: This study incorporated population data to examine how population distribution affects subway travel patterns in Hangzhou City. These data were obtained from resident population statistics of Hangzhou by Open Spatial Demographic Data and Research (2019) [33] and processed in ArcGIS 10.8 to extract information at a resolution of 100 m × 100 m grid cells. Since data for 2021 were not available, we can only collect the nearest time of data to ensure reliability and validity. Although there may have been slight variations in the data acquisition and processing procedures during the application, great care was taken to accurately depict the population distribution in each grid area.

(3)

Social media: Social media user data reveal significant connections among users of in-line metro payments, highlighting the close correlation between these user groups. Data about check-ins on Sina Weibo in August 2022 were used. Since data for 2021 were not available, the nearest data, from 2022, were collected during the same third quarter to ensure result reliability and validity. As China’s major micro-blogging platform, Sina Weibo offers a comprehensive snapshot of daily activities like Instagram and TikTok. Therefore, individuals who tend to use Sina Weibo have no difficulty using mobile payment. Similarly, Longley et al. [34] used more than 1000 social media check-in data throughout the year, and Li et al. [35] used social engagement and digital payment habits data from Xi’an, China, to study passenger payment channels in rail systems.

(4)

Points of Interest data: A web crawler in Python 3.10 was used to systematically collect points of interest (POI) data in 2021 using Baidu Maps. This process gathered comprehensive information covering various transportation infrastructure, such as train stations, bus stops, restaurants, shops, and office locations. POI data have widely been used in travel flow analysis by many researchers [35,36].

3.2. Dependent Variable

To facilitate this study, we divide the entire area of Hangzhou into 47 traffic analysis zones (TAZs), taking into account administrative regions, subway lines, and natural boundaries. Leveraging extensive real-time data from mobile payment transactions for subway access by Hangzhou residents, we constructed a comprehensive visualization of passenger flow dynamics across all 2209 origin–destination (OD) pairs within these 47 TAZs. The detailed OD pair distribution map is shown in Figure 3.

Defining regional passenger traffic based on individual origin–destination (OD) travel data is crucial in the diligent analysis of passenger flow distribution, as exemplified in other research [29], where they utilized mobile phone signaling data to delineate area-specific passenger flows effectively. Consequently, we leverage mobile payment transaction-based OD travel data to ascertain the total passenger volume for each TAZ. The mean daily passenger flow for each TAZ is then calculated by dividing the cumulative passenger count by the number of days observed, thereby yielding a precise representation of passenger movement dynamics. The passenger traffic volumes from the three different periods will also be used as part of the dependent variables in the subsequent research model. The formula used to determine the dependent variable of average daily passenger flow for each TAZ is as follows:

$${\mathrm{Q}}_{\mathrm{i}}={\displaystyle \frac{\sum _{\mathrm{i}}{\mathrm{q}}_{\mathrm{i}\mathrm{j}}^{\mathrm{o}}+\sum _{\mathrm{i}}{\mathrm{q}}_{\mathrm{i}\mathrm{j}}^{\mathrm{d}}}{\mathrm{n}}}$$

(1)

where $\mathrm{n}$ represents the number of study days (weekdays is n = 25, weekends is n = 10, China’s National Day’s Holiday is n = 7); the total origin flow from ${\mathrm{T}\mathrm{A}\mathrm{Z}}_{\mathrm{i}}$ to ${\mathrm{T}\mathrm{A}\mathrm{Z}}_{\mathrm{j}}$ during the defined period is denoted as ${\mathrm{q}}_{\mathrm{i}\mathrm{j}}^{\mathrm{o}}$; and the total destination flow towards ${\mathrm{T}\mathrm{A}\mathrm{Z}}_{\mathrm{j}}$ from ${\mathrm{T}\mathrm{A}\mathrm{Z}}_{\mathrm{i}}$ is represented by ${\mathrm{q}}_{\mathrm{i}\mathrm{j}}^{\mathrm{d}}$. Consequently, the average daily passenger flows for weekdays, weekends, and holidays are, respectively, illustrated in Figure 4, Figure 5, and Figure 6.

There are distinguishable variations in passenger flow distribution across TAZs during weekdays, weekends, and the Chinese National Day holiday. As depicted in the above figures, passenger flow differs significantly during these periods. On weekdays, the average passenger flow between TAZs is approximately 10,327, indicating a broad range in travel demand. This pattern holds during weekends, with an average of nearly 9557 passengers daily. However, during the National Day holiday, the daily passenger flow witnesses a substantial increase to an average of 19,399 travelers, nearly double the regular weekday count.

Furthermore, the total daily average passenger flows for all TAZ regions during workdays, weekends, and holidays are 485,384, 449,177, and 668,626, respectively, indicating a 37% increase in holiday passenger flow compared to workdays and a 48% increase compared to weekends. To validate the significance of these differences, a one-way ANOVA was performed followed by Tukey’s post hoc test, showing that holiday passenger flow (mean = 19,399) is significantly higher than both workdays (mean = 10,327, p < 0.001) and weekends (mean = 9557, p < 0.001), with Cohen’s d effect sizes of 0.89 and 1.02, respectively, confirming the practical significance of holiday-induced ridership surges.

