Measuring accessibility of bus system based on multi-source traffic data

ABSTRACT

Accessibility is a representative indicator for evaluating the supply of bus system. Traditional studies have evaluated the accessibility from different aspects. Considering the interaction among land use, bus timetable arrangement and individual factors, a more holistic accessibility measurement is proposed to combine static and dynamic characteristics from multisource traffic data. The rationale of the proposed model is verified by a case study of bus system in Shenzhen, China, which is carried out to find the spatial and temporal discrepancy of service of bus system. It is found that the adjustment of bus schedule to time-varying travel demand can affect accessibility of bus system and that Land-use development, average bus speed and bus facilities all have positive effects on accessibility of bus system. These findings provide significant reference for transport planning and policy-making. The proposed model is not limited to accessibility measuring of bus system, but also applicable to other travel modes.

KEYWORDS:

• Accessibility
• bus system
• multi-source traffic data
• spatial-temporal distribution

1. Introduction

Accessibility of bus system can be used to assess the serviceability of public transport system in a city, which gives feedback to transport planning and demand management. The study of accessibility can trace back to 1950s (Hansen 1959). There is no standard definition and measure of accessibility due to its pluralism in economic, geographic, social or even perceptual (Kiran, Corcoran, and Chhetri 2018; Lawal and Anyiam 2019).

The flexibility of accessibility conception gives it high adaptability in several different aspects. First, the coverage of bus network can help promote urban equity (Oviedo et al. 2019). Second, the distribution of bus lines is guidance of land use planning (Lee et al. 2018; Lessa, Lobo, and Cardoso 2019) and meaningful reference to policy making. Third, density of traffic facilities has great influence on pricing of property (Mulley and Tsai 2017). Therefore, the study on accessibility of bus system has drawn many attentions from the government and bus companies. Although “accessibility” can be used in many aspects, the definition and measurement of accessibility of bus system are quite different according to various study purposes.

There are generally two kinds of accessibility measures: place-based measures and people-base measures (Neutens, Versichele, and Schwanen 2010; Chen et al. 2018a, 2019). Place-based accessibility measures consist of two parts: (1) the potential opportunities; (2) the spatial distance or the travel time between the reference location and the activity location. Liu and Kwan (2020) measured the job accessibility for each census tract based on a gravity model integrating both transit-based travel time and transit fare of poor job seekers. Ding, Zhang, and Li (2018) introduced attractiveness and impedance function to model accessibility of bus system. They take busload, time cost in travel, and bus schedule frequency as attractiveness, arrival time and station distribution as impedance. Lee et al. (2018) used the mean travel time and time constant to calculate the accessibility of bus station, which was seen as an attractiveness. Lessa, Lobo, and Cardoso (2019) used the arithmetic mean of standardized frequency ratio, point density ratio and lines ratio to calculate the accessibility index of bus system in study units. Rodriguez et al. (2017) used the number of labor opportunities can be obtained by a public travel mode to define employment accessibility. Place-based measures represent aggregated models, providing basic reference for policy-makers in urban traffic planning. People-based measures take into consideration of an individual’s activity schedule, emphasizing the individual factors such as occupation, age and income, which can affect people’s choice for desired destination thus influence the accessibility (Geurs et al. 2010). Beach accessibility for people with disability is measured by two distance-based access measures (Lee, Kim, and Thapa 2020). Zhang and Man (2015) explained the job accessibility of residents in low income by average single-way travel time to all the potential job opportunities, taking the affordable house as home of urban poor and the place with high job density as potential job opportunities location. To gain accessibility of bus system for people with some kinds of disability, Dell’Olio, Moura, and Ibeas (2007) concluded the measured variables and route variables from questionnaire and put them into GIS for data programming. The people-based model represents unaggregated measures, representing habitability and welfare of cities, especially for socially disadvantaged groups (Kim and Ulfarsson 2013; Chen et al. 2018b).

