Measuring the accessibility of metro stations in Tianjin: an origin-destination approach

ABSTRACT The achievement of good spatial accessibility is one of the supreme goals for metro transit planners. While many studies have measured either the accessibility of metro networks or walk accessibility of metro stations, the literature provides limited knowledge for metro station accessibility evaluations integrating both in the context of the origin-destination pair. The present study fills this gap through the use of a set of integrated measures that consider both by-metro accessibility and to-metro accessibility in combination and explores accessibility-based typology among stations. The space syntax is used to conduct the measure models for each dimension (by-metro and to-metro), and typology among stations is divided by an SOM (self-organizing map). The new approach is applied to the case of Tianjin, China. We find that the by-metro accessibility declines from the urban centre to the outskirts of the city and depends mainly on the location in the metro network and the topological depth from the transfer stations. However, the to-metro accessibility varies widely and depends on the street network structure in the station catchment area. Six typologies are identified among stations based on the different characteristics of by-metro accessibility and to-metro accessibility. Graphical Abstract


Introduction
With the increase in the sustainability concerns, accessibility becomes a central issue in the analysis of sustainable transport and urban development. Enhancing accessibility may help reduce automobile usage and relieve contemporary urban and regional problems. As shown by many scholars that metros are the backbone of the public transport system (Currie and Delbosc 2011;Hansson et al. 2021), the measures of metro accessibility have been the central of attraction. Steg (2003) found that people consider travelling by train more positively than bus (Steg 2003). In general, the better accessibility a metro station has, the more ridership it attracts and the more opportunities for integration of transport with land use. In turn, more passengers and higher land usedriven demand can strengthen the functionality of a metro station, thus further improving the urban spatial structure (Cervero and Kockelman 1997).
Actually, two levels of mobility should be studied in measuring the accessibility of metro systems. The first one is metro network mobility, or "by-metro accessibility". The by-metro accessibility means the ease of reaching other stations from a given station by the metro system. It is commonly measured by the level of metro service, including headway frequency, travel time/distance, number of transfers, and number of reachable stations within a specific travel time (Ato Xu et al. 2018;Yang et al. 2020). The second one is the pedestrian or bike mobility, or "to-metro accessibility". The to-metro accessibility means the ease of reaching a station from a giving location. It is generally measured by the level of first/last mile service around stations, such as travel time/distance to a station, length/width of sidewalks, and intersection density (Lahoorpoor and Levinson 2020;Yang et al. 2020).
The main purpose of this study is to purpose a set of integrated measures that consider bymetro accessibility and the to-metro accessibility together in order to evaluate and classify metro system's performance. To attain this purpose, the next section will review the relevant literature on accessibility in transportation studies. In the methodology section, a set of standardized by-metro accessibility and to-metro accessibility measures are introduced to draw the integrated model for the accessibility-based typology. This is followed by an empirical illustration for these concepts using Tianjin metro system as a case study. The last section briefly concludes.

Definition of metro accessibility
Accessibility, a crucial concept in the field of sustainable transport and urban development science, has been used widely. Researchers have presented different understandings and interpretations of the definition of accessibility, depending on the specific application. Hansen first put forward the concept of accessibility in 1959 and defined it as "potential of opportunities for interaction" (Hansen 1959). Niemeier (1997) defined accessibility as the capability/ease with which desired destinations may be reached from an original location using a particular transport system (Niemeier 1997). In the field of metro system, accessibility is mainly explained in relation to metro stations, representing people's ability to reach destinations by metro (Van Wee 2016). Moniruzzaman and Páez (2012) contended the ease of reaching attractive destinations by metro system and the ease of entering the system are two important factors that must be considered to analyze metro accessibility (Moniruzzaman and Páez 2012). Therefore, metro accessibility can be defined as the integration of by-metro accessibility and to-metro accessibility.

