Machine identification method of subway service quality based on smart card data

Abstract

A new automatic evaluation method of subway service quality based on metro smart card data is proposed suitable for three different levels: station pair, railway line and subway network, which has merits of overcoming the previous lagging and subjective evaluation in the system of ‘questionnaire survey plus evaluation method’. First, passengers' travel time distribution for different operating periods in station OD pairs are introduced initially for service evaluation purposes and are classified into different groups in order to infer the station's operating characteristics at the different periods. Second, the classification is verified by K-means cluster analysis and K-S tests. Third, the service quality weight indicator is proposed to identify the service quality of the entire metro network from the dual perspectives of passengers and companies. Finally, the feasibility and rationality of the proposed method are verified by Shenzhen metro smart card data as an example. The new automated evaluation method of subway service quality is suitable for online and offline application.

Highlights

• A new machine identification method based on travel time distribution is proposed for estimating the service quality.

• The proposed model employs the K-means clustering method to distinguish passenger's travel time distribution into different modes.

• Characteristics of the different modes of passenger travel time distribution reflect different service levels of the urban subway system.

• The method provides automatically identification of service levels for urban subway operations.

1. Introduction

In order to attract more subway passengers and to improve the competitiveness of the subway with other modes of transportation, subway operation companies all over the world pay attention to passengers’ travel experiences as well as railway operation safety. In the ‘Urban Rail Transit Service Quality Evaluation Specification’ issued by the Ministry of Transport of the People's Republic of China in April 2019, the urban rail transit service quality evaluation includes the evaluation of passenger satisfaction, service guarantee capabilities and key indicators of operational services. For detailed investigation, the main methods of passenger satisfaction evaluation are face-to-face survey, internet survey and telephone survey, etc. The main methods for evaluating the service guarantee capability are field experience, information review, data retrieval and on-site testing, etc. Although the evaluation of key indicators of operational services is directly obtained through the intelligent management system, it didn't implement an automated evaluation method that satisfies passengers. Moreover, two-thirds of the evaluation indicators will be affected by subjective factors and the previous two evaluation methods are based on questionnaires which are not only time-consuming and labour-intensive, but also have the subjective influence of the evaluation participants on the evaluation results.

The current subway service quality evaluation is mainly based on the needs and perceptions of passengers [1], combining expert evaluation method [2], analytic hierarchy process [3], fuzzy gradient number analysis method [4], the house of quality analysis method [5] and other qualitative and quantitative methods. To further improve the identification quality of subway services, it is urgent to propose an identification method that relies on scientific analysis of objective data and effective intelligent machine identification models to improve the objectivity and automation level of evaluation of subway services.

With the increasing popularity of public smart transportation cards, a large amount of travel data have been generated in the smart transportation system while passengers make trips. In a general way, travel data include IC card entry and exit records of subway stations, including card number, inbound credit card time, inbound site, outbound credit card time, payment information and outbound site, etc. As early as 1995, Attoh-Okine and Shen [6] analysed payment information by data of the traffic smart card and found that the use of smart card payment can reduce the level of passenger cost perception. Therefore, public transportation operators are increasingly promoting and encouraging the use of smart traffic cards. Reddy et al. [7] found that daily operational performance monitoring can be effectively and quickly realized by smart card data. Thus, the smart card data have extremely high utilization value for identifying the service level of public transportation operation at low cost.

There are many research outcomes relevant to the service level of public transport operations. Eom et al. [8] studied the quality of bus services based on bus IC card data and found that high passenger demand during peak hours can easily lead to subway delays. Uniman et al. [9] quantitatively evaluated the service reliability of rail transit based on the automated fare card data of the London Underground and determined the unreliability level of the incident. Asakura et al. [10] analysed travellers' behavioural attributes based on the fusion of smart card data and personal travel survey data and provided a basis for operational improvement, fare adjustments and bus planning. Agard et al. [11] have mined the smart card data and observed the travel behaviour of passengers to obtain the cyclical behaviour indicators of passengers' daily travel. Yin et al. [12], Shen et al. [13], have used bus IC card data to study passenger flow at bus stops and reasonable bus operating periods. Xu et al. [14] used the Nanjing Metro IC card data to count the number of times in and out of the site, the length of stay and other indicators. Sun [15] estimated the state of rail transit operations in terms of travel time delays, which he understood from a time-loss perspective, emphasizing the issue of passenger travel time reliability, proposing delay criteria from both business and passenger perspectives, respectively, and defining a calculation method for integrated delay values.

