Development of Estimating Methodology for Transit Accessibility Using Smart Card Data

Abstract

Transit accessibility is an explanatory variable evaluating the mobility of a region in consideration of the connectivity and demand among the regions, which has been used for an important index to determine transport policy on the transit network. This study aims to develop an accessibility index considering the two factors with a demand-weighted approach, that is, impedance and attraction level. Two variables, travel time and the ratio of trips, are employed to calculate the accessibility index, and comparative assessments between zones are conducted. The application of smart card data makes it possible to analyze travel information and reflect them empirically in the model. This study identifies zones with vulnerable accessibility and suggests criteria for transit investment plans with two aspects, that is, intensive transit area and spatial distribution of the accessibility index. These aspects contribute to transit planners by suggesting transit investment criteria and comprehensible statistics to evaluate accessibility. Since zones with low accessibility indexes are identified as being vulnerable to access from other zones, policymakers should focus on those zones to improve the overall transit network.

As the demand for public transportation has increased, the concept of transit accessibility has attracted scholarly attention in recent years. In the public transportation field, the accessibility index has been used as an important explanatory variable that can evaluate and quantify the level of service. Accessible transit service has a positive impact on regional development and provides opportunities for people to access social activities ( 1 ). These significant features encourage transportation planners to implement the concept of accessibility into policy implications. Despite several public transportation investments to supplement accessibility, problems of low accessibility are notably found in district areas. Since investments have been focused on the efficiency of cost and benefit in the construction of infrastructure, an imbalance concerning accessibility has arisen among various regions, with public transportation being developed more in some regions, while other underdeveloped regions being marginalized. Regardless of the various accessibility evaluation models, there are still limitations associated with applying them concerning transport policy.

Thus, many studies have been conducted to analyze transit accessibility precisely. The two commonly considered factors in the evaluation of accessibility are impedance and the level of attraction. Impedance is a factor that is reflected as the constraint of the accessibility value. Travel time is often an important determinant in reflecting the accessibility evaluation model ( 2 ). Attraction level is a factor that represents the land use characteristics of the region being analyzed, and the trips commonly reflect it. An accessible transit network is a network with low impedances for using transit to a destination with a high attraction level ( 3 ). Both impedance and attraction level should be properly considered for an efficient accessibility measure ( 4 ). Previous studies have been performed on a time-based approach by measuring transit accessibility based on the passengers’ travel time between the origin and the destination (OD) ( 5 – 8 ). However, limitations often arise in the explanatory power of the measure when the evaluation of accessibility is limited to travel time impedance. A region with good accessibility may be defined as having a short travel time from one analysis region to another. Another major problem arises when the total trips simply are implied as attraction level because economically developed areas are unconditionally overestimated with a high value of the accessibility measure. It is reasonable to consider travel patterns of OD pairs and reflect the weight of destinations with higher demand.

When travel time is applied as the impedance factor, the travel time should be calculated precisely for the performance measure. The trips should be measured accurately as well, to be applied as the level of attraction ( 9 ). The lack of detailed transit schedule information has limited scholars from measuring accurate time- and demand-dependent accessibility measures; therefore, the estimated travel time and demand were applied to measure accessibility ( 3 ). With the development of the automatic fare collection (AFC) system, it is possible to evaluate transit accessibility by reflecting actual travel information of transit. The travel data provided by the smart card makes it possible to consider the factors of impedance and attraction level empirically and to micro-analyze the travel patterns reflected in the accessibility measure.

In this study, an index that considers both impedance and attraction level is developed to accurately evaluate transit accessibility. The intention is to use travel time as the impedance factor and the trips as the attraction level of accessibility. To compensate for the aforementioned limitations, an index that involves the demand-weighted approach is proposed, as the ratio of the trips calculated by the trips between OD regions, and the total trips in a region is applied as attraction level, further described in the Methods section. Travel time and the trips are calculated accurately using smart card data, as empirical travel information is applied as impedance and attraction level. Accessibility indexes are developed for each zone, which is a regional division separated by local governments for management efficiency. After that, the calculated accessibility indexes were analyzed based on two perspectives, that is, the intensive transit area (ITA) and the spatial distribution. The implication of these aspects is expected to evaluate transit accessibility and suggest criteria for transit investment plans.

The next section presents the overview of previous measures of accessibility and the use of smart card data to evaluate the transit system. The section after that consists of a description of the data, the study network, and the methodology that was developed and used in this study. The penultimate section discusses the result of the accessibility index and the analysis of some representative zones. The final section summarizes the conclusions of this study and provides some suggestions for future research.