Measures of metro accessibility
Numerous empirical studies have focused on the methods of measuring by-metro accessibility, depending on how the metro system of concern is described as a network. Two major categories of by-metro measurement can be identified in the literature: geometry based and topology based (Li et al. 2017). Geometrybased measures represent the geometrical structure of transport system, including gravity method, opportunity method, utility method and space-time method (Kelobonye et al. 2019). Different from geometry-based measures, topology-based measures describe the topological structure of transport system, and reproduce the spatial scale by the connection between the nodes. As passengers usually have a vague perception of the space and distance while taking the metro, they pay more attention to the number of stations passed and the transfer experience between different lines. Therefore, the topological structure instead of the actual travel distance can better quantifies the bymetro accessibility (Li et al. 2017). Zhang et al. (2011) analysed the topology network of the Shanghai metro system, with each station regarded as a node and all nodes connected according to the complex network (Zhang et al. 2011). Chopra et al. (2016 analysed the topology structure of the London metro system with the space l metric (Chopra et al. 2016). Zhou et al. proposed an improved method for topology network based on space syntax and took the Guangfo metro system as an example to demonstrate the effectiveness of this method for spatial morphology, evolution and prediction of metro network accessibility distribution (Zhou et al. 2015).
Besides by-metro accessibility, a key focus interest for metro accessibility is to-metro accessibility, defined as the ease of reaching a station by walking. The metro can become the preferred transport option if to-metro accessibility is improved (Bivina, Gupta, and Parida 2019). To-metro accessibility is mainly influenced by factors relating to the design and built environment (Cervero et al. 2009;Vale, Viana, and Pereira 2018). These factors include travel time/distance to a station, length/width of sidewalks, quality of sidewalks, and intersection density. Hoback et al. concentrated on travel distance and travel time to metro stations (Hoback, Anderson, and Dutta 2008). Olszewski and Wibowo (2005) determined that urban design and sidewalk provisions influenced the accessibility to transit stations. Bivina et al. classified built environment factors that facilitate to-metro accessibility into two scales: macroscale and microscale (Bivina, Gupta, and Parida 2020). The connectivity of street as a significant factor that influences to-metro accessibility has only recently begun to receive attention. Monajem and Ekram Nosratian (2015) found that the continuous and dense spatial configuration of the street network in station areas is associated with an increase in the variety and intensity of activities, an increase in the workforce and better accessibility to the station by attracting greater pedestrian movement (Monajem and Ekram Nosratian 2015). A recent study conducted in Tehran, Iran, investigated walking potential by measuring spatial specifications and spatial parameters of street networks around metro stations using space syntax and found that integration and choice value together affected pedestrian accessibility (Pezeshknejad, Monajem, and Mozafari 2020).
In the past studies, metro accessibility are mainly modeled using a single measure, either by-metro accessibility or to-metro accessibility. While in fact metro stations may have different features of bymetro accessibility and to-metro accessibility which calling for an integrated measure considering both of them in the context of the origin-destination pair. Space syntax, one of the widely used topology-based measures, can measure both the by-metro accessibility and to-metro accessibility, which is very suitable for the development of this study.

Accessibility-based typology
Understanding the by-metro accessibility and to-metro accessibility features of metro stations can reveal their context-specific structure. Accessibility-based typology assists in this process, as it can cluster metro stations that share common characteristics. This helps policymakers and planners not only develop remedial actions to existing situation, but also formulate more targeted strategies for specific station types.
The node-place model, developed by Bertolini (1996Bertolini ( , 1999 (Bertolini 1996(Bertolini , 1999, provides an analytical framework through which to develop a quantitative station typology (Rodríguez and Kang 2020). The model summaries stations' characteristics with regard to two aspects, transit stations ("node") and their catchment area ("place"). Based on the node and place values, stations can be classified into five categories. Monajem and Ekram Nosratian (2015) has done a pioneer study by combining the node-place model with the spatial configuration of the street network to evaluate and classify station area in Tehran. With reference to the notion of metro accessibility and building on the work of Monajem and Ekram Nosratian (2015), we consider by-metro accessibility as the node value of metro stations, while to-metro accessibility as the place value of metro stations.

