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Analyzing the Passenger Flow of Urban Rail Transit Stations by Using Entropy Weight-Grey Correlation Model: A Case Study of Shanghai in China

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In this paper, the factors influencing the passenger flow of rail transit stations in Shanghai of China are studied by using the entropy weight-grey correlation model. The model assumptions and the corresponding variables are proposed, including traffic accessibility, built environment, regional characteristics of the district to which the rail transit station belongs, conditions of the station and spatial location, which affect the passenger flow of rail transit stations. Based on the assumptions and the variables, the entropy weight-grey correlation model for analyzing the passenger flow of urban rail transit stations is presented. By collecting the data of passenger flow of rail transit stations and corresponding influencing factors in Shanghai, the results of the entropy weight-grey correlation model are obtained. It is shown that the influencing factors, such as the distances from the rail transit station to the adjacent third-class hospital and the adjacent large commercial plazas, district committees, parking areas and the transaction price of important plots, and the gross output value of the tertiary industry, have significant impacts on the passenger flow of a subway station. Finally, some suggestions are proposed for the local governments to formulate improved policies for rail transit development. The conclusions can provide a reference for the development of rail transit in other large cities and countries.
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Citation: Yin, P.; Cheng, J.; Peng, M.
Analyzing the Passenger Flow of
Urban Rail Transit Stations by Using
Entropy Weight-Grey Correlation
Model: A Case Study of Shanghai in
China. Mathematics 2022,10, 3506.
https://doi.org/10.3390/
math10193506
Academic Editors: Roman Ivanovich
Parovik, Junzo Watada and Sy-Ming
Guu
Received: 18 July 2022
Accepted: 20 September 2022
Published: 26 September 2022
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mathematics
Article
Analyzing the Passenger Flow of Urban Rail Transit Stations by
Using Entropy Weight-Grey Correlation Model: A Case Study
of Shanghai in China
Pei Yin 1, Jing Cheng 2,* and Miaojuan Peng 1
1Department of Civil Engineering, School of Mechanics and Engineering Science, Shanghai University,
Shanghai 200444, China
2Department of Construction Management and Real Estate, College of Civil and Transportation Engineering,
Shenzhen University, Shenzhen 518057, China
*Correspondence: jingcheng7-c@my.cityu.edu.hk or jingcheng@szu.edu.cn
Abstract:
In this paper, the factors influencing the passenger flow of rail transit stations in Shanghai of
China are studied by using the entropy weight-grey correlation model. The model assumptions and
the corresponding variables are proposed, including traffic accessibility, built environment, regional
characteristics of the district to which the rail transit station belongs, conditions of the station and
spatial location, which affect the passenger flow of rail transit stations. Based on the assumptions
and the variables, the entropy weight-grey correlation model for analyzing the passenger flow of
urban rail transit stations is presented. By collecting the data of passenger flow of rail transit stations
and corresponding influencing factors in Shanghai, the results of the entropy weight-grey correlation
model are obtained. It is shown that the influencing factors, such as the distances from the rail
transit station to the adjacent third-class hospital and the adjacent large commercial plazas, district
committees, parking areas and the transaction price of important plots, and the gross output value
of the tertiary industry, have significant impacts on the passenger flow of a subway station. Finally,
some suggestions are proposed for the local governments to formulate improved policies for rail
transit development. The conclusions can provide a reference for the development of rail transit in
other large cities and countries.
Keywords:
rail transit; station passenger flow; influencing factor; mathematical model; entropy
weight-grey correlation model
MSC: 62H20
1. Introduction
Rail transit systems can save energy, reduce noise, lower carbon dioxide emissions
and ease urban congestion, which can promote the sustainable development of large
cities, and gradually become the core of urban public transit systems. Rail transit can be
substituted effectively for cars when rail usage is supported by land development and other
policies [
1
]. With the continuous expansion of the scale of rail transit networks in large and
medium-sized cities, rail transit operations are faced with problems such as early warning
of large passenger flows and improvement of operating arrangements. Shanghai, as one of
the most prosperous megacities in China, had a subway operating mileage of 831 km at
the end of December 2021. Figure 1shows the distribution of the rail transit network in
Shanghai in 2015. The Shanghai rail transit system has greatly relieved the pressure on the
urban environment and passenger flow. Thus, it is crucial to investigate the factors that
influence urban passenger flow in order for the Shanghai government to plan site selection
and layout, optimize subway lines, and formulate more complete policies of rail transit
Mathematics 2022,10, 3506. https://doi.org/10.3390/math10193506 https://www.mdpi.com/journal/mathematics
Mathematics 2022,10, 3506 2 of 23
development. This study can also provide a reference for the development of rail transit in
other emerging large cities and countries.
Mathematics 2022, 10, x FOR PEER REVIEW 2 of 24
ment to plan site selection and layout, optimize subway lines, and formulate more com-
plete policies of rail transit development. This study can also provide a reference for the
development of rail transit in other emerging large cities and countries.
Figure 1. Rail transit network in Shanghai.
The conditions of the rail station and built environment around the station are re-
garded as the main factors affecting the passenger flow of the station [2,3]. The conditions
of the station include the external connection between subway station and highway
network, as well as the combined transportation with other modes of transportation. The
development of stations also has a great impact on the attraction of rail transit passenger
flow. If a station can be developed well, it can attract many passengers. The built envi-
ronment is a significant factor that changes residents travel behavior, and it is also a
fundamental factor that affects the passenger flow of subways [4]. The built environment
mainly embodies the principles of the three dimensions (3Ds) of building density, variety
and design. Improvements in land accessibility around rail transit can promote activities
of regional passenger flow and attract the passenger flow to nearby rail transit corridors
[5]. In addition, the development and construction of the surrounding areas of rail transit
is an important factor for the adjustment of passenger flow trends, which can also cause
great changes in the intensity and nature of surrounding land development. Therefore, it
is necessary to further explore the impact of land conditions around the station on its
passenger flow. Some researchers found that the establishment of urban rail transit may
bring 1/3 of the value added effect of the total rail investment to the nearby real estate [6
8]. Residential prices near subway stations may rise 32.1% after a light rail system is built
[9]. The distance of the rail transit station has a significant impact on the nearby real es-
tate prices, and with increase of the distance from a rail transit station, residential values
near the rail transit decline [10]. Rail transit can promote the development and utilization
of surrounding land, further accelerating and expanding urbanization [11,12].
Traffic accessibility is one of the aspects of subway stations affecting residential
prices [13]. The development of urban rail transit consumes a large amount of govern-
ment resource reserves. Much capital investment is needed during the planning, con-
Figure 1. Rail transit network in Shanghai.
The conditions of the rail station and built environment around the station are regarded
as the main factors affecting the passenger flow of the station [
2
,
3
]. The conditions of the
station include the external connection between subway station and highway network, as
well as the combined transportation with other modes of transportation. The development
of stations also has a great impact on the attraction of rail transit passenger flow. If a station
can be developed well, it can attract many passengers. The built environment is a significant
factor that changes residents’ travel behavior, and it is also a fundamental factor that affects
the passenger flow of subways [
4
]. The built environment mainly embodies the principles
of the three dimensions (3Ds) of building density, variety and design. Improvements in land
accessibility around rail transit can promote activities of regional passenger flow and attract
the passenger flow to nearby rail transit corridors [
5
]. In addition, the development and
construction of the surrounding areas of rail transit is an important factor for the adjustment
of passenger flow trends, which can also cause great changes in the intensity and nature
of surrounding land development. Therefore, it is necessary to further explore the impact
of land conditions around the station on its passenger flow. Some researchers found that
the establishment of urban rail transit may bring 1/3 of the value added effect of the total
rail investment to the nearby real estate [
6
8
]. Residential prices near subway stations may
rise 32.1% after a light rail system is built [
9
]. The distance of the rail transit station has a
significant impact on the nearby real estate prices, and with increase of the distance from
a rail transit station, residential values near the rail transit decline [
10
]. Rail transit can
promote the development and utilization of surrounding land, further accelerating and
expanding urbanization [11,12].
Traffic accessibility is one of the aspects of subway stations affecting residential
prices [
13
]. The development of urban rail transit consumes a large amount of government
resource reserves. Much capital investment is needed during the planning, construction
and operation of rail transit. It generally requires a long time to construct rail transit, and
Mathematics 2022,10, 3506 3 of 23
the operating income after completion is low. Thus, there is great pressure for the govern-
ment to recover the construction costs. The main sources of funds to construct rail transit
are the government investment, land transfer revenues, and loans based on government
credit. The build-transfer (B-T) financing mode increases costs, which conceals the real
debt situation of local governments [
14
]. In order to solve the problem of insufficient funds
for the construction of the rail transit system, the land value-added along the subway
line can be used to promote the construction of rail transit, which combines the capital
demand with the promotion of rail transit construction, and is consistent with the concept
of transit-oriented development (TOD). Especially in the urban areas that have not yet been
developed, the government can acquire the land in the planned development area at a
lower price in advance and introduce it into public transportation to gain a time advantage
as regards the development of land. Then the government can sell the ‘ripe land’ with
complete infrastructure, and will recover the investment in public transportation from the
return of land appreciation to recoup the cost of the investment. Analyzing the influencing
factors of passenger flow can predict the passenger flow status of newly developed rail
transit stations, and provide policy suggestions for the land use around the station, leading
to an optimal development strategy and design of the station.