Literature Review

The definition of accessibility in the transportation system varies depending on the purpose of the research. Generally, the predominant definition of accessibility has been the definition proposed by Hansen, that is, “the potential of opportunities which an individual at a given location possesses for an interaction or activity,” where a basic gravity model with the reflection of attraction levels of regions was suggested ( 10 ).

Researchers have defined accessibility to public transportation in various ways as represented by the following: that is, “how easy it is to access public transportation facilities,”“how easy it is to travel to the desired destination,” and the “degree of service opportunity during the trip” ( 11 ). In addition, accessibility has been defined as “the ease with which any land-use activity can be reached from a location using a particular transport system,” or opportunities perceived by an individual for satisfying their needs at certain areas ( 12 – 15 ). One study applied an opportunity-based transit accessibility measure that is sensitive to the availability of opportunities for travelers ( 9 ). Some literature has suggested accessibility measures with a socially equitable aspect, and public transit supply has been measured by its frequency and access distance ( 16 , 17 ). The concept of accessibility has been disputed, although it is clear that the fundamental goals are to evaluate transit services.

Travel time has been used as the kernel determinant of the accessibility measure in various publications. One study measured accessibility indexes using door-to-door travel time between OD pairs, and another analyzed the disparity of accessibility between different travel modes with travel time ( 5 , 18 ). Fu and Xin proposed a public transit accessibility model called Transit Service Indicator (TSI), which can be used to evaluate the quality of service of a transit system based on travel time ( 6 ). Some studies have developed an accessibility analysis on a GIS data structure, considering travel time ( 8 , 11 ). Other research generated a new measure of accessibility with travel time and transit fares as constraints ( 19 ). Then, the calculated accessibility measures were analyzed to determine whether accessibility is experienced equitably by different social groups. A study measured transit accessibility concerning time dimension about the number of trips that have been exposed to transit services. Then, the time-of-day distribution of the number of trips was used to evaluate the efficiency of transit services provided during each period of the day ( 7 ). Another study suggested an accessibility evaluation model on a road network with a standard travel time of a given roadway as an impedance factor ( 20 ).

With the introduction of the AFC system, personal transit information has been collected, which facilitated the analysis of ridership statistics on a precise time scale ( 21 ). Almost all public transportation boarding and alighting data have been collected with the smart card, allowing researchers to access travel time, the number of trips, and travel patterns ( 22 ). Various studies have used smart card data to assess transit records and networks. One study used smart card data to analyze passengers’ travel patterns using transit travel time. Another analyzed transit competitiveness with autos, where transit travel time was obtained through smart card data ( 23 , 24 ). Another study proposed a model for evaluating the coverage area of transit centers. The trips and the travel time were calculated with smart card data, and the results were used in the development of the coverage area index ( 25 ).

This research contributes to: 1) developing an index of transit accessibility considering impedance and attraction level; 2) applying for actual transit passengers’ travel information collected through smart card data; and 3) implementing suggestions for transport policies to build a sustainable transit network.

Methods

The summary of the overall methodology developed in this study is described in Figure 1, which consists of two parts: development of the accessibility index and the elaboration of the accessibility index with ITA and spatial distribution.

Figure 1.

The overall workflow of this study.

Development of the Accessibility Index

Two factors were considered in the accessibility evaluation model, that is, impedance and the level of attraction. Impedance is reflected as the average travel time between OD pairs. The attraction level is reflected by calculating the ratio of the trips between OD pairs and the total trips. As described above, if the weight is applied only at the absolute amount of generated trips in the origin zone, the accessibility of zones with active economic activity may be overestimated. The consideration of the frequency of OD travel may be excluded. The accessibility measure proposed by Hansen considered attraction level with the absolute amount of generated trips, and it is calculated, as shown below (10):

A_{ij} = \frac{S_{j}}{T_{ij}^{x}}

where

$A_{ij}$ is the measure of accessibility at zone i to an activity located within zone j;

$S_{j}$ is the size of activity in zone j, that is, the number of employees, population, or number of trips;

$T_{ij}$ is the travel time or distance between zone i and zone j; and

x is the scale factor.

The accessibility measure suggested by Allen et al. has considered the travel time of the roadway as the impedance factor. The accessibility measure proposed by Allen et al. is calculated as shown below:

A_{i}^{'} = \frac{1}{(N - 1)} \sum_{\begin{matrix} j = 1 \\ j \neq 1 \end{matrix}}^{N} a_{ij}, i = 1, 2, \dots, N

where

$A_{i}^{'}$ is the accessibility index of location i;

$a_{ij}$ is the travel time between locations i and j;

N is the number of zones; and

E is the normalized integration of $A_{i}^{'}$ over location i.

