Dynamic Evaluation for Subway–Bus Transfer Quality Referring to Benefits, Convenience, and Reliability

Abstract

The integration of urban bus and subway services is critical for attracting passengers and for the sustainable development of public transit, as it helps to boost ridership with an extensive service that combines the attractions of buses and subways. To identify barriers in transferring from bus to subway or vice versa at different periods of the day, this research develops the popular evaluation indices found in the literature and revises them to reflect the most critical attributes of transfer quality. Thus, the deficiencies of transferring from subway to bus or vice versa are independently examined. Motivated by the changes in the indices at different periods, the day is divided into multiple periods. Then, dynamic transfer-volume-based TOPSIS is developed, instead of assigning index weights based on period sequence. The index weight is revised to emphasize the peak periods. Taking a case study in Suzhou, the barriers to inter-modal transfer are identified between subways and buses. It is found that subway-to-bus transfer quality is only one-third of that of bus-to-subway transfers due to the great changes in bus runs (19–45 vs. 14–26), lower bus coverage rates (0.42–0.47 vs. 0.50–0.55), and larger deviation of connected POIs (9.0–9.4 vs. 1.1–1.8), as well as the lower reliability of connected bus lines (0.3–0.47 beyond peaks vs. 0.58 and 0.96). Multi-faceted implementations are recommended for inter-modal subway-to-bus transfers and bus-to-subway transfers, respectively. The research provides insights on enhancing bus–subway transfer quality with finer detail into different periods, to encourage the loyalty of transit passengers with more stable and reliable bus as well as transit service.

1. Introduction

Transfer extends public transit service both intra-modally and inter-modally to better attract passengers and enhance its sustainability [1]. Transfer provides passengers with more choices to reach destinations that may be inaccessible by a single route or mode. Transfer is also emphasized as a way to connect newly built subway routes with neighboring bus routes to deliver passengers extensively. According to the statistics, 48% of subway trips are connected to bus trips in Melbourne [2], and 56% of commuters make a single transfer between bus and subway in Madrid. Note that transfer impedance is significantly larger compared with in-vehicle time [3], where passengers can be faced with more tasks and difficulties, including getting out of the current vehicle, walking to the connection point, keeping an eye on the coming vehicle, and getting onto the target vehicle. In addition, passengers usually get impatient and complain a lot when they wait a long time at transfer points [4]. Thus, transfer evaluation and the pertinent improvement of the identified weak attributes may significantly improve the quality of connected public transit services. Also, a comprehensive bus-transit transfer level may extend the research on integrated public transit for resilient and high-quality trip services [5,6,7,8].

Transfer evaluation includes two fundamental components, i.e., evaluation indices and evaluation methods, which can be developed for bus–bus, subway–subway transfer, and bus–subway transfer. For bus–bus transfers, it is found that long waits at transfer points strongly drive the reduction and cessation of transit use [9]. Actually, a long wait is one of the most negative experiences of riding a bus, which is comparable to the delay of being unable to board a crowded bus. To diagnose transfer problems, the indices of the number of connected lines, average transfer distance, average wait time, and the proportion of transfer volume at the transfer stop are incorporated into data envelop analysis, where the transfer nodes with high transfer rate and transfer volumes receive higher evaluation scores [10]. Moreover, transfer is more attractive to passengers with mandatory trip purposes, while it is not statistically related to trip distance [11]. To decode the factors of transfer behaviors, the attributes of bus service frequency, reliability, bus stop locations, travel time, night service, comfort, and information provision are analyzed, finding that bus service reliability and frequency are critical to transfer, followed by comfort, information, and night service [12]. The timeliness of bus service is also proven to be the most effective measure to improve the overall transfer satisfaction [13].

For subway–subway transfer, factors such as a long walking distance [14], crowded transfer environment, and walking up/down stairs [15] strongly affect transfer efficiency and reduce passenger transfer satisfaction. Compared to the above factors, the fare for subway transfers is less important [16]. In addition to the above indices, the attributes of information facilities, the area of waiting spaces, station temperature, and facility convenience can also be employed to evaluate transfer quality [17]. It is also found that transfers between different subway lines can be less efficient if they are managed by different operators [14]. Further, studies on transfer indices may come to different results for different cities due to passengers’ sensitivity to the same indices. For example, the indices of physical factors of accessibility, road crossings, and vertical circulation influence transfer comfort to a greater degree in India compared to Germany [18].