These indicators distinguish subjective and objective behaviours. This method provides a basic evaluation for subway operation management and ticketing policy-making. However, these studies focus on the quality evaluation of the local service process and do not involve the machine evaluation method of the service quality of the subway system in the time and space dimensions.

In this article, passengers’ travel time distribution extracted from railway smart card data is picked out to establish a scientific assessment method of railway service with efficiency of time and financial costs. Based on smart card data, this paper uses 1 hour as the statistical duration and 5 minutes as the rolling interval to construct an array of passenger travel time distribution between different stations during the operation period. Then the K-means clustering method [16] is used to classify the passenger travel time distribution array into different sets and combine the Kolmogorov-Smirnov (K-S) test [17] to determine whether the classification set of passenger travel time distribution is rational or not. Finally, according to the pattern set of passenger travel time distribution established, the current travel time distribution types of passengers are compared and analysed, and the service quality level of the station and the service quality level of subway train operation is judged on station pair. Based on the service quality evaluation results of the station pair, a service quality weight indicator |$Q( {{S_k}} )$| of the line k is defined, and then an effective quantitative measurement method for the service quality of the entire subway network is proposed.

The main innovation points of this paper are as follows.

1. Based on smart card data, a new railway service quality assessment method for three levels such as stations pair of urban rail transit, railway line and railway network is established, and the method is suitable for online and offline application automatically.

2. The service quality weight indicator |$Q( {{S_k}} )$| of line k defined from characters of passengers’ travel time distribution classified by the K-means clustering method and verified by the K-S test is initially proposed as a measurement tool of integrated operational intention and passenger satisfaction.

The paper is organized as follow: Section 2 gives data description and classification. Passengers’ travel time distribution application follows in section 3; in Section 4, network service quality identification is developed. Finally some conclusions are presented.

2. Data and Classification

The subway service quality identification model based on smart card data mainly includes four parts: data preprocessing, route and time division, travel time feature analysis, and pattern set establishment of travel time distribution.

2.1 Data preprocessing

The Shenzhen Metro card data contain the card number, time of entry/exit, entry and exit state (21 means entry, 22 means exit) and the station. The structure of the raw subway card data is shown in Table 1. We used Python 3.8.8 to preprocess the raw data, and then match the corresponding date and time according to the card number to extract the arrival station, arrival time, departure station and departure time of passenger for each OD trip and further calculate the travel time of this trip.

Being affected by factors such as the failure of the card swiping device, the original data have many problems, such as incorrect swiping status, abnormal OD time and repeated recording. Therefore, data preprocessing such as data cleaning and filtering valid data has first been carried out. Second, data cleaning mainly includes data deduplication and abnormal data processing. Abnormal conditions include only inbound or outbound credit card records, and OD time is too short so as to be less than the shortest travel time between the two stations. The structure of subway card data after preprocessing is illustrated in Table 2.

2.2 Classification of route type

According to whether passengers could reach the destination directly by one train or by transferring on different subway lines, the travel route of passengers on urban railway system can be classified into different types. The specific process of the travel route is shown in Fig. 1.

When the train operation diagram is executed normally, the stay time in the paid area of the station can reflect the passenger flow organization level of the station and the quality of service in the station. Due to passenger behaviour has randomness and uncertainty in time and space, passengers' travel time distribution from subway card data can eliminate the impacts of personal behaviour discrepancy.

It can be seen from Fig. 1 that the composition of the process of taking the subway is different, and the travel time would also be different. Therefore, it is necessary to identify and divide the passenger travel event according to conditions as follows.