Given specific assumption for various study purposes, the existing studies measured accessibility of bus system by choosing few suitable variables. The easier access to information inevitably brings more interaction between different indicators. For example, higher attractiveness of a destination makes travel time more acceptable, thus increasing the possibility of obtaining opportunities from the destination. In another word, accessibility of bus system in a study region can be higher if it can relate to a more attractive destination by bus lines. So, accessibility of bus system should be expressed as a compromise of multiple factors to reflect the level of service of bus system more holistically.

Considering some real-time factors into the accessibility analysis, a method for measuring accessibility of bus system is proposed based on multi-source traffic data. The proposed method outperforms the traditional ones in the following aspects. First, the proposed method combines the factors of land-use, bus facility distribution, road condition and individual factors. Second, the proposed method takes the bus schedule into consideration, representing the fluctuation of accessibility of bus system to adjust the time-varying travel demand. Third, the results show the interrelationship between bus facility distribution and the nearby land development.

The main contributions of this study include (1) a data-driven method for measuring accessibility of bus system, in which the dynamic service level of bus system is analyzed; (2) usage of area partition, which can accelerate the data processing and makes the spatial distribution of accessibility be described more simply and more effectively; (3) a framework of factors extraction and information condensing from multi-source traffic data.

The rest of this paper is organized as follows. Section 2 presents the detailed functions and variables in the proposed method. Section 3 shows a case study of Shenzhen City based on the proposed method, using multisource data. In Section 4, some novel findings from detailed results are discussed. The rational of selected variables are also proved. The last section concludes this study.

2. A holistic measurement for accessibility of bus network

The proposed method for measuring accessibility of bus system is based on position-based measures, which consist of the attractiveness of facility and spatial competence.

(1) $A\left(i\right)=\sum _f{O}_{f}D\left(d_{if}\right)$(1)

where $A\left(i\right)$ is the accessibility of residents living in region $i$; $O_f$ is the attractiveness of facility $f$; $D\left(\cdot \right)$ is a distance discount function that depends on the travel cost between region $i$ and facility $f$. Different definitions of $D\left(\cdot \right)$ makes various accessibility models. A negative exponential function is the most commonly used in the gravity model.

(2) $A\left(i\right)=\sum _f{O}_f\mathrm{e}\mathrm{x}\mathrm{p}\left(-\beta c_{if}\right)$(2)

where $\beta$ is the competence parameter of travel cost $c_{if}$ which can be represented by spatial distance or travel time (Guy 1983; Tsou, Hung, and Chang 2005; Fu and Lam 2018). The larger the value of $\beta$, the more sensitive the attractiveness is with respect to the travel cost $c_{if}$.

Using a binary cutoff function $B_{i,t}\left(f\right)$, the cumulative opportunities measurement was proposed by Breheny (1978).

(3) $\begin{array}{rl}& A\left(i\right)=\sum _f{O}_f{B}_{i,t_b}\left(f\right)\\ & B_{i,t_b}\left(f\right)=\left\{\begin{array}{cc}1,& t_{if}\le t_b\\ 0,& t_{if}>t_b\end{array}\right.\end{array}$(3)

where $B_{i,t_b}\left(f\right)=1$ means the travel time spent from region $i$ to facility $f$ is less than the time budget $t_b$.

Figure 1. Cumulative opportunities measurement.

As shown in Figure 1, the accessible facilities within the time budget can be counted into accessibility of bus system in region $i$. The inaccessible facilities outside the time budget cannot be cumulated. The time budget line is not a regular circle considering that the road condition and driving speed are different among travel traces in different directions.

By dividing the study area into equal-size regions and considering the space within each region having the same attributes, with certain values (region attributes), the spatial distribution of accessibility can be described simply and effectively (as shown in Figure 2).

Figure 2. Accessibility of bus system based on region partition.