Different mathematical models have been presented to study the factors influencing
the passenger flow of rail transit stations in metropolitan areas. Sohn et al. applied multiple
linear regression (MLR) to investigate the influencing factors of subway passenger flow
demand in the metropolitan area of Seoul in Korea [
2
]. Blainey used the geographically
weighted regression (GWR) method to predict the use of the Ebbw Vale branch line and
the factors influencing passenger flow in South Wales of England [
15
]. Gutiérre et al.
used a distance-decay weighted regression model to explore the influencing factors of the
subway passenger flow in Madrid, Spain [
16
]. The ordinary least squares (OLS) method
has been applied widely to analyze the influencing factors [
17
19
]. Sung and Oh used the
OLS global spatial regression method to discuss the factors influencing passenger flow on
weekdays, rest days and in the morning rush hour in Seoul, Korea [
20
]. Cardozo applied
OLS and GWR methods to estimate the passenger flow of the Madrid subway station
of Span, and compared the results obtained by these two methods [
21
]. Zhao et al. and
Sun et al. proposed the direct passenger flow prediction model to investigate the factors in-
fluencing the passenger flow of subways in Nanjing and Beijing of China, respectively [
3
,
22
].
Sung et al. used the OLS global spatial regression method to study the impact of land use,
railway service coverage and railway station accessibility on the passenger flow of rail
transit stations in Seoul [
23
]. Jun et al. applied stepwise regression method and mixed
geographically weighted regression (MGWR) method to investigate the factors influencing
the passenger flow of subways in Seoul [24].
From the previous studies, it can be seen that most researchers have used the global
linear regression method to analyze the index factors. The coefficients of the classical linear
regression model (CLRM) are constant. Thus, the most of these studies are based on the
premise of homogeneity, and spatial heterogeneity in the real environment is often ignored
in the analysis process. Therefore, besides the built environment and the station’s own
conditions, the impacts of traffic accessibility and spatial location factors on the passenger
flow of the station are considered in this paper to make up for the difference caused by the
uneven spatial distribution of the passenger flow of the station. Moreover, the maturity
level of the urban economy and infrastructure differs, and even within the same city,
the policies, economic and regional conditions between districts and counties are vastly
different. Besides considering the characteristics of land within the attraction range of the
station, it is also necessary to analyze the regional characteristic of the district to which the
station belongs.
The MLR model for analyzing the impact of passenger flow in rail transit consid-
ering spatial heterogeneity requires that sample data should satisfy typical probability
distribution. In addition, if using a linear relationship between the characteristic and the
factors, the factors should be independent. In particular, the current domestic statistical
Mathematics 2022,10, 3506 4 of 23
data is limited, while the grey-scale of data is relatively large, and the data have irregular
discrete distributions. The related methods, such as dynamic modeling, system dynamics
and discrete-event and agent-based modeling, are very good for multi-factor analysis, but
they are difficult to combine with the traditional theory of degrees of grey correlation.
The grey correlation model is an important method to quantitatively analyze the dynamic
development process, examine whether the relationship between the various factors is
close and identify the factors that affect the developments. Under the condition of fuzzy
initial information, the decision-making methods of multi-factor analysis, which are based
on measurement theory, mainly include TOPSIS, VIKOR and grey correlation analysis
methods [
25
,
26
]. Grey correlation analysis has been successfully applied to multi-factor
decision-making problems, such as interval number, linguistic information, intuitionistic
fuzzy information, interval intuitionistic fuzzy information and hesitant fuzzy informa-
tion [
27
29
]. This paper proposes the grey correlation model in grey system theory to
analyze the factors influencing the passenger flow of Shanghai rail transit stations in 2015.
The grey correlation model makes up for the shortcomings of using mathematical statis-
tics methods for systematic analysis. The calculation process is efficient and simple, and
quantitative results can be consistent with the results of qualitative analysis. Because of the
disadvantage of low accuracy in the grey correlation model, the entropy is considered in
the weight calculation to improve the accuracy of the solution.
Taking Shanghai as an example, this paper investigates the factors that affect the
passenger flow of rail transit stations and how the passenger flow of rail transit stations is
affected by the changes of these factors. The assumptions of factors affecting the passenger
flow in Shanghai and the corresponding variables in the mathematical model are proposed,
and the entropy weight-grey correlation model is used. Based on the grey correlation
degree, it is shown that the traffic accessibility, built environment, regional characteristics
of the district to which the rail transit station belongs, the conditions of the station and the
spatial location will affect the passenger flow of the station. Finally, some policy suggestions
for planning rail transit stations are proposed.
2. Variables in the Mathematical Model
To present the mathematical model of the factors influencing the passenger flow of
rail transit stations, the factors including traffic accessibility, built environment, regional
characteristics of the district to which the rail transit station belongs, station conditions and
spatial location are proposed.
2.1. Traffic Accessibility of the Rail Tansit Station
The distances from the i-th rail transit station in Shanghai to the important transporta-
tion hub station (D
i
), the district committee (DDC
i
), the nearest large commercial plaza
(DCP
i
), the nearest university or key high school (DUNI
i
), the nearest third-class hospital
(DTH
i
) and the nearest park (DPAR
i
) are considered as traffic accessibility indicators in this
paper. Lots of important transportation hubs, such as Shanghai Hongqiao Transportation
Hub, are built in Shanghai [
30
]. Shanghai Hongqiao International Airport and Pudong
International Airport are two of the three major gateway complex hubs in China. Shanghai
Railway Station is the second largest railway station in Shanghai. This station, Shanghai
Hongqiao Railway Station and Shanghai South Railway Station together constitute the
largest railway hub in the eastern coastal area of China. In this study, Shanghai Hongqiao
Railway Station, Shanghai Railway Station, Hongqiao International Airport and Pudong
International Airport are considered as the important transportation hubs affecting the
passenger flow of the rail transit stations.
The district committee is an organization that has overall leadership over the political,
economic, cultural and social development of the district, and is a vital organization related
to the policy of local rail transit development [
31
]. The distances of the rail transit station to
the adjacent large commercial plazas, universities or key high schools, third-class hospitals
and parks reflect the difficulty of taking the subway to the nearest core economic, education,
Mathematics 2022,10, 3506 5 of 23
medical and green area, which is an important indicator to measure the service capacity
of the public transportation system. Figure 2shows the distribution of traffic accessibility
indicators in Shanghai.
Mathematics 2022, 10, x FOR PEER REVIEW 5 of 24
related to the policy of local rail transit development [31]. The distances of the rail transit
station to the adjacent large commercial plazas, universities or key high schools,
third-class hospitals and parks reflect the difficulty of taking the subway to the nearest
core economic, education, medical and green area, which is an important indicator to
measure the service capacity of the public transportation system. Figure 2 shows the
distribution of traffic accessibility indicators in Shanghai.
Figure 2. Distribution of traffic accessibility indicators in Shanghai.
2.2. Built Environment around the Rail Transit Station
The built environment around the rail transit station includes building density, di-
versity and design [32]. Indices, such as floor area ratio (IPRi) and area (IPAi) of important
land within the attraction range of the i-th station, reflect the density. Four types of land
use, including residential land, commercial or office land, industrial land and compre-
hensive land, are considered in this paper. Pedestrian friendliness around the station re-
flects the rational design of the station, and it is the average time spent by residents of
nearby land walking to the station (IPTi). The average travel time of residents is deter-
mined by the size of the area where passengers are located and the complexity of the road
network. The better the road environment is, the smaller the personal cost to residents in
travel time and distance. Figure 3 shows the distribution of important land within the
attraction range of the station. Investment in urban rail transit projects can promote land
appreciation, save travel time, and improve travel comfort [33]. Therefore, in this paper,
the land transfer price (IPPi) is also regarded as a variable in the built environment fac-
tors.
Figure 2. Distribution of traffic accessibility indicators in Shanghai.
