Spatiotemporal Characteristics of Bike-Sharing Usage around Rail Transit Stations: Evidence from Beijing, China

: As an emerging mode of transport, bike-sharing is being quickly accepted by Chinese residents due to its convenience and environmental friendliness. As hotspots for bike-sharing, railway-station service areas attract thousands of bikes during peak hours, which can block roads and pedestrian walkways. Of the many works devoted to the connection between bikes and rail, few have addressed the spatial-temporal pattern of bike-sharing accumulating around station service areas. In this work, we investigate the distribution patterns of bike-sharing in station service areas, which are inﬂuenced not only by railway-station ridership but also by the built environment around the station, illustrating obvious spatial heterogeneity. To this end, we established a geographic weighted regression (GWR) model to capture this feature considering the variables of passenger ﬂow and the built environment. Using the data from bike-sharing in Beijing, China, we applied the GWR model to carry out a spatiotemporal characteristic analysis of the relationship between bike-sharing usage in railway-station service areas and its determinants, including the passenger ﬂow in stations, land use, bus lines, and road-network characteristics. The inﬂuence of these factors on bike-sharing usage is quite di ﬀ erent in time and space. For instance, bus lines are a competing mode of transport with bike-sharing in suburban areas but not in city centers, whereas industrial and residential areas could also heavily a ﬀ ect the bike-sharing demand as well as railway-station ridership. The results of this work can help facilitate the dynamic allocation of bike-sharing and increase the e ﬃ ciency of this emerging mode of transport.


Introduction
In recent years, bike-sharing has grown significantly in many Chinese cities, as it caters to the public transport policies of convenience, sustainability, and energy saving [1,2]. Essentially, bike-sharing is an oriented production-service system (PSS), whereby the ownership of bicycles is retained by providers (e.g., Ofo, Mobike, 99bicycle, and Wisdom-Enjoyed Cycling) who sell the functions of the bikes. Bike-sharing has benefits for short-distance travel and connecting "the last kilometer" in a given city [3], which is especially evident in the vicinity of rail transit stations. Bike-sharing is a convenient way for residents to travel, but it also suffers from some shortcomings, such as unreasonable bicycle parking and the failure to transfer bikes in time. Thus, a better understanding of the spatiotemporal characteristics of bike-sharing is needed and could provide management and operational support for enterprises and government departments [4][5][6]. Station service areas are especially interesting for their unique characteristics that affect bike-sharing usage. and the influence of the passenger flow, land use, bus lines and road-network characteristics on the bike-sharing usage are analyzed; and Section 5 concludes our work and declares further study.

Data
We selected bike-sharing in Beijing, China as our case study. The data observation points were all rail transit stations in Beijing, China, as shown in Figure 1. Wang et al. studied the attraction range of Beijing rail transit and other modes of transportation, concluding that areas within 500 m of rail transit stations are walkable [30]. Ji et al. counted the cumulative percentages of "Metro-Bikeshare" and "Bikeshare-Metro" by transfer distance, finding that more than 90% of transfer trips were finished within 300 m [31]. Accordingly, we used data within a 500 m range around rail transit stations in our work. Bike-sharing usage records, the passenger flow, and the built environment were considered to analyze spatiotemporal characteristics, as described in detail hereafter.

Bike-Sharing Usage Records
Bike-sharing usage records from 19 April 2018, are shown in Figure 2. It is clear that the use characteristics of bike-sharing differ by period. We selected the morning peak (8:00~9:00), off peak (12:00~13:00), and evening peak (18:00~19:00) for further analysis in an attempt to ensure comprehensiveness and reliability. The bike-sharing usage records during the morning and evening peaks clearly exceeded those for the off peak, as expected. We obtained the bike-sharing usage records on a workday (19 April 2018) from four companies (Ofo, Mobike, 99bicycle and Wisdom-Enjoyed Cycling)-a total of 2,272,490 usage records, with Ofo and Mobike accounting for 39.62% and 60.02% of the total, respectively. Specific data information is shown in Table 1. Each usage record contained a great deal of information, including the record number, corporate identity, bike ID, record time, rental time, latitude and longitude of the bike lease, longitude and latitude of the bike return, leasing price, and usage status. These data provided the basis for the travel-characteristics analysis of bike-sharing. Data cleaning was needed, because some collected data were obviously illogical. Ultimately, 2,041,720 usage records remained for further analysis, accounting for 89.85% of the original data.
To reduce analysis error, stations reporting fewer than 200 bike-sharing usage records per day were excluded, so that a total of 207 stations were finally studied and analyzed.