For each region, combining the two kinds of cost decay functions mentioned above, the proposed accessibility model of bus system can be represented as:

(4) $\begin{array}{rl}& A\left(i,j\right)=\sum _{j}O\left(j\right)B\left(i,t\left(i,j\right)\right)\\ & B\left(i,t\left(i,j\right)\right)=\left\{\begin{array}{cc}\mathrm{e}\mathrm{x}\mathrm{p}\left(-\beta t\left(i,j\right)\right),& t\left(i,j\right)\le t_b\\ 0,& t\left(i,j\right)>t_b\end{array}\right.\end{array}$(4)

where $A\left(i,j\right)$ is accessibility of bus system in region $i$ gained by bus lines from region $i$ to region $j$; $O\left(j\right)$ is the opportunities in region $j$ which can be reached by a direct bus ride within the time budget $t_b$ from region $i$; $B\left(i,t\left(i,j\right)\right)>0$ when the travel time from region $i$ to region $j$ ($t\left(i,j\right)$) is less than time budget $t_b$; $\beta$ has the same meaning as mentioned above, which can be calculated by

(5) $\mu =g\left(\beta ,t_x\right)$(5)

where $\mu$ is the proportion of passengers whose bus travel time is less than the predetermined time threshold $t_x$; $\beta$ can be calculated by

(6) $\beta =g^{-1}\left(\mu ,t_x\right)$(6)

Taking $\phi \left(\cdot \right)$ as the inverse function of $g\left(\cdot \right)$, $\beta$ can be represented by

(7) $\beta =\phi \left(\mu ,t_x\right)$(7)

Points of Interest (POI) refer to some geographic entities closely related to people’s daily life, which plays an essential role as an indicator in traffic planning (Liu et al. 2016; Xing and Meng 2018). POI indicate the potential opportunities of residents, so the number of POI is used to quantify attractiveness in study region. The more POI in a study region, the more attractive the region is. So, $O_j$ can be represented by the number of POI in region $j$.

We assume that accessibility of bus system in each region in the study area comes from POI in two kinds of travel destination: (1) which can be reached by a direct bus ride, represented by region $j$; (2) which can be reached by a transfer and two bus rides to reach, represented by region $k$ (as shown in Figure 3).

Figure 3. Accessibility of bus system gained from two kinds of destination.

To consider the number of POI in region $k$ into accessibility of bus system in region $i$, $A\left(j,k\right)$ is calculated by Equation (4)(4) $\begin{array}{rl}& A\left(i,j\right)=\sum _{j}O\left(j\right)B\left(i,t\left(i,j\right)\right)\\ & B\left(i,t\left(i,j\right)\right)=\left\{\begin{array}{cc}\mathrm{e}\mathrm{x}\mathrm{p}\left(-\beta t\left(i,j\right)\right),& t\left(i,j\right)\le t_b\\ 0,& t\left(i,j\right)>t_b\end{array}\right.\end{array}$(4) and added in to the total accessibility of bus system in region $i$. Combining the POI reached from two kinds of destinations, total accessibility of bus system in region $i$ can be obtained by

(8) $A\left(i\right)=\alpha \left(i\right)\sum _{j}A\left(i,j\right)+\frac{1}{N\left(i,j\right)}\delta \left(x\right)\sum _j\sum _k\alpha \left(j\right)A\left(j,k\right)$(8)

where $A\left(i\right)$ is total accessibility of bus system in region $i$; $A\left(i,j\right)$ and $A\left(j,k\right)$ can be obtained by Equation (4)(4) $\begin{array}{rl}& A\left(i,j\right)=\sum _{j}O\left(j\right)B\left(i,t\left(i,j\right)\right)\\ & B\left(i,t\left(i,j\right)\right)=\left\{\begin{array}{cc}\mathrm{e}\mathrm{x}\mathrm{p}\left(-\beta t\left(i,j\right)\right),& t\left(i,j\right)\le t_b\\ 0,& t\left(i,j\right)>t_b\end{array}\right.\end{array}$(4) ; $\alpha \left(\cdot \right)$ represents the proportion function of onboard time in the total time budget of residents in a study region, which can be gained by Equation (9)(9) $\alpha \left(i\right)=\lambda \left(s\left(i\right),v\left(i\right),l\left(i\right)\right)$(9) ; $\delta \left(x\right)$ is proportion of transfer bus trips in total bus trips in study area $x$; $N\left(i,j\right)$ is the number of bus traces from region $i$ to region $j$. When the number of POI in region $k$ is to considered, the previous bus ride has already been completed, which means there is only one region $j$ connecting region $i$ and region $k$, so the average value of $A\left(j,k\right)$ is taken into consideration to represent the extra accessibility of bus system in region $i$ from the second bus rides starting from region $j$.