Therefore, in this approach, the larger the value of the index becomes, the lower the accessibility becomes; and the smaller the value of the index becomes, the higher the accessibility becomes.

An accessibility evaluation model was developed, based on Allen et al. and Hansen’s related work with consideration of impedance and attraction level to overcome the limitations of the previous literature. The accessibility index proposed in this study is presented in Equation 1:

A I_{i} = k \cdot \frac{1}{(n - 1)} (\sum_{j = 1, i \neq j}^{n} \frac{1}{T_{ij}} \cdot \frac{D_{ij}}{D_{i}} + \sum_{j = 1, i \neq j}^{n} \frac{1}{T_{ji}} \cdot \frac{D_{ji}}{D_{j}})

(1)

where

i and $j$ are the zones;

$A I_{i}$ is accessibility index of zone i;

$n$ is the number of zones;

$T_{ij}$ is the average travel time from zone i to j;

$T_{ji}$ is the average travel time from zone j to $i$ ;

$D_{i}$ and $D_{j}$ are the total number of trips that occurred in zones i and j, respectively;

$D_{ij}$ is the number of trips that occurred from zone i to j;

$D_{ji}$ is the number of trips that occurred from zone j to $i$ ; and

$k$ is an arbitrary scale factor.

A sample network is illustrated in Figure 2. The accessibility of zone A of the sample network in Figure 2 is calculated as:

$A I_{A} =$ 100 × $\frac{1}{3} \times (\frac{1}{18} \cdot \frac{12}{32} + \frac{1}{15} \cdot \frac{15}{32} + \frac{1}{45} \cdot \frac{5}{32} + \frac{1}{20} \cdot \frac{10}{27} + \frac{1}{25} \cdot \frac{10}{45} + \frac{1}{40} \cdot \frac{8}{23}) = 3.06$ ;

$A I_{B} = 2.64$ ;

$A I_{C} = 3.33$ ; and

$A I_{D} = 2.00$ .

The values of $A I_{i}$ are compared to identify which zones have accessible public transit. Since zones B and D have relatively small accessibility indexes, it is necessary to focus on those zones to improve transit accessibility by connecting the transit network.

Figure 2.

An example of calculating accessibility index.

Elaboration of the Accessibility Index with ITA and Spatial Distribution

The developed accessibility index is interpreted on the basis of two analyses. The first perspective is identifying the ITA. ITA is defined as “destination zones with the high demand of trips from origin zone.” When the ITA analysis is integrated with the developed accessibility index, it is possible to elaborate the reflected weight of zones with the high demand of trips. In other words, considerations can be conducted on zones that transit users frequently travel. The second perspective is interpreting the spatial distribution of the developed accessibility index. The spatial distribution is defined as “the degree to which the accessibility of an area is composed of distance.” A criterion of whether accessibility improvements should be applied at a local or regional level is suggested with the spatial distribution. Furthermore, it is possible to analyze zones with similar accessibility values in different perspective strategies or transport policies.

Cumulative percentage curves were generated to explain the above two perspectives. To analyze ITA, the following procedure is applied: (i) zones are arranged in descending order of generated trips $D_{ij}$ ; and (ii) the cumulative percentage of the number of generated trips $D_{ij}$ is calculated. A similar process is also applied for the assessment of the spatial distribution of the accessibility index. As defined in Equation 1, the accessibility index $A I_{i}$ is calculated as the sum of multiple index values between i and j. The index value between zone i and j, $(\frac{1}{T_{ij}} \cdot \frac{D_{ij}}{D_{i}} + \frac{1}{T_{ji}} \cdot \frac{D_{ji}}{D_{j}})$ , is considered as sub-index values. To consider spatial distribution, the following procedure is applied: (i) the zones j are sorted in the distance from zone i in ascending order; and (ii) the cumulative percentage of the sub-index values between i and j is calculated. Now the following question remains: by which attribute of the calculated cumulative percentage is it possible to identify the disparity of characteristics of each zone? To accomplish the matter, the Kneedle algorithm was utilized to find the knee point of each curvature. The knee point—the point where the curve visibly bends—can represent the analysis benchmark to identify the attributes for change in the spatial distribution or generated trips. The Kneedle algorithm developed by Satopää et al. can be used to determine knee points in discrete data based on the mathematical definition of curvature shown in Equation 2 ( 26 ):

K_{f} (x) = \frac{f ″ (x)}{{(1 + f' {(x)}^{2})}^{1.5}}

(2)

where

$K_{f} (x)$ is the curvature of the given equation $f (x)$ .

