Introduction

Background

Bike-sharing systems (BSS) have grown swiftly in cities since the 2000s. Until January 2021, survey1 reports 2007 bike-sharing programs and approximately 9,440,776 bikes in service worldwide. Compared to motor-based travel, cycling activities are considered economical, flexible, and novel methods to mitigate traffic congestion2. Free-floating bike sharing (FFBS) systems such as Mobike gradually showed up with modern technology development. Compared to the dock-based BSS (DBSS), the FFBS system (FFBSS) allows users to rent a bike and return it almost anywhere as long as they adhere to traffic rules3. The short walking distance for reaching a bike from FFBSS promotes its development with increasing popularity and unprecedented speed in many large cities worldwide.

FFBS is equipped with locator devices that generate itinerary records, including renting time, returning time, and real-time position trajectory. These digital footprints benefit in portraying user behaviors, predicting travel demands, and improving city-wide traffic systems. Accordingly, researchers have gradually focused on BSS users' characteristics and behaviors from theory and practice perspectives37. Due to the contrast in usage, the trips for recreation and food can explain why there is more ridership of FFBS on weekend nights, especially the first hour after the service of the public transportation system. The determinants for the promotion of usage will be discussed in the section “Spatial comparison of usage patterns among periods”.

Based on the users' perspective, we further investigate the usage frequency between any two periods, as shown in Fig. 2. The number of trips with the same user is gathered and then categorized into four time ranges. The point with a higher frequency represents more users taking the corresponding scale of trips in both two-time ranges. Interestingly, there is no apparent linear relationship between the usage in nighttime and other periods, consistent with previous results in Bei**g53. It speculates that the requirement of FFBS is low for people who want entertainment places at night. Moreover, although shop** places are mainly out of service at night, shop** places have a similar function and are even adjacent to food places.

As shown in Table 1, the FFBS trips are then divided into origins and destinations to capture the characteristics of flows among various POIs. As expected, transport significantly affects both the origin and destination of trips. However, the coefficient of origin is more extensive than it is for the destination, stating that bus stations generate more FFBS trips rather than attract them. Besides, employment has a higher effect on origins than destinations, while the household has the reverse tendency. This unbalanced effect explains that the FFBS provides a popular mode of transportation for leaving the workplace and going home at night. In the daytime, the opposite flows (i.e., leaving homes or going to work) tend to take another urban transit system, such as the metro. Interestingly, the effect of entertainment becomes significant only with the view of origins. Several FFBS trips are generated from entertainment places rather than going home.

The usage of FFBS during the whole day or the daytime has been investigated, and several primary purposes of trips have been summarized55. The effect of shop** is not apparent in the daytime (especially in the morning and afternoon) but significant at night. We attribute this difference to the concentrated distribution of shop** places and the small size of grid cells for analysis. Based on the above analysis of the FFBS trips within a week, the differences observed in sections “Time-varying usage and distribution characteristics of travel distance” and “Spatial comparison of usage patterns among periods” compel us to analyze the usage patterns of FFBS during weekday and weekend nights.

The average number of trips per day with decimals cannot be applied in the ZINB, which requests the integral dependent variables (i.e., the number of trips). Therefore, the number of trips is multiplied by 2 for weekends and 5 for weekends for an equivalent quantitative comparison. Table 3 illustrates the estimation results based on the nighttime trips on weekdays and weekends. More estimation results with origin or destination view are provided in Table S2.

Table 3 Regression results of FFBS during the nights on weekdays and weekends.
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A larger transport coefficient with a more significant effect on weekend nights is uncovered, consistent with Fig. 1, that more trips are observed on Friday and Saturday nights. A visible difference is the coefficient increment about food on weekend nights, reflecting that people have more time for dinner or are likelier to take night snacks. The employment coefficient is higher on weekend nights, which is counterintuitive since the number of people working on day offs has naturally dropped. However, this remarkable decrement mainly occurs in the daytime rather than the nighttime. This result suggests that more trips are generated from employment due to more working people on weekend nights. The coefficient increment about food and employment can partly support Fig. 4, especially in Bei**g's east and northeast areas.

The POIs of shop**, hotels, education, and households have similar decrement variations. Education, which has both functions of household and employment, has a more similar characteristic to a household. These results are consistent with the findings in Table 1. The hotel is significant in the single view of origins and destinations only weekly (see Table S2), reducing the coefficient. Additionally, shop** is more significant for FFBS usage only as the weekday destination.