(9) $\alpha \left(i\right)=\lambda \left(s\left(i\right),v\left(i\right),l\left(i\right)\right)$(9)

In the Equation (9)(9) $\alpha \left(i\right)=\lambda \left(s\left(i\right),v\left(i\right),l\left(i\right)\right)$(9) , the $\lambda \left(\cdot \right)$ is the discount function; $s\left(i\right)$, $v\left(i\right)$ and $l\left(i\right)$ represent the density of bus station, the number of bus traces and the average speed in region $i$, which all affect the time spent to the bus station.

To summarize the explanation of the variables mentioned above and provide a more intuitive understanding of the proposed method, the definition and represented information of the variables are concluded as Table 1.

Table 1. Detailed explanation of variables.

Variable	Definition	Information represented by the variable
$A\left(i\right)$	Total accessibility of bus system in region $i$	Level of service of bus system in region $i$
$\delta \left(x\right)$	Proportion of transfer bus trips in total bus trips in study area $x$	The ratio of passengers that are willing to arrive at their destinations by transfer
$A\left(i,j\right)$	Accessibility of bus transit network in region $i$ from its indirect destination region $j$	Potential POI that can be reached in region $i$ from region $j$
$A\left(j,k\right)$	Accessibility of bus system in region $j$ obtained from region $k$	Potential POI that can be reached in region $j$ from region $k$ through bus system
$O\left(j\right)$	Total opportunities in region $j$	Represented by the number of POI in cell m
$t\left(i,j\right)$	Time interval from the region $i$ to region $j$ by bus	Dynamic “distance” between region $i$ and region $j$
$N\left(i,j\right)$	The number of bus tracks that connect region $i$ and region $j$	Ensures the uniqueness of the former bus trip
$\beta$	Coefficient of impedance	The impact of road condition on the travel cost and the passengers’ willingness of getting destination by bus transit system
$\alpha \left(i\right)$	Coefficient of convenience of taking a bus in region $i$	Reflects the walking time to transit station, waiting time for taking a bus and road condition in region $i$

Table 2. GPS data of bus in 10:00–11:00 a.m. on April 5th, 2017.

Bus id	Longitude/(°)	Latitude/(°)	Time	Speed/(km·h^–1)
BS00000D	114.330 39	22.586 73	10:00:00	0
BS00000D	114.336 30	22.582 46	10:00:05	11
BS00000D	114.346 73	22.542 49	10:00:12	21
BS00000D	114.346 73	22.542 53	10:00:18	32
… …	… …	… …	… …	… …
H2332	113.933 15	22.769 69	10:59:50	0
H2332	113.935 14	22.768 56	10:59:59	0

3. Case study

The study area is the city of Shenzhen, a special economic zone and national economic center of China. On 15th October 2019, the Ministry of Transport determined Shenzhen as the first batch of pilot areas for the goal of making China a powerful transportation country. By the end of 2019, there are 3.482 million civilian vehicles, of which 2.73 million were private cars. There are average 1.836 4 million civilian cars on the road every day, of which 1.668 7 million are private cars. The rapid growth of private cars has brought a lot of pressure to the road traffic, so it is necessary to improve the position of bus system in the transportation system to reduce the road pressure (Wang and Jie 2011). Measuring service level of bus network is indispensable to expose the problems existing in the management of bus system, which can help promote its development.