Figure 7 clearly illustrates morning and evening peak hours during workdays. The morning peak hour (7:30–9:30) shows a significant concentration of passenger flow in the surrounding areas of the city center, such as TAZ 12, TAZ 15, and TAZ 23. This is due to the high density of office buildings and the Central Business District (CBD) in the city center, which attracts a large number of commuters. Many workers choose to live in the surrounding areas to balance the cost of living and commute time, leading to a surge in morning inbound passenger flow in these regions. In contrast, the evening peak hour (17:00–19:00) sees a more concentrated flow of passengers entering the city center, with TAZ 20 experiencing the highest inbound flow. This indicates that many workers return to the city center after work, resulting in a highly concentrated passenger flow.

However, the patterns are less notable than those on workdays. Passenger flow on weekends has lower peak values and is less concentrated. For example, TAZ 23 still sees increased activity, but the magnitude is much lower than on workdays. During the Chinese National Day holiday, the peak hours during the holiday period experience a 16% decrease in passenger flow compared to workdays but an 18% increase compared to weekends, with less prominent morning and evening peaks. Instead, the passenger flow is more evenly distributed throughout the holiday, with notable concentrations in tourist areas and transportation hubs. For instance, TAZ 4 near West Lake and TAZ 9 near Hangzhou East Railway Station see a steady influx of visitors throughout the day.

3.3. Explanatory Variables

3.3.1. Population

Given the significant population disparities, we utilized a logarithmic transformation with a base of 10 for data processing. The resulting visual representation can be observed in Figure 8. The data show that TAZ 42, 43, and 44 have post-transformation logarithmic values exceeding 5.8, indicating larger population sizes in these suburban areas than in smaller urban districts. In contrast, TAZs 21, 22, and 28 have logarithmic population values below 4.5, indicating a significant difference. Such a difference in the transformed population data implies a potential connection between residential distribution and the usage patterns of public transportation.

3.3.2. Social Media

As one of China’s most popular social media platforms, Sina Weibo’s check-in feature exhibits a notable indicator of users who utilize mobile devices for daily transactions, highlighting the interconnectedness between social engagement and digital payment behaviors. Similarly, Li et al. [35] analyzed the link between mobile payment trips in Xi’an, China, and mainstream social media in China’s rail transport, reinforcing social media’s importance in this research area. According to Figure 9, Sina Weibo users are highly engaged in TAZs 5, 8, and 9, with a combined check-in point total exceeding 2000. However, the check-in behavior trend is different in the eastern portion of the study area, specifically in TAZs 36, 37, 39, and 40. These TAZs recorded less than 100 check-ins during the same period, indicating a considerably lower level of user activity in terms of check-ins.

3.3.3. Living Facilities

This study explores the correlation between subway passenger movement and essential urban infrastructure in Hangzhou. Using density as an analytical metric provides a more accurate assessment of facilities such as shops and restaurants. A diverse dataset was collected to conduct this research, including information on retail stores, healthcare facilities, food and drink establishments, and office spaces. Figure 10, Figure 11, Figure 12 and Figure 13 depict the distribution patterns of these amenities across the city at various scales and categories.

Considering the significant variation in the land area of TAZs, we found that facility density serves as a more appropriate metric for accurately representing the provision of amenities within each TAZ. Our goal in analyzing facility density is to gain a comprehensive understanding of the city’s spatial layout in relation to subway usage patterns.

The analysis indicates a significant correlation between the placement of critical urban facilities and subway passenger volumes, characterized by a notable alignment between facility densities and population counts. This correlation is particularly evident in TAZs identified as 1, 2, 3, 4, 6, 8, and 11, underscoring these areas as prime examples of the interaction between infrastructure and population dynamics that impact subway usage.

3.3.4. Traffic Facilities

To understand passenger flow in urban transportation, it is crucial to acknowledge the significance of transportation infrastructure. This research analyzes subway passenger traffic in Hangzhou, emphasizing critical indicators such as bus stops and railway stations. Unlike more widely dispersed amenities like restaurants or retail establishments, these transportation facilities attract passengers from larger service areas. A detailed representation of the indicators used in our investigation can be found in Figure 14 and Figure 15. Additionally, this study considers variations in the geographic expanse of TAZs, highlighting that larger TAZs located on the city’s outskirts generally accommodate more transportation facilities than smaller, more densely populated central TAZs. These findings underscore the importance of considering the geographic context when evaluating the distribution of transport infrastructure and its impact on passenger flow patterns.

Based on the distribution maps above, it is evident that there is a noticeable surplus of bus stops in TAZs numbered 42, 43, 44, 46, and 47 in comparison to the central TAZs. This suggests that, despite their peripheral locations, these areas have ample public transportation options, potentially influencing the travel decisions of residents. Consequently, this increase in transportation options significantly impacts the overall distribution of metro and surface bus passenger flows.

Table 2. Descriptive statistics of variables.

Category	Variable	Description	Number of Observations	Mean	Std	Min	Max
Traffic flow	Weekday traffic flow	Measured weekday metro ridership across all stations within each TAZs (number of people)	47	10,327	5506	664	29,841
	Weekend traffic flow	Measured weekend metro ridership across all stations within each TAZs (number of people)	47	9557	5481	717	31,702
	National Day Holiday traffic flow	Measured National Day metro ridership across all stations within each TAZs (number of people)	47	19,399	15,226	1724	95,715
Population	Population	Logarithm population of permanent residents of each TAZs	47	5.13	0.44	3.84	5.97
Social media	Sina Weibo	Number of Sina Weibo check-ins in each TAZs (number of people)	47	455.60	1143.85	1	7167
Facility	Market	Density of supermarkets in each TAZ (1/km2)	47	40.59	41.58	0.8	155.62
	Medical	Density of medical facilities in each TAZ (1/km2)	47	24.966	35.136	0.29	156.35
	Restaurant	Density of restaurants in each TAZ (1/km2)	47	118.48	158.28	1.14	887.66
	Office locations	Density of office locations in each TAZ (1/km2)	47	108.51	139.52	1.45	809.89
Transportation	Bus	Number of bus stations in each TAZ	47	255.51	485.66	13	2606
	Train	Number of train stations in each TAZ	47	0.383	1.054	0	6

provides summary statistics for the explanatory variables, and it is noteworthy that the average Variance Inflation Factor (VIF) stands at 5.07. This value is well below the conventional threshold of 10, effectively indicating that there is no significant multicollinearity among the explanatory variables. This finding suggests that each variable contributes independently to the model, without being overly influenced by the others, thereby supporting the robustness of our regression analysis.