Discussion and conclusion

FFBS has developed rapidly with its convenience, health, and flexibility, attracting more users, primarily used for short-distance mobility and bike-and-ride trips56,57. Understanding the variation of FFBS usage patterns and the effects of a non-linear built environment can help traffic managers initiate appropriate measures at the planning stages by identifying usage distribution, source of demand, and its relationship with urban transit systems58,59. The nighttime also provides an excellent time window to observe the relationship between FFBS and other transit systems, such as the night buses. The FFBS is a superior option for unavoidable nighttime travel demand because of its cost-efficient expense and easy accessibility when most urban transit systems are unavailable.

To intuitively observe the variation of FFBS usage patterns, we divide each day into four typical periods, including night, morning, afternoon, and evening, and the nighttime is the focus period of this paper. The temporal-spatial analyses are first conducted to investigate the usage patterns of FFBS at various time ranges. The temporal characteristics are illustrated in views of additional half-hours and different nights, and imbalanced spatial usage distribution in different periods indicates the various mobility patterns. We then concentrate on correlations between different periods by comparing the O-D flow of FFBS. Finally, the usage of FFBS is explored according to a zero-inflated negative binomial statistical model. The main findings are summarized below:

  1. I.

    Besides the public knowledge of the morning and evening perk trend, the temporal usage on various nights has a similar U-shaped variation with abrupt changes on both sides, which implies the wide usage of FFBS for connecting to the last or first urban transit systems. The usage of FFBS on weekend nights is more significant than on weekday nights, although the number of trips throughout the day on a weekday is higher than that on the weekend. Although there are differences in the amount of FFBS usage in various periods, the distance of trips presents a stable distribution.

  2. II.

    From a spatial perspective, the usage of FFBS at night is significantly more dispersive than in daytime periods, as evidenced by the NNI index and ODPFG similarity measurement. The hotspots during the daytime are more concentrated and tend to become hotspots at night. The nighttime has more scattered hotspots, especially in areas with employment, leisure, food, education, etc.

  3. III.

    The relationship between FFBS and multi-mode urban transportation is summarized. The night bus has a strong favorable attraction to FFBS and has become the origin of trips, similar to the metro. The day bus has a significant and balanced impact on FFBS usage. As a result, the FFBS tends to be a mode linking the night bus and metro to solve the last-mile problem.

  4. IV.

    The correlation analysis between FFBS and POIs reveals the source of FFBS demands. The FFBS is positively encouraged by the POIs, who may still be available at night except for medicine. The impacts of household, shop**, and education are relatively significant, and these locations are often the destinations for FFBS trips. Besides transport, places with food and employment have a higher impact on FFBS on weekday nights.

Our results raise awareness of the variation in usage patterns of FFBS by focusing on the night pattern and the difference between nighttime and daytime. It can benefit various applications, such as transportation planning and urban management, in deploying free-floating bike sharing according to complicated travel requirements. The valuable information provided by bike sharing makes it possible to distinguish the hotspots of nighttime travel and accurately plan new night bus lines, mainly relying on human surveys60. The correlation between FFBS and POI proposes a new perspective for the coordinated development of transport and land use, emphasizing the time-varying relationship between travel demand and land types.

While the results are exciting, the paper leaves several limitations owing to the datasets and approaches to be desired. First, due to the availability of the dataset, possible biases may occur in catching mobility patterns from one FFBS company (i.e., Mobike). Secondly, only a 7-day FFSB dataset is used in the analysis process, which limits the long-term usage pattern variation and comparison, such as the seasonal changes. The dataset with more sources and longer time ranges helps enhance the generality of findings. Thirdly, while the statistical analysis of FFBS and POIs reveals the built-environmental effect on the usage, it cannot figure out the purpose of travel, as there may be many possible activities in the grid cell with various POIs. A more accurate dataset of POI is required to elaborately identify the purpose of the trip and improve the practical application of this paper.

Dataset and Method

This section begins with various datasets collected from Bei**g, including public transportation networks, points of interest, and trip data obtained from Mobike. Then, a series of methods for data processing, statistical analysis, and visualization of results are put forward.

Study area

Bei**g is one of the typical big cities in the world, with a population of more than 21 million and an administrative area of 16,410 \({\text{km}}^{2}\). Rapid urban roads enclose the central area of Bei**g, namely Rings 2–5. As shown in Fig. 6, the adopted research area is a square with a size of 30 \(\times\) 30 \({\text{km}}^{2}\) centered by Tian'anmen, mainly covering the urban area within Ring 5.

Figure 6
figure 6

The research area in Bei**g. Rings 2–5 are bolded with red, brown, green, and purple colors. The blue circle indicates the service frequency of the night bus within the nearby area.