For discrete data sets, the detection of the knee point is done by the following procedures: (i) a threshold value is decided for the data points; (ii) a line is drawn from the first point ( $x_{min,} y_{\min}$ ) to the last point ( $x_{max,} y_{\max}$ ) of the curve; (iii) the point with the largest distance from the line is chosen as the knee point. Considering the transit characteristics, the travel time from the origin zone to the far-distant zones is inevitably large. With the same approach, the demand for trips from the origin zone to the far-distant zones is comparatively small. Therefore, with a statistical approach, a 95% cumulative percentage was considered the threshold value of the knee point detection ( 27 , 28 ).

Figure 3a illustrates the detection of knee points for identifying ITA. The knee point of the cumulative percentage curve of generated trips is defined as $\emptyset$ . Zones located to the left-hand side of the knee point $\emptyset$ are defined as ITA. Figure 3b illustrates the detection of knee points for interpreting the spatial distribution of the accessibility index. The cumulative percentage of the detected knee point is defined as $α$ . An additional knee point was further analyzed to interpret the spatial distribution in a comprehensible range. The additional knee point is detected by applying the first knee point as the threshold value of the Kneedle algorithm, and the cumulative percentage of the additional knee point is defined as $β$ .

Figure 3.

(a) Determining the knee point for intensive transit areas (ITA) analysis, and (b) determining the knee point utilized in the interpretation of the spatial distribution.

Jenks’ Natural Breaks

Jenks’ natural breaks classification theory is used to determine arrangements of the calculated accessibility index. The calculated accessibility index values are classified into three groups, that is, high accessibility index, medium accessibility index, and low accessibility index. Classifications are made by repeatedly comparing sums of the squared difference between observed accessibility indexes within each group and group means ( 29 ). The mean deviation is minimized based on the average of all of the accessibility indexes in the same group, and the variance between each group is maximized. Jenks’ natural breaks make it possible to reduce the variance within the group while maximizing the variance between groups and creating choropleth maps that reflect the accurate representations of trends in the accessibility index. Applying the natural breaks method makes it possible to optimize classification based on the quantifiable homogeneity and cluster concept in statistics, as it is distinguished as vulnerable and developed zones. The mathematical expressions of Jenks’ natural breaks classification are shown in Equation 3:

SS D_{i \dots j} = \sum_{k = i}^{j} A {[k]}^{2} - \frac{{(\sum_{k = i}^{j} A [k])}^{2}}{(j - i + 1)}, 1 \leq i < j \leq N

(3)

where

i, j, and N are the normalized class bounds of the developed accessibility index;

SSD is the sum of the squared difference; and

A is the set of normalized accessibility indexes ordered from 1 to N.

Data Description

Description of the Network

As a result of analyzing the public transportation smart card data in Seoul, it was found that a total of 20.98 million trips were taken on the subway and buses on May 17, 2017. The scope of the study only includes trips that occurred inside the Seoul metropolitan area; thus, a total of 9,912,275 trips were extracted based on the boarding and alighting stations recorded on the smart card. The two fundamental transportation modes of public transportation in Seoul—which are intra-city bus and subway—were analyzed in this study. About 3.19, 4.42, and 2.30 million trips were analyzed as bus, subway, and subway and bus trips, respectively. The average travel time was calculated to be 25.31, 15.20, 29.14, and 32.56 min for total, bus, subway, and subway and bus trips, respectively. The average travel time and the standard deviation of travel time of bus trips were relatively small compared with trips using subways, since the average travel distance of subway trips is comparatively longer than the average travel distance of bus trips.

In Seoul, 361 intra-city bus lines and 23 subway lines connect 46,356 bus stations and 324 subway stations. For this study, the network of Seoul was classified into 421 zones. These zones were classified based on the appropriate size and population for convenience and administrative efficiency. The numbers of bus stations and subway stations vary between zones. The zones with the largest and smallest number of bus stations are Gasan-Dong and Dong-Wha Dong, respectively, with 515 and 4 bus stations, respectively. The zones with the largest number of subway stations are Yeoido-Dong and Jongro-1.2.3.4 Dong, both of which have 8 subway stations. Not all zones have subway stations, and there are 140 zones that do not have subway stations in their district. The basic statistics of public transportation in Seoul are described in Table 1.