Methodology
To develop and implement our integrated measures of metro accessibility, the present study has three major objectives: (a) the by-metro accessibility measure module, (b) the to-metro accessibility measure module, and (c) the accessibility-based typology module, as shown in Figure 1.
As shown in Figure 1, a convex space model of space syntax is utilized to extract topology features for the metro network in module (a). The metro network can be transformed into a topological graph between stations, and the by-metro accessibility is measured by the figure of the integration and choice degree generated by the convex space model; this module is described in more detail in Section 3.2. In module (b), an axis model of space syntax is employed to measure to-metro accessibility using the topology feature of the street in the station catchment; this module is described in more detail in Section 3.3. By integrating by-metro accessibility and to-metro accessibility according to node-place model, all the metro stations in the study area are evaluated and classified into different typologies by the SOM in module (c); this module is described in more detail in Section 3.4.

Space syntax method
In this paper, the space syntax analysis previously used by Monajem and Ekram Nosratian (2015) over spatial parameters is revised and optimized. The space syntax method was developed by Hillier and Hanson, and a series of subsequent works has been applied to urban space, street networks and complex buildings (Hillier, Yang, and Turner 2012;Su et al. 2019). There are three basic concepts: convex space, axial map, and isovist field, depending on how the space is segmented (Noichan and Dewancker 2018). This research uses the convex space method to analyse the by-metro accessibility and the axis method to analyse the tometro accessibility.
The space syntax model abstracts the interrelationship of spaces into connection graphs (Hillier et al. 1976). According to the principle of graph theory, the topological analysis of the spatial accessibility of the axis or feature nodes is carried out, and a series of morphological analysis variables are derived (Li et al. 2017). Accessibility of space is measured through the concepts of integration and choice of the axis or nodes. Integration plays an important role in understanding how urban systems operate, reflecting the convenience of the movements from an origin to the destination in the system (Hillier 1998). As a result, a station with a greater integration degree in the metro network has a better chance of being chosen as a destination by passengers and a better by-metro accessibility index. Additionally, a station with a more integrated street network in its catchment area has better walkability and a better to-metro accessibility index.
According to Hillier (1998), choice value depicts the intervening spaces that must be passed between two points or nodes (Hillier 1998 regard, choice measures the through-movement potential of metro stations, which leads to a better chance of by-metro accessibility, and the ease with which a pedestrian can access/egress the station by the shortest path without too many turns, which leads to better by-metro accessibility.

Model for evaluating by-metro accessibility
The by-metro accessibility proposed in this paper is defined as the ease of passengers completing their trips among origin stations to destination stations on the metro network. As passengers usually have a vague perception of the space and distance while taking the metro, they pay more attention to the number of stations passed and the transfer experience between different lines (Li et al. 2017). Therefore, the measure is specified with the topological structure of the metro network, and the number of stations and transfers instead of actual travel distance. The convex space method of space syntax is adopted in this paper to measure by-metro accessibility. The basic principle of convex space is to divide the spatial system into the least and largest convex shapes, and each convex shape is regarded as a node. Then, based on the connection relationship between nodes, the spatial system can be transformed into a justified graph, and the syntactic variables of the spatial system can be calculated. In general, each station can be abstracted as a node, and metro lines are regarded as the connection between nodes.
To incorporate integration and choice value in the by-metro accessibility index, four significant steps are taken as follows: 1) Segregating metro station maps using ArcGIS and importing to Depthmap software.
2) Preparing convex space maps with the connection of metro stations.
3) Performing global integration analysis (Rn) to define how one node is positioned with respect to the system as a whole. 4) Determining the integration and choice values of each station (Table 1).