1. Travel route with no transfer on the same subway line. Identify the travel event where the starting point and the endpoint of the passenger trip are on the same line as a category of no transfer.

2. Travel route with one or more transfers. It is recognized that a travel event in which the starting point and endpoint of the passenger's trip includes several segments in more than one subway line with one or more transfer events.

2.3 Classification set of travel time distribution

The subway operation and management usually make adjustments based on travel demand at different periods, such as reducing the train running interval during peak hours, increasing the number of running trains, or opening the gates to increase the pass rate on pedestrian gates. These measures are generally adjusted at intervals of more than 1 hour. Therefore, an hour is set as the statistical time length in the paper.

Characteristics of passenger riding behaviour and passenger volume in the station are different during different operating periods. Travel time distribution during different periods might also present different patterns. Therefore, it is necessary to classify the different patterns into the different sets and establish a classification set of travel time distribution. The quality of subway service between the two stations could be evaluated based on the characteristics of travel time distributions.

The K-means clustering analysis method [16] is a machine learning method with the character of automatic classification, and can classify multiple objects into a limited set according to distance. It is no clear boundary division and classification requirement about the set. The K-S test [18] is a test method based on cumulative distribution function, used to test whether a distribution conforms to a certainly known distribution or to compare whether there is a significant difference between two distributions. Using the K-means clustering method and the K-S test, we could further determine whether there is a significant difference in the sample distribution classified and realize the automatic classification of the travel time distribution in each train operating period.

The K-means clustering algorithm needs to input the number of categories K value in advance manually. The method of selecting the K value in this paper is as follows:

1. According to the traffic characteristics and operating hours of each station, the sample data are divided into four time periods: morning peak, evening peak, flat peak and low peak according to the time of different demand.

2. The K-S test is performed on the sample data to extract the different travel demand periods, and the sample data subject to the hypothesis test are classified into the same distribution to initially determine the lowest number of classifications in the classification set.

3. Apply the ‘elbow rule’ to calculate the optimal number of categories based on the lowest number of categories.

To effectively and comprehensively summarize the characteristics of travel time distribution of sample travel events, eight descriptive statistics, including maximum, minimum, variance, mean, median, mode, skewness and kurtosis, were selected to describe the distribution characteristics. Then, factor analysis was used to avoid using highly correlated indicators for research, and only four statistical indicators of travel time were selected for cluster analysis as follows:

1. Average: indicating the overall size of travel time distribution in the period.

2. Variance: indicating the degree of dispersion of travel time distribution.

3. Skewness [19]: it can better reflect the occurrence of extreme values of passenger travel time distribution during this period. Bigger than zero indicates right skewness. Less than zero indicates left skewness. The larger the absolute value, the more serious the deviation.

4. Kurtosis [20, 21]: it can reflect the passenger travel time during this period between the two stations. Kurtosis greater than zero indicates the data are concentrated, which means the travel times are similar for passengers. Kurtosis less than zero indicates the distributed data are scattered, which means the travel time is uncertain.

After the K-means clustering result of travel time distribution is obtained, the K-S test is used to determine whether there is a significant difference between the travel time distributions in each period after clustering.

The process of establishing the classification pattern set of passenger travel time distribution in each period of different travel demand based on subway card data is as follows:

1. Select the optimal classification number K value according to the method described above, and choose 500 as the upper bound iterations number.

2. Randomly select K objects from the sample data of passenger travel time distribution as the initial cluster centres.

3. Calculate the distance between the characteristic value of the passenger's travel time distribution sample in each period to that of each cluster centre, and assign the sample data to the nearest cluster.

4. Once all the objects are allocated, the centroids of K clusters will be recalculated

5. Compared with the previous K cluster centres, if it is a change, repeat steps 2–4, otherwise go to step 6.

6. When the centroid no longer changes, or the upper bound number of iterations has been reached, stop the clustering process and output the classification results.

7.  The K-S test is performed on each category of the sample data in the output classification results. If the clustering hypothesis of the K-S test does not hold, the sample data will be reclassified.