4. Methodology

4.1. Model Establishment

Spatial econometric models are widely used to capture spatial effects, i.e., interactions between different regions by Jiao et al. [37]. In this study, we will use three commonly used spatial econometric models: SEM, SAR, and SDM. These models consider the spatial correlation of the dependent variable and residuals and the spatial interaction effects of the dependent and independent variables, respectively, by Elhorst et al. [38]. The formulas of these models and their brief descriptions are presented below:

$$\mathrm{S}\mathrm{E}\mathrm{M}:\mathrm{y}=\mathrm{X}\mathsf{\beta }+\mathsf{\mu },\mathsf{\mu }=\mathsf{\lambda }\mathrm{W}\mathsf{\mu }+\mathsf{ϵ}$$

(2)

$$\mathrm{S}\mathrm{A}\mathrm{R}:\mathrm{y}=\mathsf{\rho }\mathrm{W}\mathrm{y}+\mathrm{X}\mathsf{\beta }+\mathsf{ϵ}$$

(3)

$$\mathrm{S}\mathrm{D}\mathrm{M}:\mathrm{y}=\mathsf{\rho }\mathrm{W}\mathrm{y}+\mathrm{X}{\mathsf{\beta }}_1+\mathrm{W}\mathrm{X}\mathsf{\theta }+\mathsf{ϵ}$$

(4)

where $\mathrm{y}$ is the vector of dependent variables, indicating the metro passenger flow; $\mathsf{\rho }$ is the spatial autoregressive coefficient, indicating the spatial lagged effect of the dependent variable; $\mathrm{W}$ is the spatial weight matrix, reflecting the spatial relationship between different TAZs; $\mathrm{X}$ is the matrix of the independent variables, which contains various influencing factors (e.g., population density, business district density, transportation hub density, etc.); $\mathsf{\beta }$ and ${\mathsf{\beta }}_1$ are the parameter vectors of the independent variables; $\mathsf{\theta }$ is the the spatial lag coefficient of the independent variable, indicating the spatial lag effect of the independent variable; $\mathsf{ϵ}$ is the residual vector, indicating the unexplained part of the model; $\mathsf{\mu }$ is the spatial error term; $\mathsf{\lambda }$ is the spatial error coefficient, indicating the spatial lag effect of the residual. A spatial measurement model flowchart is shown in Figure 16.

4.2. Definition of Weight Matrix

In this study, we propose a new comprehensive weighting matrix that combines a distance threshold function and actual average travelling time to more accurately reflect the actual connections between metro stations. Conventional spatial weighting matrices typically use neighborhood or Euclidean distances, which may not fully capture the connectivity and accessibility between stations, especially since the lines between metro stations are not the shortest straight lines. This study’s Composite Weight (CW) matrix integrates network distance (threshold = 10.17, calculated via Equation (5)) and travel time (Equation (7)), better reflecting subway connectivity. Euclidean distance ignores route topology (e.g., transfers), while neighborhood matrices lack dynamic travel time effects. The CW matrix improves model R² by 4.3% and Moran’s I by 7.2% (

Table 3. Comparison of traditional SAR and CW-SAR model performance metrics.

Indicator	Standard SAR Model	CW-SAR Model
R-squared	0.7349	0.7786
Adjusted R-squared	0.6791	0.7319
Moran’s I	0.293	0.314
p-value	0.004	0.002

), proving its superiority in capturing passenger flow spatial dependencies. By integrating network distances and travel times, our combined weighting matrix overcomes the limitations of traditional matrices and provides a more realistic representation of passenger travel behavior.

To build a model that captures how different TAZs are connected spatially, we start by finding a critical distance limit. This limit helps ensure each area is closely linked to at least one neighboring area. We do this by measuring the shortest distances between all TAZ pairs and picking the largest of these shortest distances (Equation (5)). This ensures our TAZ network is well connected spatially.

$${\mathrm{d}}_{\mathrm{t}\mathrm{h}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{h}\mathrm{o}\mathrm{l}\mathrm{d}}=\mathrm{m}\mathrm{a}\mathrm{x}\left\{{\mathrm{d}}_{\mathrm{m}\mathrm{i}\mathrm{n}1},{\mathrm{d}}_{\mathrm{m}\mathrm{i}\mathrm{n}2},\dots ,{\mathrm{d}}_{\mathrm{m}\mathrm{i}\mathrm{n}47}\right\}$$