Model for evaluating to-metro accessibility
Although a number of different measures of tometro accessibility have been suggested, the fundamental idea of to-metro accessibility is to focus on the walking environment around the station. In this study, to-metro accessibility refers to the ease for passengers to access/egress a given station by walking. Given this definition, streets within the catchment area of metro stations are critical in assessing the to-metro accessibility, and the space syntax axis method is adopted. The axis method draws the axial map with the least and longest straight lines, and the street network can be abstracted as a relation diagram made up of the axes.
As the indicators included in the to-metro accessibility dimension are calculated for the radius for the area within a certain spatial threshold, the outcomes of the measure are, to a certain degree, affected by the accepted walking distance access/ egress to the station (Caset, Vale, and Viana 2018). Our previous research showed that 600 m is the desirable radius of walking for a pedestrian from/ to a station in Tianjin. Following Monajem and Ekram Nosratian (2015), the local metric radius (600 m) is selected to perform angular choice analysis, while 100 m is added to the catchment area size to reduce the edge effect due to cutting.
To incorporate spatial indices in the to-metro accessibility index, seven significant steps were performed as follows: 1) Gathering accurate street line data from the Baidu map.
2) Segregating gathered street maps using ArcGIS in the catchment area (700 m) of metro stations.
3) Preparing the axial map based on the segregated street maps. 4) Preparing a fewest-line map based on the axial map and processing unwanted lines if needed. 5) Creating a segment map using the fewest-line map to analyse the angular choice. 6) Performing angular choice analysis with a local metric radius (600 m) to determine the street segment quality around metro stations. 7) Determining the average integration and choice values in the catchment area (Table 1).

Accessibility-based typology
Cluster analysis is then applied to obtain classes of metro stations under the framework of node-place model. By-metro accessibility presents the node value, while to-metro accessibility presents the place value. Cluster analysis facilitates the identification of the natural segments of metro stations having common accessibility profiles. Among many clustering techniques, the present study employed the selforganizing maps (SOM) algorithm for three reasons. First, it is a powerful clustering tool that is often preferred in recent literature; second, it is more efficient for nonlinear and high-dimensional data; and third, there are no priori knowledge requirements (Delgado et al. 2017;Li et al. 2019). Different from traditional cluster methods such as K-means and hierarchical clustering offering optimum clusters based on statistical inference, this method is a type of artificial neural network inspired by how the cortical somatosensory areas are structured in the brain. With characteristics of self-organization, self-learning, fault tolerance and adaptability, the SOM has proven to be a very powerful method in terms of building typology for urban contexts (Liu, Singleton, and Arribas-Bel 2020; Qian et al. 2020).
In the SOM method, both the input layer and output layer are composed of a number of neurons, and neurons in these two layers are connected. Therefore, this study conducted an SOM analysis of two accessibility factors, namely, bymetro accessibility and to-metro accessibility, as the determinants. Then, a series of SOMs with different numbers of output neurons were trained, and the number was set to 6 (3*2), under which one neuron included similar metro stations.

Study area
The present research used the Tianjin metro network as a case study. Tianjin, located on the north coast, is one of the four main municipalities of China, with 15.6 million residents and 1,078 km 2 urban built area in 2019 (National Bureau of Statistics of China, 2020). The metro acts as the most essential component of the public transport system in Tianjin. The Tianjin metro system is China's second-oldest rapid transport system and has expanded over 30 times in terms of network length since 1984. Currently, it is a hybrid suburbancommuter rapid rail transit system with a central underground core that covers over 217 km of track serving 143 stations over 6 corridors. The  daily average passengers reached 1.2 million. Some sections of the network have been expanded to Binhai New District, a new port town. For the purpose of this study, only stations in the central urban area of Tianjin were considered (Figure 2). We identified 136 metro stations in the central urban area of Tianjin based on the metro map.
The metro network information was downloaded from Tianjin Rail Transit Group Corporation Limited. The street network data were downloaded from the Baidu map website. To measure to-metro accessibility, walkable street lines in the maps were considered sidewalks to represent the pedestrian network around stations, as shown in Figure 3. Prior to performing evaluation and categorization of metro accessibility, all indicators were checked for normality, and all relationships followed the expected directions. Simultaneously, following Suarez-Alvarez et al. (2012), all of the indicators were rescaled to values between zero and one (Suarez-Alvarez et al. 2012). The by-metro accessibility and to-metro accessibility were calculated by the average of all indicators referring to them.