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Free-floating bike sharing dataset

The data of FFBS from Mobike company contains the records of trips within a week from 07/10/2017 (Wednesday) to 07/16/2017 (Tuesday). The records include 1,830,101 trips with O-D locations and start times generated from 400,000 bikes. Each record has the following attributes: User ID, Bike ID, Check-in Longitude, Check-in Latitude, Check-out Longitude, Check-out Latitude, and start time. It is essential to note that the drop-off time (i.e., the end time) is not collected.

At the preprocessing stage for data cleaning, the valid FFBS trips are selected with complete details and no abnormal information and travel distances ranging from 0.1 to 15.0 km9,34.

Point of interest dataset

A point of interest (POI) is a specific location where people may search for or visit. The POIs near the end of the trip can reveal the likely purpose of the travel61. Combining FFBS and POIs datasets can effectively reveal the FFBS demand within various geographic features8. The POI data collected from BaiduMap is distinguished for POIs in service at night. These night POIs are classified into nine categories in Table 4, where several common POIs, such as sports and amenities, are deemed not in service56. Urban transportation at night (i.e., the night bus) constitutes the transport categories, which are visualized in Fig. 6. The available POIs on the day or night are diverse and have been carefully distinguished by opening time or categories. The information on available POIs on the day is provided in Table S3. The distribution of several typical POIs is visualized in Figures S6–S10, which is associated with the distribution of bike-sharing usage.

Table 4 Categories and classification of available POIs at night.
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Grid cell division

The free-floating mobility of FFBS generates the self-organized distribution of bikes over the cities18. The research area is partitioned into homogeneous square grid cells to facilitate the statistics and analysis. It is worth mentioning that the longitude and latitude coordinates are transformed from the World Geodetic System to a projected system (Gauss-Kruger) before building the grid cell.

For different analytical purposes, we aggregate FFBS trips into grid cells in intra-cell or inter-cell ways. First, the number of intra-cell trips starting and ending within cell \(i\) are respectively aggregated as \({s}_{i}^{O}\) and \({s}_{i}^{D}\). The demand related to cell \(i\) is further denoted as \({s}_{i}^{OD}\), and \({\text{s}}_{i}^{OD}={s}_{i}^{O}+{s}_{i}^{D}\). Then, the inter-cell travel flow between cells \(i\) and \(j\) is represented by \({s}_{ij}\) and the remaining trips whose origin and destination exist in one cell \(i\) are aggregated as \({s}_{i}\). In general, more giant cells transfer more FFBS trips inside the cells, while a small style division improves the accuracy of describing the FFBS flows but increases connections between non-adjacent cells. In this study, the size of grid cells depends on the analytical purposes and precision of the dataset.

Spatial aggregation characteristics of hotspot pattern

Spatial aggregation is one of the critical features of the FFBS usage patterns. A point pattern approach is applied to examine whether the FFBS trips tend to cluster or randomly spread across the city area, i.e., the hotspot pattern. To perform the hotspot pattern analysis of the spatial aggregation of FFBS usage quantitatively, we implemented a Nearest-Neighbor Index (NNI) method.

The \(NNI\) is counted to judge whether the distribution factors of points are scattering or clustering. These points include the origin and destination coordinates of all trips. The core of the method is comparing the average distance of nearest neighbor point pairs and that under random distribution conditions62. The \(NNI\) is calculated as:

$$NNI=\frac{\sqrt{A}{\sum }_{i=1}^{n}{d}_{i}}{2\sqrt{{n}^{3}}},$$
(1)

where \({d}_{i}\) is the shortest distance between point \(i\) and other points, \(n\) is the total number of points, and \(A\) is the area of a minimum enclosing rectangle around all points.

As a result, the FFBS usage has a clustered pattern when \(NNI\) values close to 0 and tends to be a random or scattering pattern when \(NNI\) values close to 1. The pattern with the \(NNI\) values larger than 1 means a uniform distribution mode.

Spatial structural characteristics of mobility pattern

Despite the spatial aggregation characteristics depicting the usage hotspots of the FFBS in terms of trip origins and destinations, a comprehensive understanding of the inherent travel characteristics in these usage patterns remains lacking. Therefore, we delve into the mobility pattern, which encompasses the flow between different spatial grid cells, providing valuable insights into the spatial–temporal dynamics of FFBS usage. A dedicated tool, the O-D Proportion Flow Graph (ODPFG), is developed to facilitate analysis and visualization. Within the context of FFBS, the mobility pattern refers to the movement between cells, categorized as intra-cell or inter-cell flow. By adopting the ODPFG, we present a concise yet informative visualization method for comprehending the flow patterns associated with FFBS usage.