3. Application

3.1 Data overview

This paper uses the subway card data in the Ailian (AL)–Buji (BJ) section and the Huaqiangbei (HQB)–Shenzhen North station (SZBZ) section of the Shenzhen Metro from 12 to 18 October 2014, as analysis examples shown in Fig. 2.

The operating hours of Shenzhen Metro are 6:00–24:00, and some stations will close early at 23:00. According to the sample of subway card data, the passenger's travel volume at each period is counted, and preliminary judgements are made on the daily peak hours of passengers. Hourly traffic statistics results are shown in Fig. 3, the traffic is the largest during 7:00–9:00 and 17:00–19:00, and it is relatively stable during 9:00–17:00, the traffic is flat, the passenger flow is less than the peak hours, but it is significantly higher than the low peak hours. Therefore, it can be considered that the morning peak period of Shenzhen operation is 7:00–9:00 (2 hours), and the evening peak period is 18:00–20:00 (2 hours). The flat interval includes 9:00–18:00 and 19:00–22:00 (11 hours), and the off-peak interval distributes in 6:00–7:00 and 22:00–24:00 (3 hours).

3.2 Travel time distribution classification

3.2.1 No transfer type

The study on the same line without transfer line type would select AL–BJ trip as a research example. First, in the direction of AL to BJ, the sample data are divided into statistical intervals every hour to generate data for 18 time periods. To determine the best classification number K value, we first conduct preliminary analysis and K-S test on the data of the four periods of morning peak, evening peak, flat interval and off-peak interval.

According to the statistical characteristics of travel time in Table 3 and the probability density distribution in Fig. 4, it can be seen that the distribution of travel time in the morning peak and evening peak is relatively consistent. The distribution is skewed to the right and concentrated, and the right side of the data shows a trailing phenomenon. The mean value of the off-peak interval is larger, which shows that there is a left bias. The off-peak interval is different from the distribution type of the other three periods.

The passenger travel time distribution of morning and evening peak in the direction of AL to BJ is similar, which can be judged as homogeneous distribution. In the morning peak, the probability density curve is thinner and narrower, which is a single peak curve. The performance curve of evening peak is relatively ‘fat’, and is a bimodal density. In our mind, passengers were not so nervous about travel time in evening peak. They are not in a hurry to catch the first train (29 minutes) due to passengers having an alternative choice on the second train (32 minutes).

The test results obtained by the K-S test are shown in Table 4. The distributions that were found to significantly resemble the travel time data at a significance level of 5% are marked with ‘Yes’, otherwise ‘No’.

The following observation can be drawn from Table 3. The optimal classification number for travel time distribution in the direction of AL to BJ is two categories. The first category includes evening, morning and flat interval, and the second contains off-peak interval.

According to the ‘elbow rule’ [22] and the cost curve, in the sample data with the direction of AL to BJ, the best classification number is selected as 2.

We classify the travel time distribution and perform the K-S test on each category's travel time sample data. According to the K-S test result, the K-means clustering result conforms to the travel time distribution cluster classification in each period. The proportions of various samples and cluster centres in the clustering results are shown in Table 5. The final classification results are shown in Fig. 5, and the probability density curves of travel time distributions in each classification are shown in Fig. 6

As shown in Table 5, the clustering results are in two groups with different sample sizes. Category 1 contains 72.2% of the samples, which covers nearly three-quarters of the sample data during operation; Category 2 contains 27.8%.

As shown in Fig. 4, the period of category 1 is from 7:00 to 20:00, mainly in the morning peak, part of the flat period and the evening peak period. Category 2 is from 6:00 to 7:00 and 20:00–24:00, mainly in the off-peak and part of the flat interval. Category 1 has a small average (30.93) and slight variance (5.54), and the overall distribution is concentrated, with a partial right-skewed phenomenon. Category 2 has a large average (31.67), large variance and a scattered distribution.