2.2. Built Environment around the Rail Transit Station
The built environment around the rail transit station includes building density, diver-
sity and design [
32
]. Indices, such as floor area ratio (IPR
i
) and area (IPA
i
) of important land
within the attraction range of the i-th station, reflect the density. Four types of land use,
including residential land, commercial or office land, industrial land and comprehensive
land, are considered in this paper. Pedestrian friendliness around the station reflects the
rational design of the station, and it is the average time spent by residents of nearby land
walking to the station (IPT
i
). The average travel time of residents is determined by the
size of the area where passengers are located and the complexity of the road network. The
better the road environment is, the smaller the personal cost to residents in travel time and
distance. Figure 3shows the distribution of important land within the attraction range of
the station. Investment in urban rail transit projects can promote land appreciation, save
travel time, and improve travel comfort [
33
]. Therefore, in this paper, the land transfer
price (IPPi) is also regarded as a variable in the built environment factors.
Mathematics 2022,10, 3506 6 of 23
Mathematics 2022, 10, x FOR PEER REVIEW 6 of 24
Figure 3. Distribution of important land around rail transit stations in Shanghai.
2.3. Regional Characteristics of the District to Which the i-th Station Belongs
The regional characteristic of the district to which the i-th station belongs include the
land, economic and political characteristics of the district. The transportation system is
very important to the industrial and commercial development of a city, which will affect
land prices and house prices [34]. Correspondingly, the land grade (DICi), land area
(DAAi), number of permanent residents (DPRNi), area of housing with more than eight
floors (DHAi), GDP (DGDPi), average salary of employees (DEASi), the industrial output
value (DIEOi), secondary industry output value (DSIOi), tertiary industry output value
(DTIOi) of the district, etc. will also affect the expansion and development of the trans-
portation system, which in turn will impact the station passenger flow. In addition, gov-
ernment policies and intentions can have significant impacts on rail transit development,
and the political promotion of local officials can affect their strategic decisions in rail
transit [35], which will indirectly affect the changes in the passenger flow and its distri-
bution of subway stations. Therefore, the political factors, including whether the district
party secretary is re-elected (DDSRi), whether the district head is re-elected (DDMRi), and
whether the district head is promoted to the district party secretary (WMPSi), of the dis-
trict where the i-th site belongs are considered in this paper.
2.4. Conditions of the Station
The contradiction between the limited urban land resources and the increasing traf-
fic demand is becoming more and more large, and stations should be arranged and de-
signed more rationally and scientifically to avoid waste of resources. For the factors in-
fluencing the conditions of the station, this paper focuses on the passenger service and
evacuation capabilities of the station site [36]. Therefore, reasonable transfer stations and
entrance and exit passages should be set up to avoid the phenomenon of passengers be-
ing stranded and crowded due to peak passenger flow. A transfer station is formed by
the intersection of two or more rail transit lines. It is equipped with transfer facilities such
as transfer passages and transfer station halls, and indicates the routes for passengers to
transfer. The number of entrances and exits is determined by the topography of the sta-
Figure 3. Distribution of important land around rail transit stations in Shanghai.
2.3. Regional Characteristics of the District to Which the i-th Station Belongs
The regional characteristic of the district to which the i-th station belongs include the
land, economic and political characteristics of the district. The transportation system is very
important to the industrial and commercial development of a city, which will affect land
prices and house prices [
34
]. Correspondingly, the land grade (DIC
i
), land area (DAA
i
),
number of permanent residents (DPRN
i
), area of housing with more than eight floors
(DHA
i
), GDP (DGDP
i
), average salary of employees (DEAS
i
), the industrial output value
(DIEO
i
), secondary industry output value (DSIO
i
), tertiary industry output value (DTIO
i
)
of the district, etc. will also affect the expansion and development of the transportation
system, which in turn will impact the station passenger flow. In addition, government
policies and intentions can have significant impacts on rail transit development, and the
political promotion of local officials can affect their strategic decisions in rail transit [
35
],
which will indirectly affect the changes in the passenger flow and its distribution of subway
stations. Therefore, the political factors, including whether the district party secretary
is re-elected (DDSR
i
), whether the district head is re-elected (DDMR
i
), and whether the
district head is promoted to the district party secretary (WMPS
i
), of the district where the
i-th site belongs are considered in this paper.
2.4. Conditions of the Station
The contradiction between the limited urban land resources and the increasing traffic
demand is becoming more and more large, and stations should be arranged and designed
more rationally and scientifically to avoid waste of resources. For the factors influencing
the conditions of the station, this paper focuses on the passenger service and evacuation
capabilities of the station site [
36
]. Therefore, reasonable transfer stations and entrance and
exit passages should be set up to avoid the phenomenon of passengers being stranded and
crowded due to peak passenger flow. A transfer station is formed by the intersection of two
or more rail transit lines. It is equipped with transfer facilities such as transfer passages
and transfer station halls, and indicates the routes for passengers to transfer. The number
of entrances and exits is determined by the topography of the station and the passenger
flow during peak hours. Correspondingly, the number of entrances and exits determines
the evacuation capacity of the station site, which has an obvious impact on the passenger
Mathematics 2022,10, 3506 7 of 23
flow of the station. Under normal circumstances, the number of entrances and exits of
shallow-buried stations should not be less than 4, and the number of entrances and exits of
small stations can be reduced according to the actual situation, but should not be less than
2 [
37
]. In this paper, whether the i-th station is a transfer station (WTS
i
), the number of rail
transit lines passing through the station (NUML
i
), and the number of entrances and exits
(NUMEi) are considered as factors.
2.5. Spatial Location of the Station
The spatial location factor considers the geographical location of the station, which
is whether the i-th subway station is situated within the inner ring (WIR
i
), middle of the
middle and inner rings (WIMR
i
), middle of the middle and outer rings (WMOR
i
), middle of
outer and suburban rings (WOSR
i
) and outside suburban rings (WOSR
i
) of Shanghai. The
inner ring area, as the most central area in Shanghai, is surrounded by 47.7 km of elevated
roads and covers an area of about 120 square km. A total of 89 rail transit stations are
located in the inner ring area [
38
]. There are 3 dual-rail subway stations, which are Gucun
Park Station, Gangcheng Road Station, and Yuqiao Station, in the area between the central
and outer rings. The development of dual-rail transit has an effect on the surrounding real
estate prices [
39
]. The rail transit network connects various areas between cities. Figure 4
shows the distribution of central districts, suburban districts, and a county in Shanghai.
Figure 5shows the inner, middle, outer and suburban rings in Shanghai.
Mathematics 2022, 10, x FOR PEER REVIEW 7 of 24
tion and the passenger flow during peak hours. Correspondingly, the number of en-
trances and exits determines the evacuation capacity of the station site, which has an ob-
vious impact on the passenger flow of the station. Under normal circumstances, the
number of entrances and exits of shallow-buried stations should not be less than 4, and
the number of entrances and exits of small stations can be reduced according to the actual
situation, but should not be less than 2 [37]. In this paper, whether the i-th station is a
transfer station (WTSi), the number of rail transit lines passing through the station
(NUMLi), and the number of entrances and exits (NUMEi) are considered as factors.
2.5. Spatial Location of the Station
The spatial location factor considers the geographical location of the station, which
is whether the i-th subway station is situated within the inner ring (WIRi), middle of the
middle and inner rings (WIMRi), middle of the middle and outer rings (WMORi), middle
of outer and suburban rings (WOSRi) and outside suburban rings (WOSRi) of Shanghai.
The inner ring area, as the most central area in Shanghai, is surrounded by 47.7 km of
elevated roads and covers an area of about 120 square km. A total of 89 rail transit sta-
tions are located in the inner ring area [38]. There are 3 dual-rail subway stations, which
are Gucun Park Station, Gangcheng Road Station, and Yuqiao Station, in the area be-
tween the central and outer rings. The development of dual-rail transit has an effect on
the surrounding real estate prices [39]. The rail transit network connects various areas
between cities. Figure 4 shows the distribution of central districts, suburban districts,
and a county in Shanghai. Figure 5 shows the inner, middle, outer and suburban rings in
Shanghai.
Figure 4. Distribution of central districts, suburban districts and a county in Shanghai.
Figure 4. Distribution of central districts, suburban districts and a county in Shanghai.
Mathematics 2022,10, 3506 8 of 23
Mathematics 2022, 10, x FOR PEER REVIEW 8 of 24
Figure 5. Inner, middle, outer and suburban rings in Shanghai.
3. Mathematical Model of Passenger Flow at Shanghai Rail Transit Stations
Combining the grey correlation model and entropy theory, this paper presents a
mathematical model to analyze the factors affecting the passenger flow of urban rail
transit stations. The grey correlation model is an important method to quantitatively an-
alyze the dynamic development process and examine whether the relationship between
the various factors is close. It is a measure of the relation degree between sequences,
which is expressed as the similarity of magnitude changes and the development trends
between sequences. The correlation degree is a reflection of the distance between two
points of different sequences. Based on the reliability of the correlation coefficient, the
entropy weight-grey correlation is established by weighting the grey correlation coeffi-
cient, which can control the volatility of the correlation coefficient effectively. Therefore,
the entropy weight-grey correlation model can be used to analyze the influencing factors
of urban passenger flow of rail transit stations directly and clearly.