By-metro accessibility evaluation
As shown in Figure 4, higher by-metro accessibility values were observed for the stations within the core urban metro network. The metro network has evolved around the central area (CBD) of Tianjin, and the centrality is clearly established when four lines formed "口" corridors. Moreover, the by-metro accessibility gradually decreases from the city centre to the periphery/suburb, evidencing the strong monocentric urban structure of Tianjin.
Spatially, transfer stations possess higher by-metro accessibility, reflecting their greater public transport accessibility, and the top six stations with the best bymetro accessibility are all transfer stations. In contrast, the terminal stations present the lowest by-metro accessibility. The by-metro accessibility of the general stations ranges widely and depends on their locations in the network and topological depth from the transfer stations. In addition, the by-metro accessibility of the stations within the metro lines 5 and 6 loop is fairly good, reflecting that a loop line will contribute greatly to an increase in the bymetro accessibility of the network, and overall, it presents a declining rating-circle structure.

To-metro accessibility evaluation
The stations within the core urban area have the highest to-metro accessibility. There are well-integrated, continuous and dense street networks around these stations, which leads to a better chance of walking to Table 2. Cluster description summary. the metro by passengers and for more activities to occur in their catchment area. Nanjing Road Pedestrian Street has played a positive role in improving the to-metro accessibility of stations around the CBD. Although there is an evident difference between city centre stations and those in the suburbs, they do not show an obvious decrease from the city centre to the suburbs like the by-metro accessibility. Then we calculate the average to-metro accessibility of all stations in each line. Metro Line 1 exhibits the highest to-metro accessibility value (0.69). With more than 30 years of operation, the infrastructure is truly good, and the street network is well connected along the corridor. Metro line 2 (0.57) and metro line 9 (0.56) are just above the average, while metro line 6 (0.53) is just below the average. Metro line 3 (0.50) and metro line 5 (0.51) present the worst to-metro accessibility values, with many undeveloped areas and a lack of pedestrian streets at the ends of these two lines.

Accessibility-based typology
The SOM cluster analysis is then applied among bymetro accessibility and to-metro accessibility combined indices. A series of SOM with different number of output neurons have been trained and the number is set to 6 (3*2), and the model identified six types of metro stations. In order to interpret the distinguishing features of these types, Table 2 reports the descriptive statistics of the two indices for each types. Figure 5 illustrates the spatial distributions of typology for the accessibility of metro stations in Tianjin. The majority of stations were in cluster 1 (29 stations), followed by cluster 5 and cluster 6 (all are 25 stations). Twenty-four stations were classified in cluster 3, and 21 stations were classified in cluster 2. Cluster 4 comprised the fewest stations (12 stations).
Stations in cluster 1 are located in the periphery of the study area and on the fingers of the metro system, comprising the lowest by-metro accessibility and tometro accessibility scores. Some stations, such as the South Railway, Xiaodian, and Nansunzhuang at the ends of metro lines possess an unplanned and undeveloped urban structure with few street networks.
Cluster 2 includes stations with medium by-metro accessibility (slightly lower than average) but low tometro accessibility. These stations located not far away from the transfer stations, but lacks adequate functional connectivity to stations by walking for local neighbourhoods. Establishing pedestrian-friendly street networks around these stations will greatly promote the accessibility of these stations.
Cluster 3 includes stations with high by-metro accessibility but medium to-metro accessibility. They lie between the inner and outer periphery of the city core and on the inner area of the metro network. The transfer stations in the periphery of the core urban area mainly belong to this type. This indicates that the density and connectivity of the street network around these stations should be improved to achieve coordinated development like cluster 6.
Stations of cluster 4 are located on the outer area of the metro network. The stations in cluster 4 have similar to-metro accessibility as those in cluster 3. While they had the lowest value of by-metro accessibility similar to cluster 1. The by-metro accessibility conditions of these stations are lower than they should be in terms of adequately matching the travel demand arising from their feature of to-metro accessibility. This requires more transportation development to meet region-driven demand.
Cluster 5 presents stations with well-balanced bymetro accessibility and to-metro accessibility. These stations lie in the periphery of the inner urban area. The station areas are characterized by well-planned street networks and proximity to metro stations. Many stations in the northern section of metro line 1 belong to this type. With more than twenty years of development, these regions have well-connected streets and good infrastructure.
Cluster 6 is analogous to cluster 5 with wellbalanced by-metro accessibility and to-metro accessibility but higher values on both by-metro accessibility and to-metro accessibility. Cluster 6 includes stations with the highest value in by-metro accessibility and tometro accessibility, and coordinated development between transport and catchment areas is realized. These stations lie in the central and historic neighbourhoods of the city and on the inner area of the metro network. Although these areas are under stress, they operate at maximum efficiency.