The classification result can obtain backstepping, for passengers at the direction of AL to BJ, most travel events can be classified into category 1, it is a normal travel classification, the station operation also performed well in morning and evening peak periods. It shows that the station service could still maintain regular and high-quality service when the passenger flow increases.

A small number of travel events could be classified as category 2. When passenger flow is low, operating companies could reduce service frequency to reduce operating costs, which could lead to lower service quality. However, at 20:00, the station traffic was still heavy, the peak crowd had not wholly gone. Therefore, stations should improve their operation and service quality between 20:00 and 21:00.

Using the same method as above, we processed and analysed the travel time sample data set in the direction of BJ to AL. The optimal cluster classification number of travel time distribution in the direction of BJ to AL was 3. The K-means cluster analysis method combined with the K-S test is employed to obtain the classification results, as shown in Table 6. Passenger travel incidents from BJ to AL can be divided into three groups with different scales. Category 1 contains 66.7% of the samples, which covers nearly two-thirds of the sample data during operation. Category 2 contains 16.7% and category 3 contains 16.7%.

As shown in Fig. 7, the periods included in category 1 are 7:00–9:00, 10:00–20:00, covering morning, evening and part of the flat interval. The periods included in category 2 are 6:00–7:00 and 22:00–23:00, mainly appearing in the off-peak interval. The periods included in category 3 are 9:00–10:00 and 20:00–22:00, which mostly occur in the part of the peak period and immediately after the end of morning peak and evening peak.

Combined with the probability density curve of each category in Fig. 8 and Table 6, category 1 has a relatively normal performance, with a small mean (31.11), small variance (5.66) and a more concentrated overall distribution. In comparison, category 2 has a large mean (32.78), a large variance (12.00) and a scattered distribution, indicating that the low peak period of the route in this direction is generally flat.

According to the above research, due to the less flow of passengers during the low peak period, the train interval is lengthened. Because of the uncertainty of passengers, the data during the low peak period present a random and scattered state.

Category 3 could be regarded as a derived distribution of category 1. Its mean and variance are between category 1 and category 2 and the skewness is large (0.49). The distribution curve has a tailing phenomenon. This is because the morning peak and evening peak are not completely dissipated, but the operation measures are not adjusted in time, resulting in a longer travel time for passengers in this period. Based on the analysis of the classification results of travel time distribution in the two directions, it can be seen that the service quality in the BJ to AL direction is worse than that in the AL to BJ direction.

3.2.2 One-time transfer type

For the one-time transfer type, the preprocessing data are the same as that of the no-transfer line in the same line, so they will not be described here.

For the travel events in the direction of HQB–SZBZ, the data of the four time periods of morning peak, evening peak, flat peak and off-peak interval are preliminarily analysed as shown in Table 7 and Fig. 9. The data during the evening peak hours are different from the travel time distribution in other periods. The travel time distribution during the peak period is also more scattered and the travel behaviour of passengers in the morning and the afternoon is quite different, affecting travel time.

The K-S test results are shown in Table 8. The travel time distribution during the morning peak period is consistent with the evening peak period. The travel time distribution during the flat peak period is inconsistent with the distribution of the evening peak period. Combining the ‘elbow rule’ and the K-S test results, the minimum classification number is 2. The classification results are shown in Figs. 10 and 11. The cluster centres and sample numbers are shown in Table 9.

As shown in Table 9, passenger travel incidents from HQB to SZBZ could be divided into five groups of different scales. Category 1 contains 47.06% of the samples, category 2 contains 5.89% and category 3 contains 23.53%, etc. Among them, category 1 covers nearly half of the sample data during the operating time.

The best classification number of passenger travel events from SZBZ to HQB is 5. Through K-means clustering analysis and K-S test, the clustering results are shown in Fig. 12, and the relevant parameters of the clustering results are shown in Table 11. Category 1 contains 35.3% of the samples, category 2 contains 23.52%. Categories 1 and 2 cover nearly two-thirds of the sample data during operation.