Multi-source traffic data of Shenzhen are collected including the coordinate range, POI, bus station, and bus GPS records in four typical time frames on weekday and weekend (8:00–9:00 a.m. and 10:00–11:00 a.m. on Tuesday, April 5th, 2017, 8:00–9:00 a.m. and 10:00–11:00 a.m. Saturday, April 9th, 2017) (Chen et al. 2019). The information contained in GPS data is shown in Table 2.

According to the general purposes of bus travel, this paper selected six kinds of POI to quantify opportunities in regions, including transportation hub, financial services, scenic spots, scientific study and education, automobile facilities, leisure and entertainment. A total of 47 314 records of POI data including longitude and latitude were collected for case study. The locations of 31 986 bus stations were provided by the bus company in Shenzhen, which contains the location of bus stations. Through locating them, the number of stations in each region can be recorded.

A total of 16 016 364 records of GPS data of bus were also collected in the mentioned four typical time frames mentioned before, which represented peak and flat period of weekday, weekend, respectively. The GPS records include bus id, longitude, latitude, time and speed, from which we can get the number of bus traces, road condition, and the travel time between origin and destination.

Based on the collected data, we apply following four steps to investigate accessibility of bus system in divided regions in Shenzhen by using MATLAB software:

(1) Divide the city into equal-size regions

The longitude span is 51ʹ and the latitude span is 25ʹ in Shenzhen. Considering the distance between bus stations and the acceptable walking distance to bus stations, we divide the city into 40 × 80 grids. The size of each region is approximately 1 km × 1 km (Tomasiello, Giannotti, and Feitosa 2020).

(2) Investigate the static characteristics in each region

The number of POI and bus station can be counted by their position, which indicates the attractiveness and bus facility in study regions. Strictly speaking, the attractiveness can be seen as dynamic characteristic in the long term, for example, a new school site or a new shopping mall will increase the attractiveness of a region (Mfuka, Byamukama, and Zhang 2020). This study only focuses in the four typical time frames in a week, so the attractiveness is considered as static.

(3) Evaluate the dynamic characteristics in each region

The average bus speed and average number of bus traces in different time periods can be obtained from GPS records in regions, which can reflect the influence of dynamic bus schedule arrangement and road condition on accessibility of bus system.

(4) Estimate the distribution of accessibility

By integrating the results of each region in different time periods, we can conclude the spatial and temporal distribution of accessibility of bus system in Shenzhen.

4. Results and analysis

We divided the four typical time frames into 24 10-minutes time periods and collected time-varying accessibility of bus system in different time periods to gain the temporal change of the indicators. By visualizing accessibility of bus system in each region by Gaud API and HBuilder software, the spatial distribution of accessibility of bus system in Shenzhen can be concluded.

4.1. Distribution of static characteristics

The distribution of POI and bus station in Shenzhen are shown in Figures 4(a) and 4(b), respectively. It can be seen that POI and bus stations have similar spatial distribution. They are both mainly concentrated in Futian District, Luohu District, Nanshan District and the upper left part of Bao’an District, where the density of POI in a region exceeds 100 and the maximum number of bus stations in a region reaches 174. The similar spatial distribution of POI and bus station indicates the mutual attraction between land development and the input of bus facilities.

Figure 4. Distribution of POI and bus station in Shenzhen.

(a). Distribution of POI. (b) Distribution of bus station.

4.2. Distribution of dynamic characteristics

After processing GPS records of bus in Shenzhen, the maximum average speed in a region reaches 90 km/h (as shown in Figures 5(a) and 5(b), and the maximum number of bus traces in a region is 287 lines/h (as shown in Figure 5(c) and 5(d). Because of the similar regulations between the spatial distribution of average bus speed and average number of bus traces in four typical time periods, only the results of two time periods on April 5th, 2017 are visualized.

Figure 5. Distribution of average bus speed and bus traces number on April 5th, 2017.