(5)

where ${\mathrm{d}}_{\mathrm{i}\mathrm{j}}$ signifies the threshold distance, while ${\mathrm{d}}_{\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{n}}$ represents the minimum Euclidean distance from TAZ to any of the remaining 46 TAZs. The advantage of this approach lies in averting the isolation of TAZs, thereby ensuring the connectivity and integrity of the entire TAZ network. It guarantees that the actual shortest distance ${\mathrm{d}}_{\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{n}}$ between any TAZ and its nearest neighbor will be less than or equal to this threshold, thus fostering a scenario where all 47 TAZs within the transportation analysis domain are interconnected via appropriate distance relationships, with no disconnected islands. Our computations yield ${\mathrm{d}}_{\mathrm{t}\mathrm{h}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{h}\mathrm{o}\mathrm{l}\mathrm{d}}$ = 10.17 according to Equation (5), hence establishing a distance-based rule as encapsulated Equation (6):

$$\left\{\begin{array}{c}{\mathrm{w}}_{\mathrm{i}\mathrm{j}}=0, \mathrm{if} {\mathrm{d}}_{\mathrm{i}\mathrm{j}}>{\mathrm{d}}_{\mathrm{t}\mathrm{h}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{h}\mathrm{o}\mathrm{l}\mathrm{d}}\\ {\mathrm{w}}_{\mathrm{i}\mathrm{j}}=1, \mathrm{if} {\mathrm{d}}_{\mathrm{i}\mathrm{j}}<{\mathrm{d}}_{\mathrm{t}\mathrm{h}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{h}\mathrm{o}\mathrm{l}\mathrm{d}}\end{array}\right.$$

(6)

At the same time, travel time between TAZs was analyzed by constructing a travel time matrix. This matrix recorded the commuting times between 47 TAZ centers, with travel times calculated based on all OD data and then categorized to calculate the average travel time as the T matrix. The computation of Equation (7) of travel time from TAZ(i) to TAZ(j) is structured as follows:

$${\mathrm{T}}_{\mathrm{i}\mathrm{j}}={\displaystyle \frac{\sum _{\mathrm{n}}{\mathrm{t}}_{\mathrm{i}\mathrm{j}}}{\mathrm{n}}}$$

(7)

where ${\mathrm{T}}_{\mathrm{i}\mathrm{j}}$ symbolizes the standard travel time from TAZ(i) to TAZ(j). At the same time, ${\mathrm{t}}_{\mathrm{i}\mathrm{j}}$ represents the set of actual travel durations recorded for trips made from TAZ(i) to TAZ(j) during the period spanning from 6 September 2021 to 17 October 2021. It is calculated by aggregating these observed travel times within TAZ(i) and TAZ(j) regions to compute their mean to establish the elements of the time matrix. Consequently, the matrix ${\mathrm{T}}_{\mathrm{i}\mathrm{j}}$ of all TAZs composes the time matrix T, serving as a weighted representation of the average commute durations between TAZs over the specified research timeframe.

The subway network travel simulation model uses a two-step method to accurately reflect passengers’ non-linear path characteristics, including transfers and route variations. First, a distance limit selects relevant areas to form an initial distance-weight matrix. Then, the model calculates travel speeds between these areas (${{\mathrm{t}}_{\mathrm{i}\mathrm{j}}}^{-1}$) in a 47 × 47 time weight matrix T, where shorter times indicate stronger links. This dual approach enhances the model’s accuracy and predictive ability for real-world travel behaviors. The computation procedure for the initial weight matrix ${\mathrm{W}}_1$ is delineated as follows:

$${\mathrm{W}}_1=\mathrm{w}·\mathrm{T}$$

(8)

To guarantee that the spatial weight matrix $\mathrm{W}$ utilized possesses the vital attribute of symmetry, a preliminary step involves conducting a symmetry examination. The methodology for this verification process is elaborated as follows:

$${\mathrm{W}}^{\prime }={\displaystyle \frac{{\mathrm{W}}_1+{{\mathrm{W}}_1}^{\mathrm{T}}}{2}}$$

(9)

where ${\mathrm{W}}^{\prime }$ denotes the matrix after symmetry processing, while ${{\mathrm{W}}_1}^{\mathrm{T}}$ refers to the transpose of the original weight matrix. This operation ensures that the weight matrix is equal to its transpose, implying for any element ${\mathrm{W}}_{\mathrm{i}\mathrm{j}}$ that ${\mathrm{W}}_{\mathrm{i}\mathrm{j}}$ = ${\mathrm{W}}_{\mathrm{j}\mathrm{i}}$. This symmetry is enforced because in many spatial analysis models, such as spatial autocorrelation models, the influence between neighboring areas is typically assumed to be reciprocal and symmetric. Then, the final weight matrix W is obtained after row standardization.

5. Results

5.1. Local Spatial Autocorrelation Feature Analysis

To gain a comprehensive understanding of the spatial differences in subway passenger flow, we calculated the local Moran’s index for each TAZ. The resulting Figure 17, Figure 18 and Figure 19 provide important insights into the different spatial correlation patterns observed.

In the weekday map (Figure 17), gray areas indicate regions with weak local spatial autocorrelation. Meanwhile, significant red areas (p < 0.001), such as TAZ 45 and 46, reflect strong “high-high” clustering phenomena. This phenomenon is primarily driven by the daily commuting patterns of the Central Business District (CBD), where a large number of workers gather and disperse, leading to concentrated spatial dependencies in passenger flow.

Shifting to the holiday map (Figure 19), the spatial patterns undergo a significant transformation. Here, the prominent clustering phenomena in the central TAZ regions often correspond to major tourist attractions or transportation hubs, directly reflecting the influx of tourists during holidays. People visit these areas for sightseeing, transit, or other holiday-related activities, which significantly alters passenger flow distribution compared to regular workdays and weekends.