According to the clustering results in Fig. 12 and Table 10, both category 1 and category 3 appear in the flat peak period. Category 1 appears more frequently, and its mean and variance are larger than other categories. As shown in Fig. 13, The result shows that the station's operation is not stable during the peak period, and sometimes passengers' travel time is prolonged. The station cannot make timely adjustments to changes in passenger flow. Category 2 mainly occurs in the morning peak and evening. It is a large and gentle distribution similar to the classification during the normal peak period. However, due to the large traffic volume at the transfer station during the morning peak period, the congestion of the station makes the travel time in the morning peak increase and uncertain.

Category 4 mainly appears in the evening rush period. At this time, the overall travel time is reduced and concentrated. The subway could achieve the purpose of efficient travel during the evening peak.

Compared with the classification results of distribution in the direction of HQB to SZBZ, the service quality of SZBZ to HQB is poor, the passengers' travel time is unstable, and the overall travel time has been extended.

3.2.3 Multi transfer type

For the type of routes with two or more interchanges, the passenger travel time from FT to XL was chosen as an example in this paper.

For the travel events in the direction of FT–XL, the basic analysis data for the four periods of morning peak, evening peak, flat peak and off-peak periods are shown in Table 12. The K-S test results for these four time periods are shown in Table 13. The data are most concentrated in the morning peak period, while they are scattered in all other time periods and the reliability of passenger travel time is low. Combining the ‘elbow rule’ and K-S test results, the minimum number of classifications is 2. The classification results are shown in Figs. 14 and 15, and the cluster centres are shown in Table 14.

Category 1 contains 50% of the samples and category 2 contains 50%. As shown in Fig. 15, category 1 is mainly found in the morning peak and evening peak hours, where the data are more concentrated. Category 2 could be identified as off-peak hours with more stable service quality levels.

4. Network service quality identification

We studied the service quality of the OD pair between different stations. From this section, the research scope would be expanded from the two dimensions of time and space to study the service quality of the subway network.

4.1 Model Specification

First, assume that the total length of the research operation time is |$L$|⁠, which could be divided into |$N\ $|statistical periods. Here we still start with analysing passengers' travel time from the departure station to the destination station in a single statistical period. At the same time, it is assumed that the subway area evaluated is |$k$|⁠, which is a subset of the subway network |$K$|⁠, that is, |$k \subseteq K$|⁠. We define the service quality weight indicator |${S_k}$| in area |$k$|⁠, which is used to measure the service quality of subway subregion |$k$|⁠. For subway subregion |$k$|⁠, the symbol |$i$| is used to represent the departure station and |$j$| is the destination station. The transferring station between the two stations is |$e$|⁠, and the trip from station |$i$| to station |$j$| can also be regarded as a trip on transferring station |$e$|⁠, denoted as |${e^{i,{\rm{\ }}j}}$|⁠.

We obtain the travel time in the route with one-time transferring |${e^{i,{\rm{\ }}j}}$| based on historical subway card data and consider |${\rm{\alpha }}$| percentile of the passenger travel time |$T_n^{i,\ j}$| from station |$i$| to station |$j$| during the statistical period |$n$|(⁠|$n \in \{ {1,2, \ldots ,\ N} \}$|⁠), which can roughly reflect the travel time of the service quality within the current two-station section with one time transferring. Symbol |$C_{e,\ n}^{i,\ j}$| is the planned section travel time in section |${e^{i,{\rm{\ }}j}}$| during statistical period |$n$|⁠, and |$R_{e,\ n}^{i,\ j}$| is defined as the ratio of the |${\rm{\alpha }}$| percentile of travel time |$T_n^{i,\ j}$| in section |${e^{i,{\rm{\ }}j}}$| during statistical period |$n$| to the section planned travel time |$C_{e,\ n}^{i,\ j}$|⁠.