(a). Average bus speed in 8:00–9:00 a.m. (b) Average bus speed in 10:00–11:00 a.m. (c) Average number of bus traces in 8:00–9:00 a.m. (d) Average number of bus traces in 10:00–11:00 a.m.

Compared with the spatial distribution of bus traces, Futian District and Luohu District have higher density of bus traces, which is more than 280 lines/h, while average bus speed in Futian District and Luohu District is lower than other parts in Shenzhen. On the one hand, there is more bus stations causing more stops; on the other hand, the large number of bus traces reflects higher vehicle density in the road resulting in increased road congestion and reduced vehicle speed on the road.

Figure 6 shows that the average bus speed in 8:00–8:30 a.m. Tuesday, April 5th is generally lower, and increase 1.5 km/h per 10 minutes in the next 30 minutes. It indicates the improvement of bus turnover rate to accommodate the higher traffic demand. The average bus speed of the two time frames on Saturday, April 9th fluctuate less, which are both lower than the average value on April 5th.

It can be seen from Figure 6(a) that high-demand period on Tuesday is 8:30–9:00 a.m., lasting half an hour, while there is no obvious high-demand period on Saturday. The average bus speed in 10:00–11:00 a.m. on Saturday is significantly lower than that in the other three periods, which expresses the lower travel demand than other periods, reflecting the adjustment of the bus schedule for the difference level of residents’ travel demand on weekday and weekend.

Figure 6(b) shows the bus timetable accommodates for travel demand. It can be seen obviously that the average number of bus tracks in 8:00–9:00 a.m. on Tuesday is about 5 lines higher than the other time periods, which means more buses are settled to satisfy more travel demand. The number of bus tracks increased significantly in 8:40–8:50 a.m. on Saturday, indicating that there still exist part of commuters showing the same travel regulations as that on the Tuesday. The number of tracks is obviously higher in 8:30–9:00 a.m. on Tuesday, showing the adaptation of departure frequency of buses to the travel demand in the peak period, which is also indicated by Figure 6(a).

Integrating the information of Figure 6(a) and 6(b), it can be summarized that there is an adjustment of average speed and travel traces to time-varying travel demand. The combination of Figures 6 and 4 indicates that the attraction of land use on bus transit facility makes a large gap in the service level of bus system among districts in Shenzhen.

Figure 6. Results of 10-minute periods in four typical time frames.

(a) Average bus speed. (b) Average number of bus traces

4.3. Accessibility of bus system

The spatial distribution and fluctuation of final total accessibility of bus system in Shenzhen is also visualized after collecting the calculation results of the four time periods, as shown in Figures 7 and 8. Accessibility of bus system in Shenzhen in four typical time frames shows the average number of POI can be reached within the predetermined time budget by passengers from a boarding region in Shenzhen. Accessibility of bus system in Shenzhen in 8:00–9:00 on April 5th, 10:00–11:00 a.m. on April 5th, 8:00–9:00 a.m. on April 9th, and 10:00–11:00 a.m. on April 9th are 333, 302, 318, and 291 facilities/h, respectively.

Figure 7 shows that bus accessibility in Futian District and Luohu District are obviously higher than that in the other districts in Shenzhen. Combining with the results above, we can conclude that the boom of a region can affect its attraction of traffic resources.

Figure 7. Bus accessibility in Shenzhen.

(a) 8:00–9:00 a.m. on Tuesday, April 5th, 2017. 10:00–11:00 a.m. on Tuesday, April 5th, 2017. (c) 8:00–9:00 a.m. on Saturday, April 9th, 2017. (d) 10:00–11:00 a.m. on Saturday, April 9th, 2017

By analyzing the indicators included in the method proposed for measuring accessibility of bus system, we can conclude that the results of accessibility are greatly influenced by the bus arrangement. The bus schedule adjusts to the travel demand. As can be seen from Figure 8, accessibility of bus system in Shenzhen continuously increases in 8:00–9:00 a.m. on Tuesday, April 5th, which is also significantly greater than the other three periods, showing similar trend with Figure 6.