Table 1.

Basic Statistics of Public Transportation in the City of Seoul

Division	Attributes classified by travel modes
Division	All	Bus	Subway	Subway and bus
Trips information
Number of trips	9,912,275 (100%)	3,190,073 (32%)	4,424,322 (45%)	2,297,880 (23%)
Average travel time per trip (minutes)	25.31	15.20	29.14	32.56
Standard deviation of travel time per trip (minutes)	22.17	12.02	26.19	19.12
Network information
Number of zones			421
Number of intra-city bus lines			361
Number of bus stations			46,356
Number of subway lines			23
Number of subway stations			324
The average number of bus stations in a zone			110.11
The average number of subway stations in a zone			0.84

Data Preprocessing

Since 2004, an AFC system based on the use of smart cards has been operating in Seoul. With the AFC system, 20 million bits of personal transit information per day are collected through smart card data, which covers 99% of the passengers who use public transportation. The smart card data consist of records of boarding and alighting stations along with their usage time, which allows the calculation of the number of trips and total travel time.

The passengers’ waiting time between one mode of transportation and another was estimated from the boarding time tagged in the smart card ( 22 ). Some records of the smart card were connected in a trip chain, as multiple transfers are possible during trips. The card ID and OD were found, to make the transfer data into a single trip chain. The transit systems of Seoul allow free transfers for trips made within 30 min. Therefore, ID card information boarded and disembarked within 30 min were sorted and made into a chain with a single OD pair, and the travel time of each trip was added as the total travel time. The boarding and alighting stations provided by the smart card made it possible to aggregate trips in zonal units.

This study was focused on evaluating how convenient it is to travel from one zone to another. Therefore, trips that occurred inside a single zone were removed from the dataset. The process of generating a trip chain with smart card data is described in Figure 4.

Figure 4.

Data preprocessing: (a) description of the workflow, and (b) description of generating a trip chain with smart card data.

Results

Results of Developed Accessibility Indexes

The proposed methodology was applied to 421 zones in Seoul, and each accessibility index was developed. The scale factor k was set as 10,000 to calculate the accessibility index of this study. The developed accessibility index of 421 zones ranged from 1.73 < $A I_{i}$ < 15.50, and the average value of the accessibility index was calculated and found to be 4.34. The 421 zones were classified into three groups with the Jenks’ natural breaks classification. Among Seoul’s 421 zones, 240 zones fell into the first area range of 1.7 < $A I_{i}$ ≤ 4.2, 156 zones fell into the second range of 4.2 < $A I_{i}$ ≤ 7.1, and 25 zones fell into the third range of 7.1 < $A I_{i}$ ≤ 15.5.

Six representative zones were selected for analysis to analyze the locally distributed trends of accessibility indexes. These zones were labeled from 1 to 6, as illustrated in Figure 5a. The zones with the highest accessibility index, the medium accessibility index, the lowest accessibility index, and each zone from the three major districts of Seoul were selected for sample analysis. The three major districts of Seoul are the Central Business District (CBD), the Yeoido Business District (YBD), and the Gangnam District (GD). The CBD district is currently becoming the center of finance of Seoul through urban redevelopment. The CBD area is the central area of transit, which includes Seoul Station and Seoul City Hall Station, where transit gathers and spreads rapidly. YBD is the business district where the financial industry is concentrated, leading to concentrated business trips. The GD area includes Gangnam Station, Samseong Station, and Gangnam-daero, where the floating population is very large. Samsung Station has developed as the center of global business through the trade center, and Gangnam-daero has been activated to facilitate the inflow and outflow of bus transits resulting from the development of the regional bus transportation network. Subway Line 2 spans the entire GD area, and, with the extension of Subway Line 9 to penetrate GD, two major subway lines are connected to GD, facilitating inflow and outflow of transits.

Figure 5.

Analysis results: (a) zones classified by the developed accessibility index, (b) zones classified by the number of generated trips, (c) zones classified by the number of attracted trips, (d) zones classified by the developed accessibility index by Hansen, and (e) zones classified by the developed accessibility index by Allen et al.