The entropy weight coefficient method is used to analyze the subjective data. Based
on the change of the value of the index, the weight coefficient in the model can be ob-
tained from the utility value reflection of the information entropy of the data. The en-
tropy represents the degree of disorder of the system according to information theory.
The lower the entropy value of information, the lower the degree of disorder, and the
higher the utility value. Contrarily, the increase of the entropy value of information will
lead to the increase of the degree of disorder and the decrease of the utility value [40].
Based on the order degree and utility value of the information, the judgment matrix and
information entropy are used to calculate the weight. This method eliminates the influ-
ence of human factors on the weight calculation, and makes up for the weaker aspects of
the grey correlation model. The model is not easily affected by subjective factors when
there are many indicators, and this can makes the evaluation results more realistic [41].
The factors influencing the passenger flow of Shanghai rail transit stations are ana-
lyzed in this paper, and the annual passenger flow of each station in Shanghai in 2015 is
selected as the reference sequence. Five types of influencing factors, including traffic ac-
cessibility, built environment, regional characteristics of the district to which the i-th sta-
Figure 5. Inner, middle, outer and suburban rings in Shanghai.
3. Mathematical Model of Passenger Flow at Shanghai Rail Transit Stations
Combining the grey correlation model and entropy theory, this paper presents a
mathematical model to analyze the factors affecting the passenger flow of urban rail transit
stations. The grey correlation model is an important method to quantitatively analyze
the dynamic development process and examine whether the relationship between the
various factors is close. It is a measure of the relation degree between sequences, which
is expressed as the similarity of magnitude changes and the development trends between
sequences. The correlation degree is a reflection of the distance between two points of
different sequences. Based on the reliability of the correlation coefficient, the entropy
weight-grey correlation is established by weighting the grey correlation coefficient, which
can control the volatility of the correlation coefficient effectively. Therefore, the entropy
weight-grey correlation model can be used to analyze the influencing factors of urban
passenger flow of rail transit stations directly and clearly.
The entropy weight coefficient method is used to analyze the subjective data. Based on
the change of the value of the index, the weight coefficient in the model can be obtained from
the utility value reflection of the information entropy of the data. The entropy represents
the degree of disorder of the system according to information theory. The lower the entropy
value of information, the lower the degree of disorder, and the higher the utility value.
Contrarily, the increase of the entropy value of information will lead to the increase of the
degree of disorder and the decrease of the utility value [
40
]. Based on the order degree and
utility value of the information, the judgment matrix and information entropy are used to
calculate the weight. This method eliminates the influence of human factors on the weight
calculation, and makes up for the weaker aspects of the grey correlation model. The model
is not easily affected by subjective factors when there are many indicators, and this can
makes the evaluation results more realistic [41].
The factors influencing the passenger flow of Shanghai rail transit stations are analyzed
in this paper, and the annual passenger flow of each station in Shanghai in 2015 is selected
as the reference sequence. Five types of influencing factors, including traffic accessibility,
built environment, regional characteristics of the district to which the i-th station belongs,
Mathematics 2022,10, 3506 9 of 23
the conditions of the station, and spatial location, of passenger flow of rail transit stations
are used as a comparison sequence, which includes a total of 31 index factor of variables.
Suppose the reference sequence is
Y
,
Y= [Y1
,
Y2
,
· · ·
,
Ym]
, the comparison sequence is
Xi
k
,
Xi
k= [X1
k
,
X2
k
,
· · ·
,
Xm
k]
, where
m
represents the m-th rail transit station,
i
denotes the i-th
station,
i=
1, 2,
· · ·
,
m
;
n
indicates that there are a total of nindex factors,
k
(
k=
1, 2,
· · ·
,
n
)
is the k-th index factor.
The optimal index set Fis
F= [X
1,X
2,· · · ,X
n](1)
where X
kis the ideal value of the k-th index.
For a certain type of index, the larger its value, and the more advantages it reflects,
then the maximum value of this index in all stations should be taken; this type of index is
called a positive index. Conversely, the smaller the value, the more fully the advantage can
be exerted. The minimum value of this index in all stations should be selected, and this
type of index is called a reverse index.
Combining with the reference and comparison sequences, the initial matrix is
M=
YX
1X
2· · · X
n
Y1X1
1X1
2· · · X1
n
.
.
..
.
..
.
.....
.
.
YmXm
1Xm
2· · · Xm
n
(2)
Suppose the change interval of the passenger flow
Y
value is
[minY
,
maxY]
, where
minY
is the minimum value of the passenger flow of Shanghai rail transit stations in 2015,
and
maxY
is the maximum value among those of all stations. The variation interval of the
k-th indicator is
min
iXik, max
iXik
,
min
iXik
is the minimum value of the k-th index in all
stations, and max
iXik is the maximum value of the k-th index in all stations.
The normative formula is
Vy=yminy
maxyminy(3)
Vik =
Xik min
iXik
max
iXik min
iXik
(4)
After normalizing the original matrix, the matrix converted from Mto Vis obtained as
V=
VyV
1V
2· · · V
n
VyV1
1V1
2· · · V1
n
.
.
..
.
..
.
.....
.
.
VyVm
1Vm
2· · · Vm
n
(5)
The correlation analysis method is used to obtain the correlation coefficient
ξi(k)
between the passenger flow of the rail transit station and the optimal value of the k-th index
in the i-th station, and
ξi(k) =
min
imin
k
VyVi
k
+max
imax
k
VyVi
k
VyVi
k
+ρmax
imax
k
VyVi
k
(6)
Mathematics 2022,10, 3506 10 of 23
where
ρ[
0, 1
]
, and in general,
ρ=
0.5. In the formula,
VyVi
k
is the absolute deviation
between
{Vy}
and
Vi
k
of the k-th index at the i-th station.
min
imin
k
Vy,Vi
k
is the two-
level minimum deviation, and max
imax
k
Vy,Vi
k
is the two-level maximum devitation.
To understand these variables more easily, we need to introduce the concept of range.
The range is the deviation between the largest one and the smallest one in a set of data. The
range can reflect the distribution and dispersion range of data. The deviation between the
standard values of any two units cannot exceed the range. The larger the range, the greater
the degree of dispersion.
According to the definition of entropy, an analysis matrix
X= [xik ]m×n
(
i=
1, 2,
· · ·
,
m
;
k=
1, 2,
· · ·
,
n
) is established by a data table consisting of mstations and nitems of
influencing factors. The entropy of each index is defined as influencing factors.
The entropy of each index is defined as
Hk=
m
i=1
fik ln fik
ln m(7)
where fik =xik
m
i=1
xik
. When fik =0, ln fik is meaningless, then let fik ln fik =0.
Further, the weight of the k-th index can be calculated as
wk=1Hk
n
k=1
(1Hk)
(8)
where 0 <wk<1, and n
i=1
wk=1.
From ξi(k), the analysis matrix Eof each index can be obtained as
E=
ξ1(1)ξ1(2)· · · ξ1(n)
ξ2(1)ξ2(2)· · · ξ2(n)
.
.
..
.
.....
.
.
ξm(1)ξm(2)· · · ξm(n)
(9)
The determined weights can be expressed as
w= [w1,w2,· · · ,wn]T
. Then the compre-
hensive evaluation result is
ri=
n
k=1
w(k)ξi(k)(10)
4. Data Collection
This paper collects data from 85 rail transit stations in Shanghai in 2015. The annual
passenger flow data of each rail transit station is obtained by converting the monthly
average card swiping data of each station, which was provided by Shanghai Shentong
Metro Co., Ltd (Shanghai, China).
The data of GDP, average house price, paid-in foreign investment, fixed asset invest-
ment, total industrial output value, total industrial assets, secondary and tertiary industry
output value of 19 districts in 2015, and important land, land area, land use type, floor area
ratio, residential area and other data within the attraction range of the site are collected
from the ‘Land Planning Database’ [
42
], based on the statistical yearbooks of the city and
the districts of the city and the official website of the Municipal Bureau of Planning and
Natural Resources. The Land Planning Database is a relational data management system
that stores and manages all district-level data in big cities such as Shanghai. The map
platform in this database was used to determine the spatial geographic location of each rail
transit station in Shanghai.