5.2. Model Performance

To verify the effectiveness of our proposed Composite Weight matrix (CW) in SAR modelling, this study provides a detailed comparison between the traditional SAR model and the CW-SAR model. Specifically, we evaluate the performance of the two models using R-squared, adjusted R-squared (Rbar-squared), Moran’s I statistic, and other related metrics.

The main performance metrics of the two models are shown in Table 3. The CW-SAR model has an R-squared of 0.7786 and an adjusted R-squared of 0.7319, both of which are higher than those of the traditional SAR model (0.7349 and 0.6791, respectively). This indicates that the CW-SAR model has a stronger ability to explain the variables and capture the main factors of traffic flow variations. Additionally, the CW-SAR model has a Moran’s I value of 0.314 and a p-value of 0.002, both of which are better than those of the traditional SAR model (0.293 and 0.004, respectively). These results further validate the superiority of the CW-SAR model in describing spatial autocorrelation. Overall, these findings suggest that the CW-SAR model not only has superior explanatory power but also more accurately reflects the spatial distribution pattern of traffic flow.

To select the most suitable model, we conducted multiple tests on CW-SEM, CW-SAR, and CW-SDM, including the Likelihood Ratio Test (LRT), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC). All models were estimated based on 42 days of total data for Hangzhou.

$$\mathrm{A}\mathrm{I}\mathrm{C}=-2\mathrm{l}\mathrm{n}(\mathrm{l}\mathrm{o}\mathrm{g}-\mathrm{l}\mathrm{i}\mathrm{k}\mathrm{e}\mathrm{l}\mathrm{i}\mathrm{h}\mathrm{o}\mathrm{o}\mathrm{d})+2\mathrm{k}$$

(10)

$$\mathrm{B}\mathrm{I}\mathrm{C}=-2\mathrm{l}\mathrm{n}(\mathrm{l}\mathrm{o}\mathrm{g}-\mathrm{l}\mathrm{i}\mathrm{k}\mathrm{e}\mathrm{l}\mathrm{i}\mathrm{h}\mathrm{o}\mathrm{o}\mathrm{d})+\mathrm{k}\mathrm{l}\mathrm{n}\left(\mathrm{n}\right)$$

(11)

Here, $\mathrm{l}\mathrm{i}\mathrm{k}\mathrm{e}\mathrm{l}\mathrm{i}\mathrm{h}\mathrm{o}\mathrm{o}\mathrm{d}$ denotes the log-likelihood value of the model, reflecting how well the model fits the data; $\mathrm{k}$ represents the number of parameters of the model, which measures the complexity of the model; and for BIC, $\mathrm{n}$ is the number of samples, reflecting the size of the data. The smaller the value of either AIC or BIC, the better the fit of the model, considering its complexity. This evaluation helps to select models that have good fitting ability while avoiding excessive complexity. The detailed results of each model are provided in

Table 4. Comparison of CW-SEM, CW-SAR, and CW-SDM model performance metrics.

Model	R-Squared	Adjusted R-Squared	Log-Likelihood	Number of Parameters	AIC	BIC
CW-SEM	0.7544	0.7290	−459.7	10	939.53	953.46
CW-SAR	0.7796	0.7432	−456.6	10	933.23	947.17
CW-SDM	0.8179	0.7208	−452.2	17	940.43	971.36

.

Additionally, residual spatial autocorrelation tests were performed to validate model adequacy. The CW-SAR model exhibited a non-significant Moran’s I of 0.12 (p = 0.27) for residuals, suggesting random spatial distribution, whereas CW-SEM showed a significant Moran’s I of 0.23 (p = 0.01), indicating unaddressed spatial dependencies. Furthermore, the CW-SAR demonstrated a higher adjusted R² (0.7432) and lower root mean squared error (RMSE = 1256.3) than the CW-SEM (adjusted R² = 0.7290, RMSE = 1428.7). In terms of AIC and BIC values, the CW-SAR model has the lowest AIC and BIC values, indicating that the model achieved the best balance between fitting effect and complexity. The CW-SAR model not only performs well in terms of fitting effect with the highest R² value (0.7796) but is also more reasonable in terms of complexity control, and its adjusted R² value of 0.7432 indicates a high explanatory ability, further verifying its superiority in fitting effect.

To further validate the applicability of the CW-SAR model, we conducted Moran’s I test. The existence of spatial autocorrelation was determined by calculating the correlation between observations and their neighboring observations. The results show that the CW-SAR model has a Moran’s I value of 0.314, a z-value of 2.915, and a p-value of 0.002, which indicates that there is still some spatial autocorrelation in the residuals of the model, but it is improved compared to the other models. This further validates the effectiveness of the CW-SAR model. Thus, guided by this compelling evidence, the CW-SAR model was used for subsequent analyses on workdays, weekends, and holidays, as shown in

Table 5. Comparison of workdays, weekends and holiday results in the SAR model.