The developed accessibility index indicates the various distribution of accessibility index over zones in Seoul, and comparisons between zones were performed. The zone labeled 1 is Changsin-2 Dong, and it has the highest accessibility index, that is, 15.50. Changsin-2 Dong is located in the CBD district, and the average travel times, that is, $T_{ij}$ and $T_{ji}$ , were calculated and found to be 34.57 and 41.14 min, respectively, which is comparatively small compared with other zones. The zone labeled 2 is Naksungdae Dong, which was calculated to have an accessibility index of 4.80, which is a relatively average value. The average travel times, that is, $T_{ij}$ and $T_{ji}$ , of Naksungdae Dong, were calculated to be 47.41 and 47.46 min, respectively. The zone labeled 3 is Naegok Dong, which had the lowest accessibility index of 1.73. The average travel time from Naegok Dong to other zones was calculated to be 56.89 min. Thus, it takes a considerable amount of time to travel from Naegok Dong to another location, which had a critical impact on the result of the low accessibility index. The zones labeled 4, 5, and 6 are Jongro-1.2.3.4 Dong, Yeoi Dong, and Yeok-Sam 1 Dong, each from CBD, YBD, and GD, respectively. These zones were analyzed to have high accessibility indexes because they are located in the three major districts with developed transit networks. Analyzed statistics and regional characteristics are described in Table 2. The figures of the accessibility indexes, along with generated and attracted trips of each zone, are shown in Figure 5.

Table 2.

Description of Statistics and Regional Characteristics of Representative Zones

Division	1	2	3	4	5	6
Statics of representative zones
Zone	Changsin-2	Naksungdae	Naegok	Jongro-1.2.3.4	Yeoi	Yeok-Sam1
Characteristics	Highest AI	Average AI	Lowest AI	CBD	YBD	GD
AI value	15.50	4.80	1.73	10.87	8.42	9.10
Average travel time $(T_{ij})$ (minutes)	34.57	47.41	56.89	37.17	41.13	42.99
Average travel time $(T_{ji})$ (minutes)	41.14	47.46	54.45	35.01	38.77	41.53
Number of generated trips $(D_{i})$	460	11,078	16,021	226,003	163,248	255,445
Number of attracted trips $(D_{j})$	1,290	25,431	9,420	206,494	168,244	239,120
The average number of trips $(D_{ij})$	5.68	33.07	42.38	538.10	389.61	608.20
The average number of trips $(D_{ji})$	8.38	79.47	25.95	491.65	401.54	572.06
Number of bus stops/subway station	17/0	128/0	246/2	298/8	287/8	147/6
Statics of ITA
Number of ITA	9	51	60	130	107	96
Average distance between ITA (km)	2.32	10.16	13.34	6.33	12.51	7.84
Average travel time to ITA (minutes)	19.11	45.35	52.48	26.37	40.81	37.39
SD of travel time to ITA (minutes)	14.83	10.20	8.42	9.80	13.10	8.98

Note: AI = accessibility index; CBD = Central Business District; GD = Gangnam District; ITA = intensive transit areas; SD = standard deviation; YBD = Yeoido Business District.

Evaluation of Index Performance

To validate the improvements of the proposed accessibility index of this study, the results of the developed accessibility indexes were compared with accessibility indexes proposed by Hansen and Allen et al. ( 10 , 20 ). To apply the accessibility index by Hansen, the size of the activity in zone j, defined as $S_{j}$ , was determined as the generated trips in zone j. The remaining parameters of the accessibility index were applied as the values used to create the accessibility index suggested in this study. Zones were classified into three groups with the Jenks’ natural breaks classification, shown in Figure 5, d and e .

Previous accessibility indexes focused on the convenience of using transit systems in an origin-based aspect, limited to the consideration of travel time from origin zone i to destination zone j. However, accessibility is a measure evaluating the mobility of a region in consideration of the connectivity among the regions. Therefore, a zone with high accessibility should take into consideration travel time originating from other zones. Furthermore, consideration of the weighted-demand of trips between zones remains elusive.

The trips from origin to each destination were distributed differently, as the demand for some destination zones was concentrated. Therefore, overestimation of accessibility occurs when at the absolute amount of generated trips is considered. These limitations result in high accessibility zones becoming centralized; limited statistics are provided to evaluate accessibility between geographically similar located regions.

The distinctions of this study can be validated with the graphical results. The zones classified by previous literature both show patterns of high accessibility index along the centroid. Since zones located in the centroid have the geometrical advantage of small travel time to another zone, this is an expected result. The accessibility index of this study can reflect the travel patterns of transit users microscopically with a demand-weighted approach. The proposed demand-weighted approach can compensate for the overestimation of accessibility in economically developed areas. In other words, the accessibility index of this study is considering actual demand-weighted travel patterns, which provides the advantage of a clear distinction between adjacent zones and the overall distribution of accessibility.