Mathematics 2022,10, 3506 11 of 23
For the data on traffic accessibility characteristics, this paper uses the network analysis
provided by ArcGIS to calculate the distances from each rail transit station to important
transportation hubs, district committees and the nearest large commercial plazas, univer-
sities or key high schools, third-class hospitals, parks and important land. The average
walking speed of residents is assumed as 1.2 m/s [
43
], and thus the approximate time cost
of residents walking from nearby plots to rail transit stations is calculated. Figure 6shows
the heat map of passenger flow distribution at various rail transit stations in Shanghai.
Mathematics 2022, 10, x FOR PEER REVIEW 11 of 24
4. Data Collection
This paper collects data from 85 rail transit stations in Shanghai in 2015. The annual
passenger flow data of each rail transit station is obtained by converting the monthly
average card swiping data of each station, which was provided by Shanghai Shentong
Metro Co., Ltd (Shanghai, China).
The data of GDP, average house price, paid-in foreign investment, fixed asset in-
vestment, total industrial output value, total industrial assets, secondary and tertiary
industry output value of 19 districts in 2015, and important land, land area, land use
type, floor area ratio, residential area and other data within the attraction range of the site
are collected from the ‘Land Planning Database’[42], based on the statistical yearbooks of
the city and the districts of the city and the official website of the Municipal Bureau of
Planning and Natural Resources. The Land Planning Database is a relational data man-
agement system that stores and manages all district-level data in big cities such as
Shanghai. The map platform in this database was used to determine the spatial geo-
graphic location of each rail transit station in Shanghai.
For the data on traffic accessibility characteristics, this paper uses the network
analysis provided by ArcGIS to calculate the distances from each rail transit station to
important transportation hubs, district committees and the nearest large commercial
plazas, universities or key high schools, third-class hospitals, parks and important land.
The average walking speed of residents is assumed as 1.2 m/s [43], and thus the ap-
proximate time cost of residents walking from nearby plots to rail transit stations is cal-
culated. Figure 6 shows the heat map of passenger flow distribution at various rail
transit stations in Shanghai.
Figure 6. Heat map of passenger flow distribution of rail transit stations in Shanghai.
Google Earth (GE) is the virtual software of the earth developed by Google, and the
global geomorphological imagery provides high-precision images with a resolution of
about 1 m and 0.5 m for large cities and building areas, and the heights of viewing angle
Figure 6. Heat map of passenger flow distribution of rail transit stations in Shanghai.
Google Earth (GE) is the virtual software of the earth developed by Google, and the
global geomorphological imagery provides high-precision images with a resolution of
about 1 m and 0.5 m for large cities and building areas, and the heights of viewing angle
are about 500 m and 350 m, respectively. In this paper, GE high-resolution image software
is used to obtain the data on the conditions of the rail transit stations. The high-resolution
image with a spatial resolution of 0.5 m is selected, and through visual interpretation, the
number of rail lines and the number of entry and exit channels for by each rail transit
station can be identified. Table 1summarizes the statistics of the passenger flow and its
influencing factors.
Table 1. Summary statistics of passenger flow of stations and their influencing factors.
Variable Observation Mean Standard
Deviation Minimum Maximum
APSi211 705.6567 672.5237 63.2235 4679.2010
D1i211 233.5913 135.8824 4.7150 595.4320
D2i211 238.4747 153.6188 6.7170 686.0370
D3i211 233.8802 148.8693 22.1220 672.5820
D4i211 417.7905 147.1100 6.0840 737.9900
DPARi211 13.9371 10.1799 0.9610 72.3710
Mathematics 2022,10, 3506 12 of 23
Table 1. Cont.
Variable Observation Mean Standard
Deviation Minimum Maximum
DUNIi211 32.1301 22.7869 1.3720 99.2150
DCPi211 48.9716 47.5769 3.4030 246.6420
DDCi211 109.8904 108.9377 0.2160 451.4720
DPLi211 7.3663 7.2217 0.4330 34.1900
DTHi211 80.4863 75.0101 1.5400 302.5380
IPAi211 47,246.8800 38,565.9500 1658.0000 260,118.8000
IPRi211 1.9836 1.0436 0.2200 10.0000
IPPi211 79,180.5500 140,362.2000 186.0000 881,500.0000
IPTi211 104.6643 112.3101 1.7479 467.9843
DICi211 5.7109 2.7493 1.0000 9.0000
DAAi211 625.2144 370.4273 23.4800 1210.4100
DPRNi211 196.2970 149.1328 69.1100 547.4900
DHAi211 2769.6540 2790.2910 135.0000 9233.0000
DGDPi202 2002.3940 2457.6720 291.2000 7898.3500
DEASi177 80,474.4900 23,749.0800 60,285.0000 129,368.0000
DIEOi211 2926.2760 2784.0890 104.8800 9177.8000
DSIOi202 722.2753 646.8724 71.4100 2186.5200
DTIOi202 1228.5050 1844.4640 137.6000 5684.9100
DDMRi211 0.5687 0.4964 0.0000 1.0000
DDSRi211 0.4550 0.4992 0.0000 1.0000
WMPSi211 0.3649 0.4826 0.0000 1.0000
WTSi211 0.1327 0.3401 0.0000 1.0000
NUMLi211 1.1801 0.5655 1.0000 5.0000
NUMEi211 3.1138 1.4331 1.0000 8.0000
WIRi211 0.0427 0.2026 0.0000 1.0000
WIMRi211 0.1327 0.3401 0.0000 1.0000
WMORi211 0.0900 0.2869 0.0000 1.0000
WOSRi211 0.5355 0.4999 0.0000 1.0000
WSRi211 0.1991 0.4002 0.0000 1.0000
At present, the domestic statistical data is limited and the grey-scale of data is relatively
large. Among the statistical data, the panel data of Shanghai rail transit stations in 2015
is very complete, and the data information of the same stations in other years has many
missing values. Besides, the theory of grey correlation degree can make up for the problem
of large grey-scale of data, and will not cause distortion of the analysis results due to the
smaller amount of data.
5. Results and Discussion
Based on the collected data and the mathematical model, the results of grey correlation
between the passenger flow and the five influencing factors are calculated. The normalized
processing of passenger flow and five types of influencing factors and the average value
of their correlation coefficients are shown in Table 2. The entropy weight of influencing
factors and the average value of comprehensive correlation degree are shown in Table 3.
In this paper, the range method is applied to deal with the forward index and the reverse
index, respectively. This method can remove the units involved in the physical quantity
equation to simplify the calculation. Meanwhile, the indexes in the normalized matrix are
all positive indexes. The maximum value of each column in the obtained normalized matrix
is 1, and the minimum value is 0. There is no need to distinguish the positive and negative
index factors in the subsequent correlation results. The calculated correlation degree should
range from 0 to 1. The larger the value, the stronger the correlation between the index
sequence and the reference sequence. If the result is less than 0, it does not conform to the
calculation principle of grey correlation analysis, and should be used as ‘Null’. In addition,
Mathematics 2022,10, 3506 13 of 23
the higher the weight, the greater the entropy, which means that the corresponding index
system is more chaotic, the degree of variation is smaller, and the value information carried
is less; on the contrary, the smaller the entropy weight, the more orderly the system is, and
the more value information it carries. As shown in Table 3, most of the entropy weights in
this study fluctuate between 0.025 and 0.3, indicating that the data of the entire system is
relatively orderly, and the analysis of the results based on the collected data is more scientific
and rigorous.
Table 2.
Standardization and average correlation coefficients between passenger flow of stations and
five types of influencing factors.
Variable Mean of Normalized Values Mean of Correlation
Coefficient
APSi0.139175995 -
D1i0.612545015 0.538013464
D2i0.658838724 0.516097799
D3i0.674448592 0.509567495
D4i0.437487242 0.651135896
DPARi0.818286843 0.436537605
DUNIi0.685637774 0.501344371
DCPi0.811458170 0.443615288
DDCi0.756957541 0.475163430
DPLi0.794611798 0.451009159
DTHi0.737718280 0.484190583
IPAi0.176386037 0.791569735
IPRi0.819669979 0.431951516
IPPi0.089632691 0.837244805
IPTi0.779261382 0.464259136
DICi0.588862559 0.540888762
DAAi0.506967052 0.582531502
DPRNi0.265870154 0.767995587
DHAi0.289586072 0.771334204
DGDPi0.224945425 0.798307755
DEASi0.292249699 0.744312855
DIEOi0.310968924 0.739375654
DSIOi0.307721714 0.758834759
DTIOi0.196154863 0.782534508
DDMRi0.568720379 0.545436215
DDSRi0.454976303 0.624641057
WMPSi0.364928910 0.640739983
WTSi0.132701422 0.763090882
NUMLi0.045023697 0.814275221
NUMEi0.301963415 0.753517275
WIRi0.042654028 0.794643939
WIMRi0.132701422 0.764587451
WMORi0.090047393 0.763897732
WOSRi0.464454972 0.601352034
WSRi0.800947867 0.478019161
Mathematics 2022,10, 3506 14 of 23
Table 3.