Figure 8. Bus accessibility per 10 minutes in different time frames.

The total accessibility in 8:40–9:00 a.m. on Saturday April 9th is still growing rapidly due to some commuters’ travel demand but still lower than the same time period on Tuesday, which is also shown by Figure 6. Figure 6 indicates the least travel demand in 10:00–11:00 a.m. on Saturday, leading to the lowest accessibility of bus system among the four time periods, as shown in Figure 8. Combining the results above, it can be summarized that accessibility of bus system is influenced by factors of three aspects: (1) the spatial distribution of facilities in a city, which attracts bus facilities; (2) the adjustment of bus schedule and bus speed to accommodate time-varying travel demand, which affect time spent onboard; (3) residents’ duration for time cost in the bus travel and during the transfer, which affect the time budget for bus travel and the extra accessibility gained from transfer bus travel.

5. Conclusions

The proposed method for measuring accessibility of bus system combined factors from traffic, road and land-use, as well as indicator factors including the process to station, onboard process, and transfer process. Firstly, the proposed method used the framework of gravity model to express the basic accessibility of bus network in a study region, where the positive effect of land development and negative effect of travel cost were taken in to consideration.

Secondly, it highlighted a framework of extracting static and dynamic characteristics from multi-source data in reflecting the road condition and arrangement of bus transit timetable. Specially, usage of proportion functions was proposed to reflect passengers’ acceptance of travel time and transfer, which is an important consideration in urban and traffic plan.

Thirdly, the results of case study not only showed the spatial and temporal distribution of accessibility of bus system in the study area, but also disposed the interrelation of land prosperity and the bus facility, the more prosper a region is, the more bus facilities in it, thus producing high accessibility of bus system. From that, it can be concluded that unbalanced development among regions will inevitably lead to unequal service level of bus system among regions. The temporal distribution of the accessibility of bus system also reflected the effects of residents’ time-varying travel demand on accessibility of bus system in a city. To feed more travel demand, more bus are allocated on the road and higher speed is applied to complete transportation tasks faster, which can improve accessibility of bus system in a city. Furthermore, the results of the accessibility of system showed the change of accessibility of bus system, which can explain the final compromise of influence from various aspects, representing the adjustment of some factors to the fluctuation of other factors.

The proposed method provided an idea of integrating static and dynamic information using multi-source traffic data, which provides significant guidance for the future study on the interaction of land use, management of traffic system, and passengers’ behavior. The proposed method can be applied to not only bus system but also other travel modes, like rail transit or taxi (Fu and Lam 2014, 2018).

Although this study uses static and dynamic characteristics from multi-source data for measuring accessibility of bus system, several limitations remains. In this study, we assume that the six kinds of POI have the same attraction to the residents. Considering their various attraction for different trip purpose would be helpful for analyzing travel behaviors. Extension of the proposed method to collect more traffic data of multi-mode traffic system is another topic for future study. Some other kinds of data can also be added to provide more information such as mobile phone data and check-in records of social facilities.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was jointly supported by the National Key Research and Development Program of China [grant number 2018YFB1600900]; and the National Natural Science Foundation of China [grant number 71601045].

Notes on contributors

Yufan Zuo

Yufan Zuo is a graduate student in School of Transportation, Southeast University. Her research interests include traffic geographic information system and transportation big data analysis and modeling.

Zhiyuan Liu

Zhiyuan Liu is a professor in School of Transportation, Southeast University. He received his Ph.D. in the Department of Civil Engineering, National University of Singapore. His research interests include transportation network planning and management, transportation big data analysis and modeling, public transportation, multi-mode logistics network, intelligent transportation system.

Xiao Fu

Xiao Fu is an associate professor in School of Transportation, Southeast University. She received her Ph.D. in the Department of Civil and Environmental Engineering, Hong Kong Polytechnic University. Her research interests include traffic geographic information system, spatial-temporal big data, multi-mode traffic network analysis and modeling, activity-based models, transport network reliability.