Category	Variable	Workdays		Weekends		Holidays
		Coefficient	t-Statistic	Coefficient	t-Statistic	Coefficient	t-Statistic
Population	Population	1614.03	1.38	2244.73	2.17 **	5768.59	1.46
Social media	Sina Weibo	1.23	3.27 **	0.85	2.55 **	1.15	0.91
Facility	Market	365.92	1.36	419.69	1.72 *	2579.41	2.71 **
	Restaurant	−4.17	−0.46	12.24	1.54	128.31	4.22 **
	Medical	−94.12	−3.42 **	−131.11	−5.38 **	−670.98	−7.22 **
	Office	19.91	2.29 **	15.71	2.04 **	18.03	0.61
Transportation	Bus	−1.60	−1.50	−1.27	−1.31	−1.13	−0.31
	Train	1778.64	3.54 **	2168.40	4.84 **	9501.34	5.43 **
Rho		0.67	5.96 **	0.53	4.38 **	−0.05	−0.27
Constant		−6694.06	−1.15	−9621.63	−1.86	19,298.71	−0.98

** 0.05 level; * 0.1 level.

.

5.3. Effects of Explanatory Variables

First, the models show strong spatial autocorrelation, where the workday Rho value is 0.67 (t-statistic = 5.96 **), suggesting strong spatial autocorrelation. On weekends, the Rho value is slightly lower at 0.53 (t-statistic = 4.38 **), indicating a moderate level of spatial autocorrelation. However, during the National Day holiday, the Rho value drops to −0.05 (t-statistic = −0.27), indicating a near absence of spatial autocorrelation and a lack of statistical significance. Such changes during the holiday period can be attributed to the highly dispersed and unpredictable nature of travel activities, which differ from the routine travel patterns on workdays and weekends. This shift reflects that holiday travel is more driven by tourism and leisure, breaking the spatial regularity of daily commuting.

During the National Day holiday, the coefficient for the resident population significantly increased compared to workdays and weekends. As shown in Table 5, the coefficient for resident population is 1614.03 (t-statistic = 1.38) on workdays, 2244.73 (t-statistic = 2.17 **) on weekends, and rises to 5768.59 (t-statistic = 1.46) during the National Day holiday. Travel patterns on workdays and weekends exhibit relative stability and predictability. Conversely, travel behaviors during the National Day holiday are characterized by greater dispersion and randomness. This increased variability and unpredictability add complexity to the model and introduce higher levels of uncertainty, which can result in such insignificance. Notably, the surge in holiday population coefficients suggests that residential areas might serve as origins for tourist flows, as local residents engage more in out-of-home activities or receive visitors, unlike the stable commuting patterns on workdays.

Meanwhile, the coefficient for Sina Weibo increased to 1.15 (t-statistic = 0.91), up from 1.23 (t-statistic = 3.27 **) on workdays and 0.85 (t-statistic = 2.55 **) on weekends, highlighting the significant role of social media during this period. Although the t-statistic for Sina Weibo during the National Day holiday shows insignificance, the positive coefficient suggests that social media significantly influences travel decisions, which is consistent with the findings of Liu et al. [39]. Despite the t-statistic not reaching the significance level, this outcome remains highly informative and reasonable. This may be because holiday travel relies more on social media for destination recommendations and real-time information sharing, but the diverse sources of tourist information led to less pronounced statistical significance compared to the consistent daily social media usage patterns.

The coefficients for market, office, and restaurant facilities show different trends during the National Day holiday. For market facilities, the coefficient is 365.92 (t-statistic = 1.36) on workdays, 419.69 (t-statistic = 1.72 *) on weekends, and rises to 2579.41 (t-statistic = 2.71 **) during the National Day holiday, indicating a significant increase in attractiveness due to increased leisure time for shopping and recreational activities during holidays compared with workdays. For office facilities, the coefficient is 19.91 (t-statistic = 2.29 **) on workdays, 15.71 (t-statistic = 2.04 **) on weekends, and decreases to 18.03 (t-statistic = 0.61) during the National Day holiday, reflecting a significant reduction in demand as most people take a break from work. For restaurant facilities, the coefficient is −4.17 (t-statistic = −0.46) on workdays, 12.24 (t-statistic = 1.54) on weekends, and rises to 128.31 (t-statistic = 4.22 **) during the National Day holiday, indicating a significant increase in attractiveness due to people dining out and gathering. It is likely that people tend to eat at home or in the workplace on workdays but prefer dining out on weekends and during the holiday. The sharp increase in restaurant coefficients during holidays specifically reflects that social gatherings and tourism-driven dining become dominant, as opposed to the functional dining needs on workdays, highlighting the shift from routine to recreational consumption patterns.

The coefficients for medical facilities and trains show significant changes during the National Day holiday. For medical facilities, the coefficient is −94.12 (t-statistic = −3.42 **) on workdays, −131.11 (t-statistic = −5.38 **) on weekends, and decreases to −670.98 (t-statistic = −7.22 **) during the National Day holiday, indicating a significant reduction in the proportion of travel for medical purposes, likely because most people choose excursions or family visits rather than seeking medical care. For trains, the coefficient is 1778.64 (t-statistic = 3.54 **) on workdays, 2168.40 (t-statistic = 4.84 **) on weekends, and rises to 9501.34 (t-statistic = 5.43 **) during the National Day holiday, indicating a significant increase in train usage, likely due to long-distance travel and family visits. The dramatic rise in train coefficients specifically reveals that holidays trigger intensive intercity mobility for tourism or family reunions, whereas workdays primarily involve local commuting, highlighting the holiday-specific role of rail transport as a key facilitator of long-distance travel demand.

6. Policy Implications

Based on the CW matrix, Figure 20 is constructed by dividing values numerically, providing an intuitive visualization of the connection strength and interdependencies between different traffic analysis zones (TAZs). The horizontal axis represents the origin TAZ numbers in the origin–destination (OD) data, while the vertical axis represents the destination TAZ numbers. The color of the blocks indicates the varying degrees of numerical values for each OD pair within the CW matrix. This matrix can be used to analyze the degree of mutual influence between TAZs and compare these analysis results with the effects of existing policies to assess their actual value. This analysis can provide a reference basis for policymaking, future transportation planning, and development.