The entropy weight of influencing factors and the average value of comprehensive correla-
tion degree.
Variable Mean of Entropy Weights Mean of Comprehensive
Correlation Degree
D1i0.064246000 0.034565220
D2i0.069125700 0.035675610
D3i0.066322000 0.033795550
D4i0.025575000 0.016652774
DPARi0.095696900 0.041775317
DUNIi0.098295500 0.049279866
DCPi0.139211000 0.061756123
DDCi0.141756800 0.067357677
DPLi0.147649300 0.066591187
DTHi0.152121800 0.073655940
IPAi0.164913500 0.130540504
IPRi0.058285000 0.025176313
IPPi0.490088800 0.410324289
IPTi0.286712700 0.133108991
DICi0.025456000 0.013768872
DAAi0.035685900 0.020788182
DPRNi0.040343300 0.030983443
DHAi0.072940100 0.056261209
DGDPi0.100004500 0.079834372
DEASi0.037746600 0.028095270
DIEOi0.069242800 0.051200554
DSIOi0.065469000 0.049680169
DTIOi0.139005500 0.108776577
DDMRi0.099030300 0.054014714
DDSRi0.138185700 0.081616443
WMPSi0.176884700 0.113337136
WTSi0.919859200 0.701936198
NUMLi0.035832000 0.029177141
NUMEi0.044308700 0.033387387
WIRi0.321233800 0.255266524
WIMRi0.205659700 0.157244828
WMORi0.245145600 0.187266177
WOSRi0.063589300 0.038239564
WSRi0.164371500 0.078572731
5.1. Influence of Traffic Accessibility on Passenger Flow of Rail Transit Stations
The influence of traffic accessibility is now discussed, drawing on the data in Table 3.
For the factors of traffic accessibility, the comprehensive correlation degree between
the distance from the rail transit station to the adjacent third-class hospital (DTH
i
) and the
passenger flow of the station is 0.07365594, which is the maximum value in the comprehen-
sive correlation degree column of this plate, indicating that the distance from the rail transit
station to the neighboring third-class hospitals has the greatest influence on passenger flow
among all traffic accessibility characteristics. With the acceleration of economic develop-
ment and urbanization, a large number of people have poured into megacities such as
Shanghai and Beijing, which has prompted the rapid growth of basic medical resources and
related allocations. The third-class hospitals have strong diagnosis and treatment supply
capacity, and the traffic flow generated by the patients gathered in the top three hospitals
is not less than that of an important transportation hub [
44
]. At the same time, due to
the imperfect tiered diagnosis and treatment system in China, grassroots hospitals have
not been able to form effective patient shunting, resulting in large hospitals with absolute
patient attraction, and patients from surrounding districts and counties also flocking to
the city center, as well as the sources of disease being more extensive. It is also consistent
Mathematics 2022,10, 3506 15 of 23
with the conclusion drawn in this paper that the distance from the rail transit station to the
adjacent top three hospitals has a great influence on the passenger flow of the station.
The comprehensive correlations between the distances (DCP
i
,DDC
i
and DPL
i
) from
the rail transit station to the adjacent large commercial plazas, district committees and
parking areas and the station passenger flow are 0.061756123, 0.067357677 and 0.066591187,
respectively, second only to the distance between the third-class hospitals and the station.
The magnitude of the correlation degree indicates that the distances from the rail transit
station to the adjacent large commercial plazas, district committees and parks also has
greater impacts on the passenger flow of the station. Large-scale commercial plazas form
a comprehensive high-end urban core area. Their developers choose valuable cities and
regions for development and construction, and realize the concentrated urban economic
value through comprehensive investment channels such as passenger flow and capital
flow. Large commercial plazas are often located in the areas with high land value such as
central business districts, financial centers, and transportation hubs. In order to alleviate
the pressure on land resources, the government has set up some rail transit stations inside
large commercial building complexes. The influence of the district committee on the
passenger flow of rail transit stations is mainly due to the changes in the development and
construction of rail transit stations in terms of political policies, which has an indirect impact
on the passenger flow of the stations. In China, the district committee, as the center of the
local district-level government, has overall leadership over the political, economic, cultural
and social development of the district, and is responsible for organizing special forums or
meetings to discuss development strategies with the rail transit companies, which plays an
important role in the construction of rail transit. At present, the integrated construction of
commercial buildings, underground parking lots and subways has become the mainstream
development mode. The government vigorously advocates subway parking and transfer
to non-motor vehicle parking lots, notably Biking & Riding (B-R) parking lots, to guide
more people to use the green travelling mode of ‘Bike to Subway’.
Secondly, the relationships between the distances from the rail transit station to the
nearest park, university or key high school and the passenger flow of the station are also
important. From the comprehensive correlation results, the correlations between the dis-
tances from the rail transit station to the nearest park, university or key high school (DPAR
i
and DUNI
i
) and the station passenger flow are 0.041775317 and 0.049279866, respectively.
As a part of the green space with the greatest social and ecological benefits, the accessibility
of urban parks reflects the service capabilities of public facilities and the social distribution
of public resources. There are clear requirements for the scale and service radius of parks
and green spaces at all levels in the central districts in Shanghai [
45
]. At the same time,
public rail transit provides a variety of travel options and convenient conditions for more
people in urban space. In megacities, it is normal for people to choose the subway-walking
composite transportation mode to reach parks and green spaces. The accessibility of educa-
tional resources in universities and key high schools in Shanghai is generally high, which
can better meet the schooling needs of urban residents. In general, rail transit stations are
named after their nearby landmark buildings or roads. In Shanghai, there are already some
subway stations named after nearby universities, such as Tongji University Station, Jiaotong
University Station, Shanghai University Station and Songjiang University Town Station,
and the areas with high accessibility are mainly distributed in the areas with developed
road networks and developed public transportation networks.
Finally, for the distances from the Shanghai Railway Station, Hongqiao Railway Station
and Hongqiao International Airport to the rail transit station, the correlations between the
distances (D
1i
,D
2i
and D
3i
) of the stations and the passenger flow of the stations are roughly
the same, which are 0.03456522, 0.03567561 and 0.03379555, respectively. The correlation
of the distances (D
4i
) from Pudong International Airport to the rail transit stations and
the passenger flow of the stations is the smallest, at 0.016652774, indicating that Pudong
International Airport has the weakest impact on the passenger flow of subway stations.
The dense number of the stations on Metro Line 2 leads to a long running time. The average
Mathematics 2022,10, 3506 16 of 23
time it takes for passengers to arrive at Pudong Airport by rail transit is about 1.5 h, while
that for passengers to arrive at Pudong Airport by car is only about 1 h [
46
]. In addition, the
one-way time between Pudong International Airport and Hongqiao Hub by Metro Line 2
takes 2 h; thus, there is a lack of passenger facilities for rapid communication between the
two airports [
47
]. According to the statistics, after the suspension of Metro Line 2 around
10:00 p.m., 8.8% of flights at Pudong International Airport were still arriving and 6.7%
departing [
48
]. The premature shutdown of the subway causes a lack of service connection.
Moreover, passengers can choose from various means of transportation to reach Pudong
Airport. In addition to subways and taxis, they can also take maglev trains. It takes about
45 min from Longyang Metro Station to Pudong Airport, and only 8 min from the same
starting station for maglev trains. At present, Pudong International Airport has two rail
transits, including Metro Line 2 and Maglev Line, which can connect to the urban area.
Although the subway is cheaper in price, its speed is slow, and multiple transfers may be
required, which is inconvenience and uncomfortable.
5.2. Influence of Built Environment on Passenger Flow of Rail Transit Stations
The four index factors of the built environment include the area of important land
around the rail transit station (IPA
i
), the floor area ratio of the land (IPR
i
), the land transfer
price (IPP
i
), and the time it takes residents to walk to the station (IPT
i
). As shown in
the correlation results in Table 3, the comprehensive correlation between APS
i
and IPP
i
is
0.410324289, which is the largest among the four indicators, and far exceeds other indicators
of the same type. The land use types have a greater impact on passenger flow in cities,
which are divided into four categories, including residential, commercial, office, and public
buildings. The higher the land development intensity, the higher the economic benefits of
land use and the corresponding increase in land prices. Meanwhile, it can cause increases
in land area, so that more people can be accommodated, and thus the traffic demand will
be greater. This also explains the impact of the surrounding land area (IPA
i
) on the subway
passenger flow. At the same time, the increase in land development intensity will also
increase the share of public transportation, and the passenger flow of urban rail transit will
also increase. The peak value of the cross-section passenger flow mainly occurs before and
after the transfer station where the rail transit line enters the urban area in the peripheral
area of the city and the station in the large office area. The main source of passenger flow is
the commuting passenger flow generated by the residential area around the station along
the line [
48
]. Most shops also have a competitive advantage because of the traffic created
by the subway station. The rent of shops near the subway station is generally higher than
that of other locations, so the land price will also be higher.