Passenger Flow
Because the passenger flow into and out of rail transit stations is an important influence on the use of bike-sharing, we obtained statistical data concerning the passenger flow into and out of rail transit stations from the metro operating company of Beijing. The date of the statistical passenger flow data, 19 April 2018, was the same as for the bike-sharing usage records. Statistical data for the passenger flow into and out of stations during the morning peak (8:00~9:00) are shown in Figures 3  and 4, respectively.

Built Environment
Bike-sharing usage is also influenced by the built environment around rail transit stations. Many scholars have considered attribute variables of the built environment for studying the use characteristics of bike-sharing around rail transit stations [25,29]. The use of bike-sharing does have an interactive relationship with the surrounding built environment. In our work, we select for analysis 14 kinds of attribute variables relating to the built environment within 500 m of a station: the child population density, youth population density, middle-aged population density, aging population density, residential land area, working land area, recreational land area, connecting bus line, collinear bus line, non-motorized lane density, motor-vehicle lane density, number of road intersections, number of vehicle parking spaces, and number of shared bike racks. The specific attribute variables are shown in Table 2.

Methodology
In recent years, many methods have been applied to analyze travel behaviors. A multiple linear regression model, with its advantages of simplicity, ease of operation, and explainability, is welcomed by many researchers. Ordinary linear regression models often ignore the geospatial variation between different variables. For instance, ordinary least square (OLS) assumes a spatial stability between variables, with local differences in variables not affecting the overall regression. This assumption affects the applicability and accuracy of the OLS model to some degree. Both the passenger flow data and built environment data have a certain spatial heterogeneity, probably reflecting the evolution of urban structure and the rapid development of TOD. In this paper, on the basis of our analysis of variables, we explore characteristics of bike-sharing usage around rail transit stations from the perspectives of time and space.

Analysis of multicollinearity
Multicollinearity means that the linear regression model is distorted or difficult to estimate accurately owing to the existence of precise or highly correlated relationships between explanatory variables. To solve this question, bivariate correlations among the predictors are calculated, producing an indicator for use in examining the degree of multicollinearity. The bivariate correlation between different variables is calculated as Only the correlations between different variables above the 0.7 threshold are assumed to be multicollinear variables [32].

Analysis of Spatial Heterogeneity
Spatial heterogeneity refers to the acquisition of different data caused by different spatial positions. Moran's I [33,34] is usually used to test the spatial heterogeneity of variables, and it is expressed as where n denotes the number of spatial units, w ij is the spatial weight between the units i and j, x i represents the attribute value at locations i, and x represents the average value of all of the units. Moran's I is a rational number whose value is normalized to between −1.0 and +1.0 after variance normalization. When Moran's I exceeds 0, the data are spatially positively correlated, and the larger the value, the more significant the spatial correlation. When Moran's I is less than 0, the data are negatively correlated in space, and the smaller the value, the greater the spatial difference. When Moran's I is equal to 0, the space is random. The Z-score is usually calculated to verify the null hypothesis of the Moran's I test and is defined as where E(I) and V(I) denote the expectation and standard deviation of Moran's I test, respectively.