4.2 Result

We select the credit card records of all passengers on the five lines of Shenzhen Metro Line 1 to Line 5 during the three days from 17 to 19 October 2014. After the data are processed and analysed as described above, passengers' travel time in each station section is obtained. In this section, we take BJ Station as an example. BJ Station is the transfer station of Line 3 and Line 5. From BJ Station to the stations on Line 3 and Line 5, there is no need to transfer. There is no transfer type on the two lines. But to Line 1, Line 2, and Line 4, passengers need to change trains at the station above. This paper conducted sensitivity analysis on |$\ {\rm{\alpha }}$| value and found that the model was most stable when |${\rm{\alpha \ }} = {\rm{\ }}70{\rm{\% }}$|⁠. (Sensitivity analysis results are shown in Fig. 16.) The departure interval is given in TableA1, and the planned travel time in each line is given in TablesB1, B2, B3, B4 and B5.

First, on the same line without transfer type, we can see from Figs. 17 and 18 that the deterioration of the travel time from BJ station to other stations mainly occurs at multiple stations near BJ station. On the contrary, the service quality of the farther stations is standard and there is no deteriorating trend. The result reflects the insufficient operation of the station in the BJ station, which leads to longer travel time and lower travel efficiency when passengers travel short distances. The result means that BJ station should improve the internal operation of the station itself.

An abnormal phenomenon occurred at the far-reaching Futian Station and LJ Station on Line 3. In contrast, Line 5 has fewer degraded stations. Especially at the interchange stations, such as BAZX and HQB Stations, the performance is excellent. The overall service quality of Line 5 is good.

Second, among the types of passengers needing to transfer, the deterioration of service quality on Line 1 is shown in Fig. 19 mainly occurs at the stations from BJ to LJ and stations nearby LJ. The service quality of these sections has deteriorated, reflecting the low service level of the LJ Station itself, including certain problems with outbound and transfer services. The station needs to be improved.

As shown in Fig. 20, the HBL station of Line 2 is used as a transfer station. The service quality of the BJ–HBL section has not deteriorated. However, the service quality of the other stations around HBL—BJ to XX (Xin Xiu), HB, and other stations—shows a deteriorating trend. It reflects that the outbound service of HBL Station is normal, but there are problems with the transfer service quality of this station.

Therefore, this increases the time required for passengers to transfer via HBL, which increases travel time and reduces travel efficiency. Stations should consider some measures to improve the quality of the transfer service at the transfer station, such as reasonable arrangements for train operation time, reducing passenger waiting time for transfer and appropriately arranging pedestrian routes at the transfer station. The development of unique escalators for transfers, etc., to improve the travel convenience of transfer passengers. As shown in Fig. 21, the degraded station only appeared in SZBZ on the Line 4, and the overall service quality of the line was relatively good.

According to Section 4.1, we can calculate the results of the service quality evaluation of each line of the Shenzhen Metro network (shown in Table 15). We found that the quality deterioration points of Shenzhen subway mainly appeared near BJ Station and transfer points: the surrounding sections with BJ as the centre were degraded significantly. For example, the service quality of multiple stations deteriorated and urgently needed enhancement on Line 3. Some transfer stations on the other line also experience deterioration in service quality. These stations have something in common: these mostly have heavy traffic. At the same time, the internal structure of some transfer stations is complicated, and the signs are not obvious, which makes leaving the station difficult for passengers. The efficiency is reduced and the passenger travel time is extended. These are the bottleneck areas of the Shenzhen subway line's online service quality and need to be improved urgently.

The evaluation method proposed in this paper can be carried out from different statistical periods. When the statistical time is short, such as the service quality evaluation based on the credit card data within 1 hour, the service quality evaluation result can be regarded as a real-time evaluation.

We select the corresponding travel time data samples within one hour for the off-peak interval, flat peak period and peak period. The results are shown in Table 15. We can see that the operation is reasonable during the off-peak interval and the peak period. The overall evaluation results of each line are relatively good, but the service quality effect is not suitable during the flat peak period. In the statistical time range for one day, we use the subway card data that include the entire operating period of the day. The service quality of each line is similar to the average of the previous three different periods. The service quality of Line 4 is relatively low at 0.67. When the statistical time is extended, a relatively stable and long-term service quality evaluation could be performed on the line.