The O-D Proportion Flow Graph (ODPFG) is a conventional undirected flow graph portraying linear mobility patterns between grid cells. Comprising nodes and links, the ODPFG represents the connectivity between cells, with the line (or link) denoting the linkage between two distinct cells (nodes). The width of the line in the ODPFG corresponds to the strength or intensity of the connectivity, effectively reflecting the magnitude of flow between the cells. Specifically, the link weights in the ODPFG are derived from the FFBS flows, signifying the usage intensity associated with the respective connections.

To explore the structural properties of ODPFGs, we utilize the Jaccard coefficient to investigate the similarity between two arbitrary ODPFGs through the local structural property. To this end, the trips in one period from one cell to another are selected and compared with those in another period. We apply the Jaccard similarity coefficient63 (\(J\)) and can be calculated as

$$J\left(R\left(i\right), R\left(j\right)\right)=\frac{\left|R\left(i\right)\cap R\left(j\right)\right|}{\left|R\left(i\right)\cup R\left(j\right)\right|},$$
(2)

where \(R\) is the vector of weighted edges in the directed graph, and \(i\) (\(j\)) represents the period.

Statistical correlation analysis

To identify the geographical and built-environment factors that can potentially generate or attract FFBS trips, we use a multivariable modeling technique to analyze the relationship between the usage of FFBS and POIs. The data of FFBS and POIs were divided into the 300 m \(\times\) 300 m grid cells corresponding to the precision of POI data.

In the statistical model, let \({X}_{i}\) and \({Y}_{i}\) denote the independent variable vector and the dependent variable of cell \(i,\) respectively. The dependent variables are different types of FFBS usage about a cell, which can be among \({s}_{i}^{O}\), \({s}_{i}^{D}\) and \({s}_{i}^{OD}\). The independent variables are the number of POIs corresponding to each category. More statistical information about POIs in cells is provided in Table S4. Since the dependent variables contain a large proportion of zeros, we adopted the zero-inflated negative binomial (ZINB) regression to model the usage of FFBS55. The ZINB model can effectively address two issues from the datasets. Firstly, a large proportion of zeros occurs in POI data with a finer spatial granularity, where the ZINB model can aptly account for the excessive zeroes in the independent variables. Secondly, the dependent variable (i.e., the count of bike-sharing usage) is discrete, and the binomial regression in ZINB can effectively capture the characteristic information about the dependent variables.

In ZINB regression, \({Y}_{i}\) specifically follows a zero distribution with a probability \({p}_{i}\) and a negative binomial distribution (NBD) with probability \((1-{p}_{i})\):

$$P\left({Y}_{i}={y}_{i}\right)\sim \left\{\begin{array}{cc}{p}_{i}+\left(1-{p}_{i}\right){\left(1+\frac{{\tau }_{i}}{{\lambda }_{i}}\right)}^{-{\lambda }_{i}}& {y}_{i}=0\\ \left(1-{p}_{i}\right)\frac{\Gamma \left({y}_{i}+{\lambda }_{i}\right)}{{y}_{i}!\Gamma \left({\lambda }_{i}\right)}{\left(1+\frac{{\tau }_{i}}{{\lambda }_{i}}\right)}^{-{\lambda }_{i}}{\left(1+\frac{{\lambda }_{i}}{{\tau }_{i}}\right)}^{-{y}_{i}}& {y}_{i}=\text{1,2}\dots \end{array}\right.,$$
(3)

where probability \({p}_{i}\) is calculated from a logit distribution based on independent variables:

$$logit \left({p}_{i}\right)={X}_{i}{\prime}\alpha ,$$
(4)

and \({\tau }_{i}\) is the mean value of \({Y}_{i}\) in the NBD:

$$\mathit{ln}\left({\tau }_{i}\right)={X}_{i}{\prime}\beta ,$$
(5)

and \({\lambda }_{i}\) is the dispersion parameter of NBD. The ZINB distribution will reduce to a Zero-inflated Poisson (ZIP) distribution if \({\lambda }_{i}\to \infty\), which is a widely applied model for relationship analysis.

The maximum likelihood estimation (MLE) method is applied to select the \(\alpha\) and \(\beta\) with the best fit for the ZINP regression. A natural logarithm transformation on independent variables is better for model fit54,56. Due to many zeros in the independent variables caused by no POIs belonging to one category existing in small grid cells, a linear transformation from \({X}_{i}\) to \({X}_{i}+1\) is performed before the logarithm transformation to avoid the undefined error.