Accessibility optimization
The accessibility-based typologies distinguished in this study provide valuable insights for accessibility oriented development. The distinctive characteristics among accessibility-based typologies highlight that the traditional one-size-fits-all approach is inappropriate and that planners, designers and policymakers should develop a set of targeted strategies for each type. For instance, these stations in C2 and C3 are characterized by high levels of by-metro accessibility, but show lower level of to-metro accessibility. For stations in C2 and C3, strategies could therefore focus on increasing the connectivity of street network and improving walkability to match their already high by-metro accessibility. The characteristics of stations in C4, suggest a different set of strategies. Their tometro accessibility is medium, but their by-metro accessibility is relatively low, suggesting that improving the transportation supply is a more logical strategy toward much balanced situation. Although characterized by lowest both by-metro accessibility and to-metro accessibility, stations in C1 can constitute proper development in the future and should be given extra attention. For stations in C5 and C6, the existing high by-metro accessibility and to-metro accessibility provide golden opportunities for the evolution of sustainable balanced metro stations (Su et al. 2021).

Conclusion
Although there are many methods for measuring metro station accessibility, a comprehensive measure is often required in metro network planning. A single measure, either accessibility by-metro or accessibility to-metro, uncovers different aspects of the metro system characteristics, and the results are often different, which makes it hard for planners and decision-makers to draw a conclusion. With a focus on origin-destination pairs, this paper simultaneously considered by-metro accessibility and tometro accessibility and proposed a multimodal measurement to analyse the integration of metro networks and walkability access/egress to metro stations. Space syntax was used to establish models for measuring by-metro accessibility and to-metro accessibility. The paper also developed an accessibility-based typology using the node-place model and SOM algorithm to examine the relationships between by-metro accessibility and to-metro accessibility.
By-metro accessibility aims to evaluate the rationality of the metro network layout. The space convex model eliminates the impact of the space and distance and only considers the nodes. Therefore, the convex space-based analysis of integration and choice was used to evaluate the bymetro accessibility and understand how easy it is for passengers to travel from one metro station to another by the metro network. The stations in the core part of the network exhibit the highest level of by-metro accessibility, and a general decrease from the city centre to the periphery/suburb was observed. The transfer stations always possess higher by-metro accessibility, while the terminal stations have the lowest accessibility.
The to-metro accessibility addresses the first/last mile problem and focuses on examining how street networks influence walking accessibility to metro stations at the microscale. Walking is actually the most basic connection mode and the most sustainable method for accessing/egressing metro stations. The axial-based analysis was used to evaluate to-metro accessibility. It was found that a well-integrated, continuous and dense spatial configuration for the street network around metro stations is associated with increased to-metro accessibility for the station, attracting more pedestrian movement. Stations in the central and historic areas have the highest level of tometro accessibility, but they do not drop regularly from the city centre to the suburb like by-metro accessibility.
In our study, we developed and applied an SOMbased methodology under the framework of nodeplace model for the classification of metro stations in Tianjin. With the integrated measures, we generated a better understanding and representation of metro accessibility. The similar characteristics of metro stations for different clusters can potentially help policymakers develop sustainable stations by providing new strategies to balance between by-metro accessibility and to-metro accessibility for each cluster.
The study has some limitations. First, in our by-metro accessibility analysis, only the variations in network topology were considered, and other relevant variables, such as running speed and daily frequency of metro service, were not investigated. Second, the defined catchment area size may not be mutually exclusive because the buffers may overlap. Despite such weaknesses, this paper demonstrated a new and powerful methodology for evaluating and classifying the accessibility of metro stations based on the origin-destination pair and will likely be a useful framework for other cities.

Disclosure statement
No potential conflict of interest was reported by the author(s).