In the evaluation results based on the three-day credit card data, the service quality of Line 3 is the best, with a score of 0.945, while the service quality results of Lines 1 and 4 are similar, the result of Line 1 is 0.65 and the result of Line 4 is 0.67.

Through Eq. (6), we can calculate the service quality evaluation results of the entire Shenzhen Metro network. The results are shown in Table 16. During 15:00–16:00 (flat peak period), the Shenzhen Metro network service quality score is 0.79, and during 8:00–9:00 (rush hour), the score is 0.90. During 22:00–23:00 (low peak period), the score is 0.83.

As shown in Table 16, in one day, the service quality score of Shenzhen Metro's network is 0.80. After expanding the statistical time to three days, the score is 0.85.

In addition to the above case, to verify the accuracy of our model, we also selected the FT of Shenzhen city centre as the starting point for the validation study. The results obtained through the calculation of this model are shown in Table 17. The results are similar to the final scores obtained from the previous example of BJ, which numerically validates the scientific and accuracy of the model.

We compared the models of assessing the operational status of rail transport based on travel time delays [15] using the subway card data. The evaluation results we calculated based on the Shenzhen Metro data using their method are shown in Table 18. |$( {\partial \ = {\rm{\ }}0.74,\,\beta \ = {\rm{\ }}0.26.} )$|

We could see that Line 3 has the lowest delay values, and Line 3 is in the best operating condition in Table 17. The delay value of Line 1 and Line 4 is enormous, and the operation state urgently needs to be improved. This is consistent with the previous results in Table 15 obtained from the service quality evaluation model of railway smart data, which again verifies the validity of this model. However, the operation state assessment model based on travel time delay only starts from the perspective of travel time delay and could not accurately evaluate the working conditions of stations with an effective operation that reduces the delay and improves the overall travel time.

5. Conclusions

1. This paper is based on the railway smart data of passengers generated during the previous operation. The mean, variance, kurtosis and skewness of the data were used as four indicators to perform K-means clustering of the travel time distribution for each period. To improve the reasonableness of the clustering results, we used the K-S test to validate and the results were consistent. The clustering results are used as a general condition for service quality assessment during operation. This method could be used for service quality evaluation between each pair of stations in the line network. The study found that there are two main types of abnormal service quality. First, when the traffic has not been wholly dissipated during the peak period and operation schedule remain unchanged which will reduce the quality of service. In AL–BJ, this category accounts for 27.85%. The second is congestion at interchange stations makes travel times during the peak period increased and uncertain, resulting in deterioration of service quality, accounting for 23.52% during SZBZ–HQB.

2. Based on the service quality evaluation results of station pairs, it defines the service quality weight indicator |$Q( {{S_k}} )$| in line |$k$|⁠. Then, we proposed a responsive, effective and convenient service quality-oriented metro network identification model from railway smart card data based on the indicator. Taking Shenzhen Metro as an example, the service quality result is 0.85 (out of 1). The evaluation results were matched and validated with other stations in the same period, and the results were similar to other methods' results.

The model proposed in this paper uses railway smart card data to score the quality of urban rail services objectively and scientifically, taking into account the overall situation of the metro network and minimizing the impact of the individual actions of a few passengers. By linking critical operational indicators with the subjective indicator of passenger satisfaction, the model combines both passenger and corporate perspectives and provides an intuitive assessment of the operating lines through the final score. The model uses big data to reconstruct the service quality evaluation system of urban rail transport as far as possible. With further research, it will be possible to realize online instantaneous service quality evaluation, overtaking the previous lagging evaluation method, allowing timely feedback on metro operations, responding to onsite problems in time, increasing passenger satisfaction and improving service quality and passenger stickiness.

Because the time recorded in the subway card data is from swiping into the gate to swiping out of the gate, the data do not register the time required for passengers to enter the station and pass the security check. This is the deficiency of this study, and it is necessary to combine other auxiliary data further to improve this study in the future.

Conflict of interest statement

There is no conflict of interest.

References

Appendix A. Appendix A. The departure interval for the case studies

Appendix B. Appendix B. The planned travel time for the case studies