When it comes to bus–subway transfers, it is found that wait time at bus stops is the most important factor affecting transfer experience in Bangkok, Thailand [19]. Factors such as safety and security, transfer environment, signposting, comfort, convenience, and accessibility are also important in the assessment of bus and subway transfer [20]. Specifically, bus arrival frequency is the weakest point in subway–bus transfer [21], and transfer penalty is a critical factor in transfer satisfaction [22]. Short transfer distances and high service frequency may well improve transfer efficiency [23]. For a more detailed transfer evaluation, the crowdedness of buses and walking distance are determinants of bus–subway transfer satisfaction, and bus punctuality and walking environment are closely related to transfer quality [24]. Weather also significantly influences transfer behaviors, which are discouraged with high temperatures, heavy rain, low visibility, or strong wind [25]. In addition, the coverage rate of points of interest (POIs) [26,27,28] and connection reliability [29,30,31] at connected stops also have a great impact on subway–bus transfer. Population density also positively affects subway–bus transfer efficiency, while company density works negatively in Seoul [32].

Further, inter-modal transfer evaluation can be distinguished between bus-to-subway and subway-to-bus transfers. To the best of our knowledge, there is very limited research that separates bus-to-subway transfer analyses from those of subway-to-bus. One exception is that Wu et al. [33] distinguish the impact of weather variables on bus–subway and subway–bus, pointing out that strong wind, heavy rain, and high temperature increase transfer ridership of the subway-to-bus mode, but reduce that of bus-to-subway transfer. Thus, we identify the research gap in the separate discussion of inter-modal transfer either from subway to bus or the opposite. That is critical for understanding the overall transfer experience, which plays a pivotal role in designing effective transfer systems.

Table 1. Popular indices of transit transfer evaluation.

Indices	Modes	References	Usage
Benefits
Count of transfer routes	All modes	10, 19, 26, 27, 33	Revised
POIs	Bus–subway, bus–bus	9, 23, 26, 28	Adopted
Coverage rate	Subway–bus	25, 30, 32	Adopted
Transfer cost	Subway–bus	24	-
Transfer volume	Bus–bus	10	-
Convenience
Transfer time	All modes	10, 11, 16, 19, 23, 25, 26	Adopted
Walking distance	All modes	10, 11, 22, 23, 27	Adopted
Ease of wayfinding	Bus–subway	20	-
Count of passageways	Bus–subway, bus–subway	33	-
Information	Bus–bus	9	-
Frequency	Bus–bus	9	-
Comfort
Safety	Subway–subway, bus–subway	14, 18, 19, 20, 23	-
Facility	Bus–subway	19, 20	-
Environment	Subway–subway, subway–bus	16, 22	-
Weather	Subway–bus, bus–subway	23, 32	-
Reliability
Reliability of connected lines	Subway–bus	29, 30, 31	Adopted
Variability of transfer time	Bus–bus, subway–bus	9, 12, 13, 22	Adopted

summarizes the commonly used indices in designing in public transit transfer evaluation with references to the relevant studies. Drawing on the well-accepted and popular indices on the inter-modal transfer between bus and subway services, categorization into benefits, convenience, and reliability is proposed. Note the subjective index of transfer comfort is not involved in the research, because of its variation and uncertainty in passenger feeling.

A comprehensive evaluation method is employed to quantify the level of transit transfer across multiple dimensions. The popular methods include the techniques for order preferences by similarity to ideal solutions (TOPSIS), analytic hierarchy process [34], grey evaluation method [35], and data envelopment analysis [10,25,36]. Among these methods, TOPSIS provides the optimal alternative with the shortest distance to a positive ideal solution and the longest distance from a negative ideal solution [37], which has been widely applied to the transportation evaluation of service quality, customer satisfaction, and sustainability, etc. For example, TOPSIS may be adopted to evaluate public transit service [38] or evaluate airline efficiency [39]. Note that TOPSIS primarily focuses on horizontal static data, failing to consider index changes over time [40].

Oriented to the dynamic index values throughout a day, TOPSIS can be incorporated with the time dimension to reflect the different index levels in the different periods [41]. For example, dynamic TOPSIS makes use of panel data to rank the green development level of coal-resource-based cities at different stages to propose the corresponding policy recommendations [40]. Considering the temporal variation in subway–bus transfer levels, dynamic TOPSIS is employed to calculate the index levels and weights in the different periods. This allows us to dig into the periodic difference in the transfer quality between subway and bus services, which may change rapidly in the different periods. If we do not divide a day into multiple periods, we can come to only one value for a whole day, which is not capable of reflecting the changes and the difference in transfer quality throughout a day. To examine transfer quality in detail and to trace the changes in transfer quality, we divide a day into discrete periods and the index value and weight are calculated in response for a delicate description of transit transfer.