Ggeographic Weighted Regression
Geographic weighted regression (GWR) [17,35,36] is an extension of the general linear regression model, which attempts to build a linear relationship between the dependent variable and a set of independent variables. By taking into account spatial changes between variables caused by geographic changes, a linear regression equation is established for each spatial unit, improving the explanatory ability between variables within the overall scope, so that where x ik is the independent variable, y i is the dependent variable, (u i , v i ) are the coordinates of the ith observation point, ξ i is the Gaussian error term, and β ik (u i , v i ) is the relationship weight value of the kth element at the observation point i, which is estimated bŷ Each weight function w j (i) in the weighted matrix is a distance-decay function, which is always calculated using the Gaussian kernel function, where d ij is the distance of the regression point i and other observation points j, h is the bandwidth, and the corrected Akaike information criterion (AICc) [37,38] is used to optimize the bandwidth. We setẐ(h) = L(h)Z,ε = Z T (I n − L(h)) T (I n − L(h))Z, and then With the optimal bandwidth, obtained by (corresponding to the lowest AICc value), the GWR analysis model is obtained. The bandwidth is the most important factor in the GWR model, controlling as it does the smoothness of the model. In this study, the optimal bandwidth was first calculated using the preceding formula, after which the bandwidth was further optimized based on the actual urban background of the case, and ultimately the bandwidth was determined to be within a local 5 km range. The condition number [39] is usually calculated to check the reliability of a GWR model. It has the form where A refers to the coefficient matrix of the GWR model. In mathematical problems, a problem with a low condition number is called a good condition, and a problem with a high condition number is called a morbid one. In the GWR model, a condition number for all variables less than 30 is considered to be reliable.

Model specification
Model variables included the independent variables and dependent variable. Bike-sharing usage was defined as a dependent variable, which was affected by many factors (independent variables), including the passenger flow into the station, the passenger flow out of the station, and the built environment. These independent variables were interrelated and exhibited collinearity and interdependence. It was necessary to select key factors when building the analysis model. Firstly, bivariate correlations among the different variables were calculated to highlight multicollinearity problems. Table 3 shows the results as coefficients of correlation. Because the coefficients between the population density of different ages exceeded the 0.7 threshold, these variables could not be used in the model. Then Moran's I test was used to determine the spatial heterogeneity of different variables. This process was implemented through ArcGIS, producing the outcomes listed in Table 4. Except for the variables of number of vehicle parking spaces and number of shared bike racks, the other variables presented spatial heterogeneity, indicating a low likelihood that these clustered patterns were the results of random chance, according to the Z-score. After in-depth analysis, the rest of the independent variables were defined as key factors, which are shown in Table 5. In addition, we eliminated stations for which bike-sharing usage involved fewer than 200 records, reducing analysis error.

Model Evaluation
To illustrate the effectiveness of the method proposed in this paper for analyzing the spatiotemporal characteristics of bike-sharing usage, the goodness of fit (R 2 ) and condition number were selected as the effectiveness evaluation indexes. The relationship between the bike-sharing usage records as origin (O) and destination (D) points and independent variables were analyzed by GWR during the morning peak, off peak, and evening peak. Goodness of fit is shown in Figure 5. It can be seen that the degree of fit for the GWR model is relatively high. In addition, the maximum of the condition number for the GWR model in different periods is listed in Table 6, showing that each independent variable was less than 30. As can be seen, the GWR regression results were stable and reliable.

The Effect of Passenger Flow on Bike-Sharing Usage
The effect of the passenger flow on the bike-sharing usage differs by period. Based on passenger flow characteristics, we analyzed the effect of the passenger flow on the bike-sharing usage during the morning peak, off peak, and evening peak. Taking stations as D points, the relationship between the passenger flow into the station and the bike-sharing usage during the morning peak is shown in Figure 6. Passengers' use of bike-sharing to connect to the subway during the morning peak exhibited strong local characteristics. Bike-sharing usage around the stations within the north fourth ring road of Beijing was greatly affected by passenger flow. Accordingly, the relevant management departments should focus on the connection between other regions and the north fourth ring road of Beijing when dispatching bikes.
Taking stations as D points, the relationship between the passenger flow into the station and the bike-sharing usage during the off peak is shown in Figure 7. During the off peak, bike-sharing usage that was greatly affected by passenger flow into the station was mainly distributed beyond the fourth ring road-perhaps because commuters working in the city center within the fourth ring road, who are the main service group of the subway, do not choose to go home at noon.  The bike-sharing usage during the evening peak was greatly affected by the passenger flow out of the station. Taking stations as O points, the relationship between the passenger flow out of the station and the bike-sharing usage during the evening peak is shown in Figure 8. Areas affected by the passenger flow out of the stations were mainly distributed in suburban stations located on Line 1 and the north fourth ring road of Beijing, China. In these areas, passengers preferred to use bike-sharing to travel between the station and home.