The analysis of passenger flow data and the CW matrix reveal significant spatial correlations between several TAZ pairs, including TAZ1 and 4, TAZ1 and 6, TAZ4 and 6, TAZ4 and 11, and TAZ and 11, all exhibiting CW weights above 0.15. This strong connection is not only reflected in traffic flow but also vital for cultural heritage protection and commercial development. The study’s findings align with Hangzhou’s 14th Five-Year Plan (2021–2025), a strategic plan focused on building a “National 123 Transportation Circle” (1 h intra-city, 2 h Yangtze River Delta, 3 h national connectivity) and integrating cultural preservation with commercial growth. These insights will optimize subway flow management, advance sustainable urban development, and drive synergies among transport networks, cultural sites, and commercial hubs in Hangzhou.

Based on the validated urban planning data, Figure 20 shows significant spatial correlations between TAZs (especially TAZ1, TAZ6, and TAZ11), with CW weights greater than 0.15. For example, Longxiangqiao Station (TAZ4), which is located near the West Lake Scenic Area, is strongly correlated with Ding’an Road Station (TAZ6) and Wulin Square Station (TAZ11), with CW weights of 0.18 and 0.16, respectively. This indicates that not only the geographical proximity but also the interdependence of the metro’s actual travel time would affect spatial correlations. The proposed Hangzhou Urban Renewal Plan [40] has led to a significant increase in passenger traffic at Longxiangqiao Station, over 320,000 passengers during the Labor Day holiday. The statistics confirm the effectiveness of the policy and the strong spatial correlation with the neighboring region [41]. In addition, Ding’an Road station can be used as an alternative access point to the West Lake Scenic Area when Longxiangqiao Station is congested, emphasizing convenient connectivity and strong passenger connectivity [42]. Similarly, the significant correlation between TAZ4 and TAZ11 highlighted in the Hangzhou Central Business District Development Plan (HCBDP) [43] shows how these two zones interact with each other to influence each other’s passenger flows, creating a synergistic relationship that promotes tourism and commercial activities. In summary, TAZ4, TAZ6 and TAZ11 have high weights and are correlated in terms of passenger flows, which are supported by urban planning policies and actual passenger flow data.

A strong correlation between Fuyang Passenger Terminal (TAZ43) and TAZ26 is discovered with a CW weight of 0.18. Considering the proximity of TAZ26 to the Lingshan Scenic Area, it is recommended that Fuyang Passenger Terminal be developed into a larger transportation hub. Specific data support includes the following: TAZ43’s holiday average daily passenger flow reaches 19,399, a 37% increase from weekdays, with peak hourly flows of 3210; simulation using an M/M/3 queuing model shows that expanding the terminal from its current 12,000-person capacity to 30,000 could reduce congestion by 42%; and the Fuyang District’s 14th Five-Year Transportation Development Plan projects 65% growth in intercity trips by 2025, requiring an additional 18,000 m² of infrastructure to accommodate demand. Such a recommendation has been formed in relevant policies [44], which propose expanding the terminal and increasing the frequency of metro departures to cope with the peak-hour demand.

The above recommended policies are summarized in

Table 6. Influence of CW weight matrix between different TAZs and policy verification.

Policy-Affected TAZ	Relevant Policy Background and Impact	Policy Recommendations	Prominently Affected TAZ
TAZ1 (Fengqi Road subway station)	Hangzhou Municipal Bureau of Transportation [45]: implement a ‘Song Yun’-themed renovation	Strengthen TAZ1-Wulin link Enhance TAZ1-Ding’an connection Increase peak metro frequency Boost train numbers during peaks	TAZ4, TAZ6, TAZ11
TAZ4 (Longxiang Bridge subway station)	Hangzhou Municipal People’s Government [40]: Develop cultural exhibitions and theme parks	Enhance TAZ4 transport capacity Improve TAZ6-Ding’an Road connection Strengthen TAZ11-Wulin Plaza link Better holiday passenger diversion	TAZ1, TAZ6, TAZ11
TAZ5 (Xueyuan Road Station)	Hangzhou Municipal Government [46]: the Xueyuan Road station will become an interchange station for lines 2 and 10 in 2022	Combine Line 2 & 10 at TAZ5 (Xueyuan Road) Expand capacity at TAZ5 and TAZ15 Increase station size Optimise transfers Boost peak train frequency	TAZ15
TAZ6 (Dingan Road subway station)	Hangzhou Municipal Government [46]: Construction and development of Southern Song imperial city ruins	Enhance TAZ6 metro capacity Support TAZ4 passenger flow Promote TAZ11 commercial joint development	TAZ1, TAZ4, TAZ11
TAZ9 (Hangzhou East Railway Station)	Hangzhou.com [47]: A new “hub business district” will be built.	Develop TAZ9 regional complex Increase TAZ18 capacity Boost metro frequency TAZ9 to TAZ18	TAZ18
TAZ11 (Wulin Square subway Station)	HCBDP [43]: Wulin Square CBD construction will be expanded	Leverage TAZ11 commerce Strengthen metro links to tourism areas (TAZ1, TAZ4, TAZ6) Improve tourist access and trade	TAZ1, TAZ4, TAZ6
TAZ34 (Hangzhou South Railway Station)	Hangzhou Municipal Bureau of Transportation [3]: A high-speed rail hub and a business centre will be built	Develop TAZ34 transportation hub Boost metro frequency to linked areas	TAZ22, TAZ25, TAZ35
TAZ36 (Hangzhou Grand Convention and Exhibition Center Station)	Zhejiang Provincial Department of Commerce [48]: A multi-functional project will be developed around the Hangzhou Convention and Exhibition Center.	Expand TAZ36 capacity at Convention Centre Connect stronger with TAZ33 (University District) Increase metro frequencies Enhance connectivity facilities	TAZ33, TAZ35, TAZ41
TAZ43 (Fuyang Passenger Transportation Center Station)	Fuyang District’s 14th Five-Year Transportation Development Plan (2023) [44]: Improve the infrastructure construction around the station	Develop TAZ43 transport hub Improve nearby infrastructure Increase metro frequency TAZ43 to TAZ26 Enhance key area facilities Add direct shuttles for connectivity	TAZ26