The contributions of the research are three-fold. First, an improved index system for transfer evaluation is established, focusing on transfer benefits, convenience, and reliability. The index system is based on real-world data and applicable to both subway-to-bus and bus-to-subway inter-modal transfers. Specifically, we incorporate the evaluation indices of the count of connected runs, coverage rate of connected stops/stations, count of connected POIs, transfer time, transfer distance, connection line reliability, and transfer time variability. Second, dynamic evaluations of bus–subway transfer are implemented with a revised method of the existing dynamic TOPSIS [40,41], which assigns weights based on the transfer volume of each. In the proposed method, the period with a higher transfer volume is given more weight. Third, the proposed indices and methods are validated with an empirical case study, where transfer quality is evaluated dynamically for both subway-to-bus and bus-to-subway transfer. The case study reveals that the quality of subway-to-bus transfer is significantly lower than that of bus-to-subway, which inspires recommendations for multi-faceted improvements in inter-modal transfer aimed at enhancing transfer quality in both directions.

The remainder of the paper is organized as follows. Section 2 defines the indices of bus–subway transfer evaluation, followed by the data extraction and dynamic TOPSIS Section 3. Section 4 presents a case study and discusses the results to validate the proposed index system and evaluation method. Section 5 concludes the paper.

2. Indices for Bus–Subway Transfer Evaluation

Bus–subway transfer allows passengers to make use of both bus and subway services, extending their travel options and improving availability to more destinations in a convenient and reliable manner. To evaluate transfer quality, a comprehensive set of indices is established, focusing on three main indices: transfer benefits, convenience, and reliability.

Table 2. Indices of bus–subway transfer evaluation.

Indices	Explanation	Type
Benefits
Count of connected runs	Average number of buses or subways that can be taken within the transfer range in the specified period.	$D^{+}$
Coverage rate of connected stops/stations	Ratio of the sum of the service area of the stops on the connected lines in operation to the research range in the specified period.	$D^{+}$
Count of connected POIs	Count of distinct geographical points that one can be interested in.	$D^{+}$
Convenience
Transfer time	Time when a passenger gets off the subway (or bus) before departing on a bus (or subway), weighed with transfer volume.	$D^{-}$
Transfer distance	Distance between the transfer point and the departure point.	$D^{-}$
Reliability
Reliability of transfer lines	Ratio of the routes in operation to the total routes connected to a transfer point.	$D^{+}$
Variability of transfer time	Standard variation in the transfer time between subway and bus service.	$D^{-}$

summarizes the index system used in the research to categorize these indices accordingly. The notations $D^{+}$ and $D^{-}$ refer to the set of positive and negative indices, respectively.

2.1. Transfer Benefits

Transfer benefits refer to the service advantages that passengers gain from the transfer process. Specifically, this includes the ability to reach a wider range of destinations via transfer between subway and bus services. The key indices for assessing transfer benefits include the following three.

Count of connected runs. This index measures the average number of buses or subway vehicles that can be taken within the transfer range, typically between 200 to 800 m [42] from the transfer point. That is, the count of connected runs is the sum of service frequency of each route at the transfer point. Thus, when one transfer point is connected to high-frequency routes, the index returns a higher evaluation result to reflect the advantages of a frequent transit service. Figure 1 shows the conception of the count of connected runs.

The index of connected runs is given by

$$R_{s,j}\left(t\right)={\displaystyle \frac{{\sum }_{i=1}^{N_{s,j}\left(t\right)}{f}_i\left(t\right)}{H\left(t\right)}}$$

(1)

$$R_{b,j}\left(t\right)={\displaystyle \frac{{\sum }_{i=1}^{N_{b,j}\left(t\right)}{f}_{j,i}\left(t\right)}{H\left(t\right)}}$$

(2)

where $R_{s,j}\left(t\right)$ and $R_{b,j}\left(t\right)$ refer to the count of connected buses at subway station $j$ or connected subway trains at bus stop $j$ in the period $t$, $N_{s,j}\left(t\right)$ and $N_{b,j}\left(t\right)$ represent the count of bus lines connected to subway station $j$ or subway lines connected to bus stop $j$ in period $t$, $f_i\left(t\right)$ represents the count of service shifts of route $i$ in period $t$, and $H\left(t\right)$ is the count of hours in period $t$.

Coverage rate of connected stops/stations. This index evaluates the spatial reach of the transfer network. It is calculated as the ratio of the total service area covered by the connected stops and stations to the defined research range. This helps us to access how well the transfer point connects passengers to various destinations. Figure 2 shows the conception of the coverage rate of connected stops/stations.