Interpretation of Indexes with ITA

The concept of ITA was suggested to analyze the distribution of accessibility indexes and their characteristics. The knee point $\emptyset$ can identify ITA—destination zones with the high demand of trips from origin zone. The analysis of ITA and the developed accessibility index have a complementary relationship, as the statistics of ITA can verify the validity of the calculated accessibility index. The index is influenced heavily by zones with a high demand of trips. The trips from origin to each destination were distributed differently, as the demand for some destination zones was concentrated. A zone with a larger travel time to another zone with a high demand of trips indicates that practical accessibility is low. No matter how well the public transportation network is established between all other zones, the accessibility between zones with high trips will need consideration. Conversely, even if the accessibility to all other regions is relatively low, shorter travel time between zones with the high demand of trips indicates that accessibility is still superior.

As travel time was the impedance factor, a clear association was shown between travel time and the accessibility index of each zone. However, the other basic statistics of zones, for example, generated trips, attracted trips, bus stations, and the number of subway stations, did not seem to have a clear, easily identifiable association with the developed index. The average distance and travel time between the proposed ITA showed correlations with the developed accessibility index. As the average distance and travel time between ITA increases, the values of the proposed accessibility index tend to decrease. These characteristics were considered in accordance with the definition of accessibility between zones, as destinations with intensive transit demand should be well reflected in the evaluation of accessibility. The zone labeled 1 or other zones in the CBD, YBD, and GD reflected these ITA trends.

The ITA analysis approved that the zonal characteristics of the network and the actual travel patterns were well reflected through empirical demand weighting. The results indicated that the accessibility indexes were not concentrated in the center of Seoul; rather, they were distributed, which was different from the previous indexes that were calculated high along the centroid.

Spatial Distribution Analysis

By interpreting the spatial distribution of the accessibility index, exploratory spatial data can be derived, which can contribute to transit planners presenting criteria for improving the accessibility of zones. If the knee point $α$ of the curve is detected in a zone with small distance from the origin zone, this indicates that the accessibility distribution of the origin zone is at a regional level. The knee point β is the point where accessibility of a zone is accumulated by distant zones, which can indicate the spatial extent of the origin zones’ accessibility.

With the application of spatial distribution analysis, a criterion of whether accessibility improvements should be applied at a local level or a regional level is suggested. Even for zones with the same accessibility value, the policy direction for improvement will be different according to the spatial distribution characteristics of each zone. Two zones with an equal accessibility index are considered. The zones in which the accessibility index can be improved through a local level of investment have more efficiency and higher priority in investments than zones where the accessibility index can be improved through a regional level of investments. In other words, $α$ and β values make it possible to prioritize transportation investment plans. Categorizing by the scalability of accessibility improvement policies, zones with low accessibility were classified into three groups according to the $α$ and β values. Since the analysis may be distorted according to the zonal size, the β-α value was calculated. The two cases in which β-α is calculated small—that is, both alpha and beta are small—and both alpha and beta are large were classified through data analysis. To present criteria for zones with low accessibility indexes, three representative zones with low accessibility, in the range of 1.7 < $A I_{i}$ ≤ 4.2, were analyzed.

Zone A consists of small $α$ and β values, with 1.98, 0.57, and 0.77 for accessibility index, $α$ , and β, respectively. Zone A is an example of a zone that can be improved efficiently at a local investment level, which is expected to be improved within a relatively short time and a small budget. Zone B is composed of small $α$ value and large β value, which is an example of a zone that can be improved efficiently to the zones within $α$ , but they require larger investments to improve zones that make up to β. Zone B has an accessibility index of 2.55, and $α$ and β values of 0.47 and 0.88. When transit investment plans are applied to zones similar to Zone B—that is, small $α$ value and large β value—local levels of investment should be prioritized over regional investment plans. Zone C is an example of a zone with large $α$ and β values. Zone C is expected to require large-scale transit investigation plans, as there is a need to improve accessibility distributed to remote zones. Zone C is composed of $α$ and β values of 0.86 and 0.94, respectively. The accessibility index of Zone C was calculated to be 2.13, as improvements for transit services are expected. It is necessary to consider the objectives and effects of the investment more carefully when making decisions for investments of Zone C. Whereas, considering the equity of transit services among areas, improvements in transit services of Zone C are needed. The $α$ and β values of Zone A, Zone B, and Zone C are described in Table 3, and the visualization of $α$ and $β$ values of zones are shown in Figure 6.

Table 3.