The Effect of Land Use on Bike-Sharing Usage
Our analysis revealed that the effect of land use on the bike-sharing usage showed opposite characteristics for O versus D points. Taking D points as an example, we analyzed the effect of the land use on the bike-sharing usage. During the morning peak, the bike-sharing usage was mainly related to the working land area around rail transit stations. This relationship is shown in Figure 9. Primarily, the bike-sharing usage at two types of stations was greatly affected by working land area. The first were stations in the north of Beijing, which were near much residential land. Many passengers entering these stations who preferred to use bike-sharing as an important mode of travel. The second were stations representing Zhongguancun on the north fourth ring road, which were near large amounts of working land. Some workers also used bike-sharing as an attendance tool. During the evening peak, bike-sharing usage was mainly related to the residential land around rail transit stations. This relationship is shown in Figure 10. A clear difference between north and south was noted in the bike-sharing usage on residential land area during the evening peak. Compared with those living in the northern region, residents around the stations in the southern region were more willing to use bike-sharing to return home from work.

The Effect of Bus Lines on Bike-Sharing Usage
The effect of bus lines on the bike-sharing usage was mainly reflected in connecting bus lines and collinear bus lines; we selected the evening peak for analysis. Figure 11 shows the relationship between connecting bus lines and the bike-sharing usage and Figure 12 is the relationship between collinear bus lines and the bike-sharing usage during the evening peak.  In the Chaoyang district, connecting bus lines and collinear bus lines often correlated positively with the bike-sharing usage. Most passengers return from their work offices (in the urban center) to their suburban residence during the evening peak. Due to having access to the developed bus network around the rail transit stations in the Chaoyang district, some users of bike-sharing choose to get on buses instead of subways.

The Effect of Road-Network Characteristics on Bike-Sharing Usage
Road-network characteristics were also one of the most important influences on bike-sharing. The morning peak and evening peak were selected for analysis using the number of intersections and motor-vehicle lane density, respectively. Figure 13 shows the relationship between the number of intersections around rail transit stations and the bike-sharing usage during the morning peak. Figure 14 depicts the relationship between the motor-vehicle lane density and the bike-sharing usage during the evening peak, showing that travelers in the northern suburbs of Beijing, China were more concerned about the number of road intersections near their destinations. However, travelers in the central and western regions of Beijing, China were more sensitive to motor-vehicle lane density.

Conclusions
Bike-sharing greatly increases the convenience of travel for residents, especially when connecting stations and other places. Based on historical bike-sharing usage records, we used a GWR model to analyze the spatiotemporal characteristics of bike-sharing for the entire rail transit network of Beijing, China. This study can be summarized as follows: The bike-sharing usage around rail transit stations is mainly affected by the passenger flow into and out of stations, land use, bus lines, and road-network characteristics. We built a GWR model to capture the spatiotemporal characteristics of the bike-sharing usage around rail transit stations considering the passenger flow and built environment variables; From the time perspective, the characteristics of the bike-sharing usage around rail transit stations during the morning and evening peak hours show clear differences. The bike-sharing usage during the morning peak is affected by the passenger flow into the station, working land area, collinear bus lines, and number of road intersections. The bike-sharing usage during evening peak is affected by the passenger flow out of the station, residential land area, connecting bus line, and motor-vehicle lane density; From the spatial perspective, the bike-sharing usage around rail transit stations has obvious partition characteristics. The bike-sharing usage around rail transit stations near the north fourth ring road of Beijing, is heavily affected by the passenger flow. In the north and south of Beijing, bike-sharing usage is mainly affected by working land area and residential land area. In the Chaoyang district, the bike-sharing usage is more sensitive to connecting bus lines and collinear bus lines. The effect of the number of road intersections is mainly reflected in the northern suburbs, and the effect of the motor-vehicle lane density is mainly reflected in the central and western regions of Beijing.
This work can provide technical support for the operations and management of bike-sharing services while serving as a reference for future studies on the connection between bike-sharing and other transportation modes and the influence of TOD development on bike-sharing. This method can be applied to the analysis of bike-sharing usage in other cities with the appropriate adjustments.
In our work, we only analyzed the spatiotemporal characteristics of bike-sharing usage around rail transit stations in Beijing, China, which was limited by our obtained data. The current work could be extended by obtaining more data from other cities. The spatiotemporal characteristics of bike-sharing usage in multiple cities could be compared, and more findings would be given.