Count of connected POIs. This index considers the number of significant geographical points, such as shopping malls, officials, residential areas, and parks, that are accessible from the transfer point [43]. A greater number of connected POIs indicates more potential benefits for passengers using the transfer point [44]. Figure 3 illustrates the conception of the count of connected POIs in the service range of the transfer point.

2.2. Transfer Convenience

Transfer convenience refers to how easily passenger can navigate the transfer process, minimizing delays and making the experience more efficient. The main indices used to evaluate transfer convenience include the following two.

Transfer time. This refers to the time passengers spend transferring from one vehicle to another. It includes in-station and out-of-station walking times and the waiting time at the transfer point. The transfer time is weighted according to transfer volume to reflect the actual passenger experience at different times. Figure 4 illustrates the meaning of transfer time, which is composed with in-station walk, out-station walk, and wait time at the transfer point. Note the in-station walk time is collected with filed survey, and the time between tap-out/in and swiping on the bus is collected with a smart card.

Transfer time is given by

$$\overline{T_{s,j}}\left(t\right)={\displaystyle \frac{{\sum }_{i=1}^{M_j\left(t\right)}{p}_{j,i}\left(t\right)\times t_{j,i}\left(t\right)\left|\begin{array}{c}85\%\\ 15\%\end{array}\right.}{{\sum }_{i=1}^{M_j}{p}_{j,i}\left(t\right)}}$$

(3)

$$\overline{T_{b,j}}\left(t\right)={\displaystyle \frac{{\sum }_{i=1}^{B_j\left(t\right)}{p}_{j,i}\left(t\right)\times t_{j,i}\left(t\right)\left|\begin{array}{c}85\%\\ 15\%\end{array}\right.}{{\sum }_{i=1}^{B_j}{p}_{j,i}\left(t\right)}}$$

(4)

where $\overline{T_{s,j}}\left(t\right)$ and $\overline{T_{b,j}}\left(t\right)$ are the transfer time at subway station $j$ or bus stop $j$ in the period $t$; parameters $M_j\left(t\right)$ and $B_j\left(t\right)$ are the number of bus stops connected to subway station $j$ and the number of subway stations connected to bus stop $j$ in the period $t$, respectively; $p_{j,i}\left(t\right)$ and $t_{j,i}\left(t\right)$ mean the transfer volume and transfer time from transfer point $j$ to the connected point $i$ in the period $t$. Note that the passenger transfer time may vary greatly. Here, transfer time extracted with smart card data is refined between the 15th and 85th percentile value, to avoid extremely small or large values that are related to non-transfer activities.

Transfer Distance: This index measures the physical distance between the transfer point and departure point. A shorter transfer distance contributes to a smoother, easier transfer experience. The transfer distance of subway-to-bus and bus-to-subway is given by

$$\overline{D_{s,j}}\left(t\right)={\displaystyle \frac{{\sum }_{i=1}^{M_j\left(t\right)}{p}_{i,j}\left(t\right)\times d_{j,i}}{{\sum }_{i=1}^{M_j\left(t\right)}{p}_{i,j}\left(t\right)}}$$

(5)

$$\overline{D_{b,j}}\left(t\right)={\displaystyle \frac{{\sum }_{i=1}^{B_j\left(t\right)}{p}_{i,j}\left(t\right)\times d_{j,i}}{{\sum }_{j=1}^{B_j\left(t\right)}{p}_{i,j}\left(t\right)}}$$

(6)

where $\overline{D_{s,j}}\left(t\right)$ and $\overline{D_{b,j}}\left(t\right)$ are the average transfer distance of subway station $j$ or bus stop $j$ in period $t$, respectively; $d_{j,i}$ refers to the distance between transfer point $j$ and the connected point $i$.

2.3. Transfer Reliability

Transfer reliability accesses the consistency and predictability of the transfer process. This is critical for ensuring passengers’ trust in the service, particularly during peak times of periods of high demand. The relevant indices for evaluating transfer reliability are the following two.

Reliability of connected lines. This index quantifies the reliability of the connected bus and subway lines by comparing the number of routes in operation to the total available routes. A higher ratio indicates more reliable service. Figure 5 illustrates the changes in the count of connected lines at a subway transfer station. That is, bus and subway routes may start and end service at different times of the day, causing changes in the count of the lines connected to a transfer point [45].

The reliability of connected lines is given by

$$C_{s,j}\left(t\right)={\displaystyle \frac{M_j\left(t\right)}{{max}_t{M}_j\left(t\right)}}$$

(7)

$$C_{b,j}\left(t\right)={\displaystyle \frac{B_j\left(t\right)}{{max}_t{B}_j\left(t\right)}}$$

(8)

where $C_{s,j}\left(t\right)$ and $C_{b,j}\left(t\right)$ refer to the connection reliability of subway station $j$ or bus stop $j$ in the period $t$; $M_j\left(t\right)$ and $B_j\left(t\right)$ are the number of remaining connected bus or subway lines of subway or bus station $j$ in period $t$.