Next, the impact of the time it takes residents to walk to the station (IPT
i
) on the
passenger flow of the station is discussed. By investigating the passenger flow of Shanghai
Metro Line 1, the average time spent by passengers walking from the starting point to
the nearest rail transit station is 14 min, and the approximate distance walked is 2 km
based on the average speed. The core of the user balance principle is that the users in the
transportation network all choose the shortest path to travel, and the impedance of the
final selected path is the smallest and equal. This principle reflects the behavioral criteria
of road users for route selection; an individual with behavioral decision-making ability in
any system always decides his behavioral decision by maximizing his own interests. In
this study, residents of nearby land also tend to spend less time and cost in making travel
decisions. The correlation between the floor area ratio (IPR
i
) of the land and the passenger
flow of the station is only 0.025176313, indicating that the impact of the floor area ratio
on the passenger flow of the station is minimal. Generally speaking, the higher the floor
area ratio, the lower the comfort level of residents. However, there is a certain relationship
among the floor area ratio and the building density and the number of floors. The floor
area ratio can be used to measure the level of land prices, and increasing the floor area ratio
can also improve the efficiency of land use, so it cannot be ruled out that the floor area ratio
has an indirect impact on the passenger flow.
Mathematics 2022,10, 3506 17 of 23
5.3. Influence of Regional Characteristics of the District on Passenger Flow of Stations
There are 12 factors considered in the regional characteristics of the district to which
the rail transit station belongs. The quantity of the influencing factors is large, and the
set sum of the entropy weights of each factor under each station should be equal to 1,
which leads to a very small proportion of the weight of each factor, and the calculated
comprehensive correlation is also smaller than that of other categories of influencing factors.
Thus, the results are reasonable and analyzable.
Among the first nine influencing factors in Table 3, the output value of tertiary industry
has the greatest impact on the passenger flow of rail transit stations, and its correlation
value is 0.108776577. In China, the tertiary industry is divided into two major departments,
including circulation and service, and four levels, which are the circulation department,
the department serving production and life, the department serving the improvement of
scientific and cultural level, and the department serving the improvement of residents’
quality of life [
49
]. In the definition and statistics of the tertiary industry in China, the
fourth level is categorized as belonging to the tertiary industry division, but its added value
is not included in the output value of tertiary industry or the gross national product. It
can be seen that the tertiary industry in China is still in the traditional service sector. The
traditional service industry used traditional consumption methods before the emergence of
large-scale industries, mainly including commerce and transportation. The transportation
industry is very important in the tertiary industry, and the optimization of the industrial
structure will inevitably lead to the evolution and development of passenger flow and
transportation to adapt to the new industrial structure. In comparison, the gross output
value of the secondary industry has a much smaller impact on the rail passenger flow,
and the correlation between them is only 0.049680169. From the GDP proportion of
the three industrial structures, the industrial structures of the United States and Japan
are relatively similar. In these two countries, the proportion of the added value of the
primary and secondary industries continued to decline, and the added value of the tertiary
industry kept rising until 2015. The industrial structure in China is different from other
countries. The most obvious difference is that the proportion of added value of secondary
industry in China has not declined, remaining stable at around 45%, which is higher
than the proportion of added value of the primary and tertiary industries. Because the
development of tertiary industry started late in China, although it has developed rapidly, it
still lags behind the United States and Japan, and there is still much space for development.
Moreover, rail transit is mostly located in the downtown area, and suburban rail transit is
not well developed. In recent years, Shanghai has vigorously built and developed suburban
rail transit. For example, the Disney Station of Metro Line 11 and Metro Line 15, 17 and
18 opened for operation, Metro Line 5 extends south from Dongchuan Road Station to
Fengxian New City Station, and the Phase II of Metro Line 10 extends east from the New
Jiangwan City Station to Keelung Road Station. In addition, industries related to secondary
industry are often located in the suburbs of cities, so the passenger flow of stations has little
correlation with the output of the secondary industry.
Secondly, GDP of the district has a greater impact on the passenger flow of the rail
station, and its correlation value is 0.079834372. Some studies have found that in Chengdu,
China, before 2010, subway passenger flow increased by 1% while the per capita GDP
increased by 0.33%. After 2010, that is, after the construction of the subway in Chengdu,
the coefficient of subway passenger flow increased to 0.40, indicating that the impact of
passenger flow after the construction of the subway on per capita GDP was 0.07% more
than the impact on per capita GDP before 2010. It is shown that rail transit has positively
influenced economic construction and development in Chengdu [50]. The contribution of
urban rail transit to the increased value of real estate along the line is obvious, and even
the price of commercial housing under planning has soared. When the supply is fixed and
the demand goes up, the land price will also see a gradual rise. Correspondingly, the land
grade (DIC
i
) will also increase with the growth of land price. The correlation between the
land grade and the passenger flow of rail transit stations is 0.013768872. The higher the
Mathematics 2022,10, 3506 18 of 23
land grade is, the stronger is the service capacity of the district, which attracts passengers to
gather and benefit from the better carrying capacity and service level of the infrastructure.
Districts with lower land grades also have less complete rail transit, and the development
intensity of land along the line guided by rail transit is about 30–100% higher than that of
the same type of land in general districts [
51
]. Under the premise that the total amount
of land supply remains unchanged, the local government can appropriately increase the
supply of residential land by adjusting the land supply structure, and can obtain land
revenue from the land transfer to reduce the investment pressure on the construction
of rail transit. The influences of the district area (DAA
i
) and the number of permanent
residents (DPRN
i
) on the passenger flow of rail transit stations are mainly reflected in
the station layout. In commercial and residential areas with large passenger flow, smaller
station spacing should be considered in order to meet the needs for convenient travel
of large passenger flows; in the peripheral areas of the city, the number of trips by the
population is large, so larger distance between stations can be considered. In practice, the
distance between stations increases in the peripheral areas of the city. In China, houses
with more than eight floors are generally considered as high-rise residences. In the case of
relatively poor land resources, high-rise residential buildings, which occupy a small area
and accommodate many residents, become the necessity of urban development. Shanghai
Planning and Land Resources Administration has investigated the high-rise residential
buildings, and found that there are about 240 new high-rise residential buildings per year
on average, which is equivalent to that a high-rise residence can be built in about one and a
half days in Shanghai. If the establishment of rail transit stations can facilitate the travel of
residents in a nearby high-rise residential community, most residents will choose to take
the subway, and the influx of a large number of nearby residential residents will also affect
the passenger flow. The larger the population density is, the greater the passenger flow of
rail transit. Similarly, the closer the house is to rail transit, the higher the housing price.
The accessibility of rail transit thus is very important for residents’ work and living needs.
In most previous studies, the district-level political factors of each district are often
ignored. From the results in Table 3, the re-election of district chiefs in each district
(DDMR
i
), the re-election of district party secretaries (DDSR
i
), and whether the district chief
is promoted to district party secretary (WMPS
i
) exert great influence on the passenger flow
of stations, and their correlation degrees are 0.054014714, 0.081616443 and 0.113337136,
respectively. In China, the financial decision-making of local governments shows a clear
tenure effect. For consideration of promotion, local officials tend to adopt different resource
allocation strategies at different times during their tenure, which may bring fluctuations in
financial expenditures for rail transit construction. From Table 3, the re-election of the local
district head, the re-election of the district party secretary, and the promotion of the local
district head to district party secretary have positive impacts on the passenger flow growth
of stations. At present, the existing researches mainly focus on the analysis of the impact of
official replacement on total fiscal expenditure, productive fiscal expenditure, etc., and the
research on rail transit development and expenditure on construction is sparse.
5.4. Influence of Conditions of the Station on Passenger Flow of Stations
From Table 2, it can be seen that there are small differences in the correlation coefficients
according to whether the station is a transfer (WTS
i
), the number of rail transit lines passed
by the station (NUML
i
), and the number of station entrances and exits (NUME
i
), which
are 0.763090882, 0.814275221 and 0.753517275, respectively. The weight ratio of stations as
transfer stations is 0.9198592, which indicates that the data of this indicator value show little
change or very little difference. The data of transfer stations show that only 29 items are
transfer stations (=1), and 182 items are non-transfer stations taking the station (=0), which
is consistent with the above discussion. However, whether it is the correlation coefficient
or the comprehensive correlation value, it can still be seen that the transfer station has a
more influential impact on the passenger flow of the rail transit station [
52
]. Under the
same external conditions, travelers are more inclined to choose the low-cost rail transit
Mathematics 2022,10, 3506 19 of 23
mode. However, when the low-cost mode of transportation cannot meet the passengers’
time requirements, the economic factor is no longer the primary factor affecting the transfer,
and passengers often gain time at the expense of price. For subway lines, passengers hope
to reach the station quickly from the psychological expectation, and are willing to reduce
transfer as much as possible.