below. The policy recommendations summarized in Table 6 are strategically formulated based on the CW matrix heatmap (Figure 17), which visualizes spatial correlations between TAZs (e.g., TAZ1-TAZ4-TAZ6 with CW weights > 0.15). By integrating transportation, cultural heritage, and commercial development, these policies, such as the ‘Song Yun’-themed renovation of TAZ1 and the Southern Song imperial city ruins development in TAZ6, optimize transit networks to attract tourists and alleviate congestion. Functional upgrades like TAZ5’s interchange capacity expansion and TAZ9’s hub business district plan enhance regional connectivity, while initiatives in TAZ11 and TAZ43 bridge urban–suburban divides and strengthen tourism links.

Crucially, the policies leverage model insights (e.g., holiday traffic surges and spatial autocorrelation patterns) to boost metro frequencies and optimize transfers, directly addressing peak flows. This not only enhances public transport usage efficiency but also contributes to environmental sustainability by reducing private vehicle reliance. The model’s emphasis on spatial–temporal dynamics supports data-driven strategies to minimize carbon emissions and improve urban accessibility, aligning with Hangzhou’s goal of a smart, culturally integrated transit system that drives sustainable development.

7. Conclusions

This study investigates the subway passenger volume before and after China’s National Day holiday based on mobile payment data of Hangzhou from 6 September to 17 October 2021. To consider spatial correlations among travel flows, a Composite Weight (CW) matrix combining network distance and time is defined and integrated with traditional spatial models to establish CW-SEM, CW-SAR, and CW-SDM. The results show that the average daily subway passenger flow during the National Holiday witnesses 37% and 49% increases compared with that of workdays and weekends. In addition, strong spatial correlations among passenger flow are confirmed on both workdays and weekends. Key factors such as population, social media activity, commercial facilities and transportation hubs show significant positive correlations with holiday passenger flow, while medical facility reveals significant negative correlations with holiday passenger flow. Based on the results, policy implications are derived and potential impacts on different TAZs are analyzed. These findings provide insights for holiday subway travel studies in the digital era, which facilitates urban planning and traffic management.

The main contributions of this study are as follows: (1) This study uses mobile payment data to examine the traffic patterns on workdays, weekends, and during the National Day holiday, addressing a critical gap in the existing literature with more people using mobile payment. Prior research predominantly relied on smart card data, which have limited information and could not be integrated with other data for further analysis. As such, few studies have systematically analyzed holiday-specific subway travel behaviors and their spatial correlations. (2) A new comprehensive weight matrix (CW) is introduced, combining network distance and travel time to accurately depict actual connections between subway stations. This innovation overcomes the limitations of traditional spatial weight matrices in previous studies (e.g., Euclidean distance or neighborhood-based models), which does not account for transfer behaviors and route-dependent travel times, thereby enhancing the model’s explanatory power (R² improved by 4.3%). (3) This study reveals that factors like population density, Sina Weibo check-ins, commercial facilities, and transport hubs significantly influence traffic flow fluctuations. For instance, holiday passenger flow increased by 37% and 49% compared to weekdays and weekends, respectively, with peak-hour flows shifting from commuting-driven to tourism-oriented patterns, findings that bridge the gap in prior research on holiday travel purpose shifts. (4) Aligning with Hangzhou’s 14th Five-Year Plan, the research identifies key traffic management areas and peak periods, proposing policy recommendations to optimize metro scheduling. This fills a void in the literature by integrating spatial econometric insights with urban policy frameworks, which has been underexplored in previous studies on subway passenger flow.

Despite the extensive analysis of subway passenger behavior during holidays within a specific timeframe, there are some limitations that require attention in future studies: (1) Firstly, the dataset should cover evolving trends of holiday patterns throughout the year or over longer periods to better understand the impacts of seasonality, cyclical events, and special occasions on subway passenger traffic. Longitudinal studies would help identify consistent behavioral patterns and seasonal anomalies. (2) Secondly, additional variables such as travel purposes, fare policy adjustments, and temporary traffic regulations during holidays should be included to enhance the explanatory power of future inquiries. Incorporating survey-based data or GPS trajectory logs could also enrich the interpretation of travel intentions and movement dynamics. (3) Lastly, more advanced econometric modeling techniques should be developed to better understand the spatiotemporal effects of subway passenger volumes. Future research could explore dynamic spatial panel models or machine learning algorithms to improve prediction accuracy and support real-time decision making in public transportation management. Integrating such methodologies will further strengthen the policy implications and practical applications of spatial econometric approaches in urban mobility planning.