Variability of transfer time. It measures the fluctuation in transfer times between subway and bus services. A higher variability suggests greater uncertainty in transfer times, negatively impacting the transfer experience. Here, the standard variation in transfer time [46] is adopted to represent transfer time variability, given by

$$R_{s,j}\left(t\right)={\displaystyle \frac{{\sum }_{i=1}^{M_j}{p}_{j,i}\times S_{j,i}}{{\sum }_{i=1}^{M_j}{p}_{j,i}}}$$

(9)

$$R_{b,j}\left(t\right)={\displaystyle \frac{{\sum }_{i=1}^{B_j}{p}_{j,i}\times S_{j,i}}{{\sum }_{i=1}^{B_j}{p}_{j,i}}}$$

(10)

where $R_{s,j}\left(t\right)$ and $R_{b,j}\left(t\right)$ are the transfer time fluctuations of subway station $j$ or bus stop $j$; $S_{j,i}$ refers to the standard variation in transfer time from transfer point $j$ to the connected point $i$, which is calculated with the data from the transit card, where transfer time is adopted if it falls in the range of 15th and 85th percentile to avoid the extreme data.

3. Data Extraction and Dynamic Evaluation Method

3.1. Logical Framework and Multi-Source Data

The evaluation of bus–subway transfer quality requires a structured method with support from comprehensive data. Figure 6 shows the logical framework for data processing, which outlines the flow of data extraction, processing, and analysis. Multi-source data is utilized to ensure the accuracy and robustness of the evaluation.

Figure 7 provides a detailed breakdown of the data types required for each index, including POI and stop/station distance data from application program interface (API), transit routes/stops information, and smart card data from bus and subway companies. These datasets are crucial for accurate assessment, as they ensure that every factor influencing transfer quality is accounted for.

3.2. Dynamic Evaluation Method

Given the dynamic nature of public transportation systems, where bus and subway operations vary throughout the day, a time-sensitive approach is required to evaluate transfer quality effectively. To address this, a dynamic TOPSIS method is proposed to reflect the temporal fluctuations in transfer conditions. Unlike traditional static TOPSIS, which uses fixed weights for evaluation indices, the dynamic version incorporates the influences of varying transfer volumes across different periods of one day. The dynamic TOPSIS evaluation value is given by

$$h_j={\sum }_t{G}_j\left(t\right)\times w\left(t\right)$$

(11)

where $h_j$ represents the evaluation value of transfer point $j$, $G_j\left(t\right)$ represents the closeness of the evaluation of transfer point $j$ to that of the optimal point, and $w\left(t\right)$ is the temporal weight at time $t$. Parameter $G_j\left(t\right)$ is given by

$$G_j\left(t\right)={\displaystyle \frac{S_j^{-}\left(t\right)}{S_j^{+}\left(t\right)+S_j^{-}\left(t\right)}}$$

(12)

where $S_j^{+}\left(t\right)$ and $S_j^{-}\left(t\right)$ refer to the distance from transfer point $j$ to the best and worst transfer point in the period $t$, which are calculated with

$$S_j^{+}\left(t\right)=\sqrt{{\sum }_u{w}_u\left(t\right)\times {\left[F_u^{+}-f_{ju}\left(t\right)\right]}^2}$$

(13)

$$S_j^{-}\left(t\right)=\sqrt{{\sum }_u{w}_u\left(t\right)\times {\left[F_u^{-}-f_{ju}\left(t\right)\right]}^2}$$

(14)

The notation $w_u\left(t\right)$ indicates the weight of index $u$ in period $t$; $F_u^{+}$ and $F_u^{-}$ refer to the best and worst values of index $u$ over all the transfer points in all the periods.