$α$ and $β$ Values of Representative Zones

Zone	A	B	C
Name	Chunho3	Euljiro	Gayang3
Characteristics	Small $α$ and β	Small $α$ and large β	Large $α$ and β
AI value	1.98	2.55	2.13
$α$	0.57	0.47	0.86
β	0.77	0.88	0.94

Note: AI = accessibility index.

Figure 6.

Results of spatial distribution: (a) 3D scatter plot of accessibility index, $α,$ and $β$ , (b) zones classified by $α$ , and (c) zones classified by $β - α$ .

Policy Implications

The proposed accessibility index contributes to identifying the vulnerable and developed areas of transit services. Zones with low accessibility are preferential zones that need transit investment plans. The ITA are zones that investors must consider along with the accessibility values. ITA should be considered primarily because enhancements of transits in zones with higher travel demand can benefit multiple passengers. The spatial distribution analysis suggests a criterion for investment plans based on the $α$ and $β$ values of zones.

Local investment plans are applied to zones with a small average distance to ITA or zones with small $α$ and $β$ values. By analyzing the overall trend of accessibility indexes, zones in which the subway stations are located have high accessibility values. As the subway is a major part of the transit system, it relates directly to accessibility. Therefore, the introduction of feeder buses and personal mobility services to enhance connectivity with the subway system are an example of a local investment plan. Providing efficient first- and last-mile services by reinforcing connectivity with the subway will enhance accessibility.

Moreover, regional investment plans should be applied for zones with large $α$ and $β$ values, many ITA, or a large average distance to ITA. Demand responsive transits (DRT) could be one solution to enhance accessibility in regional units. Since urban DRT differs from DRT designed for complementary use in suburban areas, urban DRT lines are designed by connecting zones with low accessibility and travel demand, covering long-distance round trips. Planning new bus lines or urban DRT services should consider the demand for round trips. In the accessibility index developed in this study, both generated and attracted trips of zones are considered. The proposed accessibility index can consider both round trips; therefore, the proposed index can perform as an indicator of proper service areas for bus lines or urban DRT services.

Conclusion

This research addressed a transit accessibility index that responds to two major factors, that is, impedance and the attraction level. The impedance factor was reflected with the average travel time between zones. To prevent the attraction level from being overestimated in the developed zones, the ratio of the trips calculated by the trips between OD zones and the total trips in a zone was used to represent the attraction level. The travel time and trips were calculated empirically with the application of smart card data. Then, the proposed accessibility index of each zone was calculated. ITA analysis and spatial distribution analysis were performed to analyze the developed accessibility index. With the suggested concepts, this study presents a criterion for establishing transit investment plans. The zones with low accessibility indexes are classified into three groups representing the priority of transit investment plans.

The ITA analysis indicated that destinations with intensive trips were well reflected in the developed accessibility index. Moreover, the results of the weighting of the empirical demand show that the developed accessibility, as the index, was well distributed and spread among the Seoul Metropolitan Area. The proposed accessibility index can reliably identify accessible and inaccessible zones because these indexes can be managed to identify areas in which transit improvements are needed the most. The spatial distribution analysis of the accessibility index suggested criteria for public transit investment plans. With the analysis of the spatial distribution, it was identified whether zones required local or regional investments. The $α$ and β values of the spatial distribution are capable of suggesting investment priorities for zones with similar accessibility indexes.

The proposed accessibility index can be applied to different metropolitan areas to identify priority areas for the development or enhancement of public transport. Other transit systems from metropolitan areas which lack alighting data can also apply this methodology by incorporating deduction of alighting information. Future research should consider detailed investment plans to improve transit services for zones with low accessibility. Currently, the accessibility index of this study considers the total travel time of a trip chain. However, a trip chain contains various attributes, for example, transfer time, walking time, and waiting time. In cases when these attributes are embedded in the trip chain, these parameters can be utilized to expand the suggested methodology and refine the attractiveness of the zones.

Footnotes

Author Contributions

The authors confirm contribution to the paper as follows: study conception and design: H. Yun, E. H. Lee, D.-K. Kim, S.-H. Cho; data collection: H. Yun; analysis and interpretation of results: H. Yun, E. H. Lee, D.-K. Kim, S.-H. Cho; draft manuscript preparation: H. Yun, S. -H. Cho. All authors reviewed the results and approved the final version of the manuscript.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was supported by South Korea Ministry of Land, Infrastructure, and Transport (MOLIT) as Innovative Talent Education Program for Smart City.

ORCID iDs

Hyunsoo Yun

Eun Hak Lee

Dong-Kyu Kim

Shin-Hyung Cho

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