Currently, among all rail transit stations in Shanghai, the fourth-line transfer station
is only Century Avenue Station, and there are 16 third-line transfer stations including
Hanzhong Road Station, Shanghai South Railway Station, Xujiahui Station, People’s Square
Station, South Shaanxi Road Station, Shanghai Railway Station, Hongqiao Railway Station,
and Nanjing West Road Station. There are 50 s-line transfer stations including Xinzhuang
Station, Changshu Road Station, Caobao Road Station, Shanghai Stadium Station, Nanjing
East Road Station, Loushanguan Road Station, Jiangsu Road Station, and Jing’an Temple
Station. The number of rail transit lines (NUML
i
) passing through the station also has
an obvious influence on the passenger flow of the rail transit station, and its correlation
coefficient is 0.814275221, which is the highest among other indicators of conditions of
the station. As the only four-line transfer station in Shanghai’s urban rail transit network,
Century Avenue Station has the highest average daily passenger transfer flow in the road
network, and its transfer passenger flow during the morning rush hour is close to its
carrying capacity.
During the station layout planning, the station entrances and exits are the only pas-
sages for passengers to enter and exit the station, and must meet the requirements of
urban planning and traffic and facilitate the entry and exit of passengers. The number of
entrance and exit passages (NUME
i
) should be determined by the number of passengers
getting on and off at the station, and the size of entrance and exit space should consider
passenger demand, station facilities, safety of waiting passengers and related specifications
of construction design.
5.5. Influence of Spatial Location of the Stations on Passenger Flow of Stations
From the comprehensive correlation degree results in Table 3, the correlation degree
between rail transit stations located within the inner ring and station passenger flow is
0.255266524, which is much higher than that of the other four factors of spatial location. It
is indicated that the rail transit stations being located within the inner ring of the city has a
huge impact on the passenger flow of the station. The location of the inner ring road in
Shanghai is completely within the city center. From the heat map shown in Figure 6, the
central area of the city is the most dynamic area of the passenger flow in Shanghai, and the
streets with high vitality show the same format characteristics. Whether a street combines
commercial streets with residential areas, or mainly combines catering, shopping and other
formats, the surrounding public transportation facilities are complete and the rail transit
stations are densely set up, which is convenient for passengers to travel. These areas also
bring great passenger flow to the subway stations in the inner ring. The central ring road is
basically located at the edge of the downtown area, which acts as a traffic barrier for the
central area, and can quickly divert the transit traffic from the periphery into the urban
area. The expressway of the middle ring buffers the traffic between the radial entrance and
exit and the downtown area, and shares the passenger flow pressure of the subway line to
a great extent. Therefore, it can also be found that the rail transit stations situated between
the inner and middle rings (WIMR
i
) have even less impact on the passenger flow than the
stations situated between the middle and outer rings (WMORi).
The stations located between the outer ring and the suburban ring and outside the
suburban ring have little impact on the passenger flow of the station, and their correlation is
only 0.038239564 and 0.078572731. From the city center to the suburbs, the distance between
rail transit stations shows an increasing correlation. The outer layer of the outer ring line
leads to the suburban ring and the expressway that diverges radially in all directions. The
Pudong section has fewer expressways connected to the outside than the Puxi section, but
it connects the Pudong International Airport, ports and other vital traffic hubs. For the
Mathematics 2022,10, 3506 20 of 23
Metro Line 2 to Pudong International Airport, the average time cost of passengers is about
an hour, and more passengers are willing to choose the expressway in the outer ring of the
city and the suburban ring to their destination. In addition, the outer ring also connects
four main roads to the urban area, including Shangnan Road, Yanggao Road, Shenjiang
Road and Jinhai Road; the Pudong section of the outer ring road is also closely connected
with the roads in the downtown area.
6. Conclusions and Suggestions
The factors influencing the passenger flow of rail transit stations is explored here based
on the mathematical model of entropy weight-grey correlation in this paper. The model
assumptions and corresponding variables are proposed, including traffic accessibility, built
environment, the regional characteristics of the district to which the rail transit station
belongs, conditions of the station and spatial location, affecting the passenger flow of rail
transit stations. The mathematical model of entropy weight-grey correlation is established,
and the results for factors influencing the passenger flow of rail transit stations are analyzed.
To sum up, the traffic accessibility, built environment, the regional characteristics of
the district to which the rail transit station belongs, conditions of the station and spatial
location will affect the passenger flow of the station. For traffic accessibility, the distance
from the rail transit station to the adjacent third-class hospitals has the greatest impact on
the passenger flow of the station, the distance to the Pudong International Airport has the
least impact on the passenger flow, and the distance to the adjacent large commercial plazas,
district committees and parking areas also have greater impacts on station traffic. Among
the built environment factors, the transaction price of important land around the station has
the greatest impact on the passenger flow of the station, and the direct impact of the floor
area ratio on the rail transit station is very small, but its indirect effect in improving land
efficiency cannot be ignored. For the regional characteristics of the district, the ones that
exert greater influence on the passenger flow of stations are the total output value of the
tertiary industry, the GDP of the district, and whether the head of the district is promoted to
the secretary of the district party committee. Among the conditions of the station, whether
the station is a transfer station and the number of track lines passed through the station
have greater influences on the subway passenger flow. For the spatial location, rail transit
stations situated between the inner ring and the middle and outer rings have the greatest
influence on the passenger flow of stations, followed by those situated in the middle
and inner rings, while the stations outside the outer ring and suburban rings have the
least impacts.
The results show that the passenger flow of rail transit stations in Shanghai is closely
related to the quality of people’s livelihood and economic conditions, and most factors with
a greater level of influence are related to people’s clothing, food, housing, transportation,
employment and medical care and other life matters. The public service of urban rail
transit is correlated to the daily travel of people’s basic life; this service is public-facing
and is an important part of people’s life security. At the same time, the construction of
rail transit stations will increase the value of the land along the line. The government
can make up for the investment in the pre-construction of rail transit by later transferring
these lands in exchange for high profits, and the construction of rail transit will also bring
new vitality to the regional economy. The results of this paper are consistent with those of
recent related studies. Based on the mathematical model and district data of Shanghai from
2007 to 2015, influencing factors such as land area, GDP, tenure of the district chief, and
distance from the land to the nearest subway station affect the land transfer behavior of
government [
35
,
53
,
54
]. There is an association between land use around a metro station and
metro passenger flow, and the composition of land use around the metro station or along
the metro line affects the passenger flow generation and the prediction accuracy [
55
]. Plot
potential, development intensity, land ownership, residential appreciation, and mix-value
of land use are closely related to the passenger flow [
56
]. In this paper, the method of
entropy weight-grey correlation is used to analyze the influencing factors of the passenger
Mathematics 2022,10, 3506 21 of 23
flow of rail transit stations. Under the condition of fuzzy initial information, this model has
higher integrity and intuitiveness, which makes it easier to understand the influence level
of each factor on station passenger flow.
Furthermore, the regional characteristics of the district to which the station belongs
have various and profound impacts on the passenger flow, which has been ignored in the
previous analysis of passenger flow. A good urban rail transit planning should be based
on the overall urban planning. It is suggested that local governments should study the
distribution characteristics of population, land use, employment and tertiary industry at
the district level of the city, as well as the distribution characteristics of large passenger flow
distribution areas, in order to determine the road network structure and station location
plan of rail transit, and promote the development of subway stations and sustainable
urban development. In addition, the rail transit stations in the Pudong section have not
achieved the expected affordability of passenger flow. When the government studies the
new round of station layout planning, factors such as the ring expressway, passenger travel
time, and transfer lines in the Pudong section should be considered as having impacts on
passenger flow.
This study will help the local governments to formulate rail transit development
policies more effectively. The conclusions can provide a reference for the development of
rail transit in other large cities and countries.
Author Contributions:
Conceptualization, M.P.; methodology, P.Y.; software, P.Y.; validation, P.Y.;
formal analysis, P.Y; investigation, M.P.; resources, J.C.; data curation, J.C.; writing—original draft
preparation, P.Y.; writing—review and editing, J.C.; visualization, P.Y.; funding acquisition, J.C. All
authors have read and agreed to the published version of the manuscript.
Funding:
This research was funded by Start-up Funds for Scientific Research of Shenzhen University,
grant number 000002112313.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement:
All data, models or code generated or used during the study are
available from the authors upon request.
Conflicts of Interest:
The authors declare that there is no conflict of interest in the publication of
this paper.
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