Parameter $w_u\left(t\right)$ is given by

$$w_u\left(t\right)={\displaystyle \frac{1-e_u\left(\mathrm{t}\right)}{{\sum }_u\left[1-e_u\left(t\right)\right]}}$$

(15)

where $e_u\left(t\right)$ means the information entropy of index $u$ in period $t$. Weight based on entropy helps to avoid biases from experts or decision-makers to emphasize the coordination among the transfer points. The smaller the entropy value, the more important the index. The notation $e_u\left(t\right)$ is calculated with

$$e_u\left(t\right)=-{\displaystyle \frac{1}{\mathit{ln}J}}{\sum }_j{c}_{ju}\left(t\right)\times \mathit{ln}\left[c_{ju}\left(t\right)\right]$$

(16)

where notation $J$ means the count of transfer points, $c_{ju}\left(t\right)$ is the proportion of index $u$ for transfer point $j$ over the sum of all the transfer points in period $t$, given by

$$c_{ju}\left(t\right)={\displaystyle \frac{y_{ju}\left(t\right)}{{\sum }_j{y}_{ju}\left(t\right)}}$$

(17)

where $y_{ju}\left(t\right)$ is the value of non-negative index $u$ for transfer point $j$ in period $t$, given by

$$y_{ju}\left(t\right)=\left\{\begin{array}{c}{d}_{ju}\left(t\right) if d_{ij}\in D^{+}\\ {max}_j\left[d_{ju}\left(t\right)\right]-d_{ju}\left(t\right) if d_{ij}\in D^{-} \end{array}\right.$$

(18)

for the positive index $D^{+}$ and negative index $D^{-}$, respectively. That is, $y_{ju}\left(t\right)$ is equal to the index value for the positive index, the larger value of which means a better performance, while $y_{ju}\left(t\right)$ of the negative index is equal to the maximal value over all the transfer points minus the original value. This progress guarantees consistent directionality over all indices.

The notation $f_{ju}\left(t\right)$ refers to the dimensionless data of positive index $u$ for transfer point $j$ in period $t$, given by

$$f_{ju}\left(t\right)={\displaystyle \frac{y_{ju}\left(t\right)}{y\left(t\right)}}$$

(19)

where $y\left(t\right)$ is the average of $y_{ju}\left(t\right)$ for all transfer points and indices at period $t$. In the following, the best and worst index values (i.e., $f_u^{+}$ and $f_u^{-}$) for index $u$ over all objects are calculated with

$$f_u^{+}={max}_t{max}_j{f}_{ju}\left(t\right)$$

(20)

$$f_u^{-}={min}_t{min}_j{f}_{ju}\left(t\right)$$

(21)

The best plan $F^{+}$ and the worst plan $F^{-}$ in all periods of Equations (13) and (14) are given by

$$F^{+}=\left(f_1^{+},f_2^{+},\cdots ,f_u^{+},\dots \right)$$

(22)

$$F^{-}=\left(f_1^{-},f_2^{-},\cdots ,f_u^{-},\dots \right)$$

(23)

where the notations $f_u^{+}$ and $f_u^{-}$ refer to the best and worst values of all periods. With respect to time weight $w\left(t\right)$ of Equation (13), the following non-linear mathematical programming has been proposed in the literature:

$$\mathrm{Mi}n{\sum }_{t}w\left(t\right)\mathit{ln}w\left(t\right)$$

(24)

$$\begin{gathered} \mathrm{s}.\mathrm{t}. \lambda ={\sum }_t{\displaystyle \frac{T-t}{T-1}}\times w\left(t\right), \forall 0\le \lambda \le 1 \\ {\sum }_{t}w\left(t\right)=1, \forall 0\le w\left(t\right)\le 1 \end{gathered}$$

(25)

where $\lambda$ is the time degree. When $\lambda =0.5$, it means that all the periods are of equal importance; when $\lambda <0.5$, the earlier periods are more emphasized; when $\lambda >0.5$, the later periods are of larger weight. Thus, the original time-based dynamic TOPSIS tends to relate weight with time sequence, which is not applicable in transport service, where the period with larger ridership is more likely to be emphasized. Here, the time-sensitive model is revised to be ridership-based for period weight calculation. It is admitted that the indices can be related to ridership, which is employed to reflect the different impact of one transit station or stop to all the transfer points. Thus, although ridership is incorporated into both index weight and index value, the proposed method is reasonable where the period with more transfer passengers is assigned a larger weight. Thus, the above model of Equations (26) and (27) is revised as follows:

$$\mathit{min}{\sum }_{t}w\left(t\right)\mathit{ln}w\left(t\right)$$

(26)

$$\begin{gathered} \mathrm{s}.\mathrm{t}. \lambda ={\sum }_t{\displaystyle \frac{{max}_{t}q\left(t\right)-q\left(t\right)}{{max}_{t}q\left(t\right)}}\times w\left(t\right), \forall 0\le \lambda \le 1 \\ {\sum }_{t}w\left(t\right)=1, \forall 0\le w\left(t\right)\le 1\hspace{1em}\hspace{1em} \end{gathered}$$

(27)

where $q\left(t\right)$ is the total number of transfer passengers in period $t$. The non-linear programming model is solved with a constrained non-linear optimization method based on sequential least squares, to effectively handle the minimization of the entropy-based objective with equality and bound constraints [47,48].

4. Case Study and Results Discussion

4.1. Case Study Area and Transit System

Suzhou, Jiangsu, China, is selected as the case study area due to its comprehensive public transit development. The GDP of Suzhou ranks sixth over all Chinese cities. It has developed a well-integrated public transit network consisting of 5 subway lines and nearly 700 bus lines in 2023. The city’s consistent focus on improving inter-modal transfers makes it an ideal candidate for this study, which may provide us with insights into the inadequacy of the implementations that have been developed with limited theoretical research. These insights may be borrowed by other cities if they share a great scale of bus and transit service or if they are on the way to it.

The case study examines subway-to-bus and bus-to-subway transfers, with the research focusing on a 5 km and 10 km radius surrounding subway stations and bus stops, respectively. These distances correspond to the average travel distances for bus and subway trips in the city. Removing the subway stations that are not connected to a bus service, a total of 128 subway stations and 275 bus stops are included in the analysis. Data was collected over a five-day period from August 12 to 16, 2023. Figure 8 displays the trend of hourly average transfer passengers, with a noticeable peak in subway–bus transfers between 7:00–9:00 AM, and 16:00–19:00 PM, corresponding to the morning and evening rush hours. These patterns highlight the importance of considering time-sensitive variations in transfer quality. Therefore, one day is divided into five periods: morning (5:00 to 7:00), morning peak (7:00 to 9:00), non-peak (9:00 to 16:00), evening peak (16:00 to 19:00), and evening (19:00 to 23:00).

Figure 9 compares the period weight for subway–bus transfers using the revised transfer volume-based model against varying $\lambda$ values. It is observed that, with $\lambda =0.4$, the revised model based on transfer passenger count emphasizes both the weight of the morning and evening peak, different from that with $\lambda =0.2$ where the morning peak is extremely emphasized, and from that with $\lambda =0.6$ where the weight difference is slight. Thus, the proposed model sets $\lambda =0.4$.

4.2. Results Discussion

Figure 10 shows the evaluation results for each transfer point of subway–bus in the different periods. Notably, the subway-to-bus transfer is consistently lower than the transfer quality of bus-to-subway. Figure 11 is the boxplot of inter-modal transfer evaluation, where the dot refers to the mild outliers that are beyond the range of higher quantile plus one and half times of the gap between 25^th and 75^th values. It is observed that the service level of bus-to-subway transfer is significantly higher than that of subway-to-bus with Mann–Whitney U test (i.e., 99% confidence level). Specifically, the inter-modal transfer level of subway-to-bus transfer is averaged to be 0.16, while that of bus-to-subway is of 0.48. This stark difference highlights the need for targeted improvements in subway-to-bus transfer infrastructure and service, especially during high-demand periods. That will help to enhance passenger loyalty to transit services and contribute to bus ridership improvement and subway ridership intensity after the strike of COVID-19 [49,50] and against the rapid development of subways all over the world.

Figure 12 provides a detailed analysis of the indices that influence subway-to-bus transfer quality. The indices exhibit significant variation across different periods, except the indices of the coverage rate of bus stops, count of POIs, and transfer distance. The results imply that the bus service is generally stable with physical attributes, while the operational attributes change significantly. Specifically, the count of transfer runs is quite low in the morning and evening except in the central area. When it comes to the indices of transfer time as well as its reliability, we observe more bus stops with quite long transfer times (≥20 min) and great variability (≥20 min) in the non-peak, which can be explained by many passengers being less sensitive to time delay in the day compared to the early morning and late night. The index of the reliability of transfer lines stays high in the day, and drops significantly in the morning and evening. The analysis on the indices of subway-to-bus transfer emphasizes the importance of coordinating bus services with subways to improve transfer quality and reduce transfer impedance.

Conversely, Figure 13 shows the spatial and temporal distribution of the evaluation indices for bus-to-subway transfers. While bus-to-subway transfers show similar variation, the overall quality is higher. The index of the count of transfer runs is low in the morning, which increases rapidly in the morning peak, drops to around 20 in the inter-peak, and increases to 26.7 in the evening peak. In contrast, the indices of transfer time and its variability show an inverse trend of being reduced significantly in the peak period, while increases in the other periods especially in the morning. The index of the reliability of transfer lines is low in the morning, which boosts to 1 in all the following periods.

Figure 14 shows the index weights for each period. In Figure 14a, subway-to-bus transfer assigns the largest weight to the count of connected POIs, followed by the connected transfer runs, and coverage rate. In contrast, the other evaluation indices share the remaining weight, with the weight of transfer time being the smallest. Figure 14b shows the index weights for bus-to-subway transfer, with the weights of reliability of transfer lines being the smallest. The weight value can be explained with the entropy of each index, where the smaller the entropy, the larger the weight. Combining the above three figures, Figure 15 shows the correspondence of each index and weight across all the periods, where the dot refers to the mild outliers mentioned before. In the following, we come to the recommended implementations for the improvement of subway–bus transfer service.

The above findings extend the results from the existing research on the separate discussion of subway-to-bus and bus-to-subway transfer [33]. Without the effect of special weather such as strong wind, heavy rain, or high temperature on specific dates, the transfer from bus to subway can be more attractive in a reliable style due to the attractive service provided by subways, with respect to service shifts, transfer point coverage rate, and line operation, as well as POI count. That motivates us to pay more attention to subway-to-bus transfer, to better address the bottleneck in mutual interaction between bus and transit.

4.3. Implications and Recommendations

Based on the above evaluation results, multiple implementations can be made to enhance transfer quality. Figure 16 summarizes the multi-faceted countermeasures to the bottlenecks of subway–bus transfer. This allows us to focus on the critical indices in different periods, making improvements in finer detail for enhancing transit efficiency against financial constraints. For subway-to-bus transfer, it is recommended to increase the frequency and extend the operating hours of the connected bus lines, particularly in the morning and evening peak periods. Coordinating bus arrival times with subway schedules can reduce waiting times and improve transfer efficiency. When it comes to bus-to-subway transfer, the implementations are suggested to increase the connected subway runs in the morning, reduce transfer distance, standardize the transfer time and distance in the morning, and extend the subway start time in the morning.

These findings suggest a more targeted approach to improving subway-to-bus and bus-to-subway transfers, tailored to the specific challenges of different periods. Thus, the operator and government may utilize the insights to adjust investments and operation strategies for efficient and integrated transit service.

5. Conclusions

Oriented to bus–subway transfer, this research presents a comprehensive evaluation of subway-to-bus and bus-to-subway transfer quality, employing a revised dynamic TOPSIS method to account for temporal variations in transfer conditions. The evaluation framework is based on three key criteria: transfer benefits, transfer convenience, and transfer reliability. Transfer benefits refer to three indices: the count of transfer runs, the coverage rate of connected stations/stops along the transfer lines, and the count of POIs near the connected stations/stops. Second, transfer convenience is analyzed with respect to transfer time and distance, which are averaged over all the passengers at all the connected stations/stops. Note that transfer time is selected between the 15th and 85th percentiles, to avoid an overly short or long transfer time. Transfer reliability is reflected by the ratio of connected routes to the total connected routes, and the standard deviation of transfer time. Dynamic TOPSIS is revised to comprehensively evaluate the subway–bus transfer system, with the index weight positively related to the transfer volume to weight the transfer points with larger transfer flows more heavily than those with smaller transfer flows.

Our case study validates the proposed subway–bus transfer evaluation with the transit network in Suzhou, China. Referring to the changes in transfer passenger flow, one day is divided into five periods, where the period between 23:00 and 5:00 is excluded from analyses because most transit routes stop operation. It is found that the weights of the subway-to-bus transfer index vary to a larger degree compared to those of bus-to-subway transfer, which can be explained by the larger entropy of subway-to-bus transfer, in comparison to the stable bus-to-subway service over the entire area. The results show that bus-to-subway transfer competes with subway-to-bus transfer thanks to the higher level of connected transit runs and connection reliability and the reduced transfer time fluctuation. Multi-faceted implementations are recommended for the improvement of subway–bus transfer: For subway-to-bus transfer, increase the frequency and extend the service time span of the connected bus lines in the morning and evening, and coordinate bus arrival time with the subway. For bus-to-subway transfer, increase the connected subway runs in the morning, reduce transfer distance, standardize the transfer time and distance in the morning, and extend the subway start time in the morning. The targeting recommendations avoid unnecessary investment and promote the attraction and sustainability of the improvement.

The limitations of the research can be summarized in three main aspects. First, the applicability of the proposed method has yet to be validated for other cities, including bus-dominated cities. Second, the suggestions addressing the barriers to bus–subway transfers require further verification under various real-world constraints. Third, differences in passenger demand across weekdays, weekends, and holidays should be considered to better capture the dynamic nature of transfer behaviors. Future research will focus on the multi-faceted implementations of bidirectional subway–bus transfer, taking into consideration constraints such as finance, maintenance, and fleet availability. Additionally, by incorporating variations in passenger ridership across different days, coordination between subway and bus services can enhance overall transit efficiency, increase ridership, and support the sustainability of the transit system.