Modeling Passengers’ Reserved Time Before High-Speed Rail Departure

Abstract

The pre-departure reserved time (PDRV) for high-speed railway (HSR) passengers, which encompasses all the time between passengers leaving their origin and the departure of the HSR train they are going to take, is a crucial factor in planning intercity travel. Understanding how passengers select their PDRV is not only important for developing effective strategies to improve HSR efficiency but also for optimizing the integration between HSR hubs and urban transportation networks. However, analyzing passenger choice behavior regarding PDRV is complex due to numerous influencing factors. Despite this, few studies have explored how HSR passengers make their PDRV choices. This paper, using Nanjingnan Railway Station as a case study, presents a novel investigation into the PDRV choice behavior of HSR passengers. An integrated latent class model (LCM) and ordered probit model (OPM) are applied to identify the factors affecting passengers’ PDRV choices. The sample data are segmented based on individual characteristics using the LCM, and OPM models are then constructed for each segment to analyze PDRV choice behavior. The results reveal that several factors—such as travel purpose, the number of times passengers used HSR at Nanjingnan Station in the previous year, the duration of HSR travel, the number of companions, feeder trip duration, and departure time—significantly impact PDRV choices. The integrated LCM and OPM approach also uncovers choice heterogeneity among different passenger groups. These insights can serve as a valuable reference for forecasting HSR passenger demand and for designing integrated HSR hubs and urban transport systems.

1. Introduction

China’s high-speed rail (HSR) system has grown remarkably due to rapid urbanization and rising inter-regional travel demand. By the end of 2023, China’s HSR network reached a total operational length of 45,000 km, making it the largest in the world. Due to its efficiency and high-quality service, HSR has become a key mode of transportation for intercity trips, carrying 3.68 billion passengers in 2023. This accounts for over 70% of the country’s total intercity travel.

However, it is important to note that HSR only accounts for a portion of the entire intercity trip. Passengers must still rely on other modes of transportation, such as buses or local trains, to reach the HSR station. Additionally, since HSR operates on a fixed schedule, passengers must allow ample time, known as the pre-departure reserved time (PDRV), to reach the station. PDRV encompasses all the time from when passengers leave their origin until the HSR train departs. This time includes several steps: (1) walking to the initial mode of intracity transport, (2) taking local transport to the HSR hub, (3) walking to the HSR station and completing necessary procedures (such as ticket purchase, entry, and security checks), (4) walking to the ticket check window, (5) waiting at the station, and (6) boarding the train after presenting the ticket.

Currently, most studies concern the in-station time, i.e., the time between when passengers arrive at the station and when the train departs. It overlooks other travel time needed before boarding the train. Therefore, the existing study is insufficient to support the design of effective methods to reduce the total time duration of intercity trips.

Travelers must estimate their intracity travel time to catch the train on time. However, this travel time can be quite unpredictable, influenced by various factors such as the mode of intracity transportation, distance to the station, departure time, walking distance to the transport location, and availability of transportation options. As a result, quantitatively modeling PDRV presents significant challenges. Additionally, factors like travel purpose, individual attributes, travel frequency, and whether the trip occurs on a holiday can also substantially affect travelers’ decisions regarding PDRV.

While research on HSR passengers’ departure time choices is limited, there is a wealth of studies examining the travel behavior of intracity transport users. The factors influencing residents’ travel time choices can be grouped into three main categories: individual characteristics, travel purpose-related elements, and intracity traffic conditions.

Individual characteristics, such as age, income, and occupation, significantly impact travelers’ departure time choice behavior [1,2,3,4]. Family dynamics also play a crucial role in departure time decision-making. Factors like socioeconomic situation [5], family composition and temporal conflicts among family members [6], children’s school journeys [7], and the presence of domestic workers [8] have all been shown to influence departure time choices. Additionally, psychological factors are recognized as significant influences on people’s decisions of departure time [9,10]. Thorhauge et al. found that personal inertia (or habit) has an impact on the choice of departure time, and the inertia in departure time is influenced by gender, the presence of children in the family, and the type of work [11].

Regarding travel purpose-related factors, most research focuses on travel for commuting purposes and concentrates on the temporal flexibility of commuting trips from home to work [12,13,14,15,16,17,18,19]. Another study considers both spatial and temporal flexibility in daily activities [20]. Their results indicate that activities conducted in the morning on the way to work or in the afternoon/evening on the way home can affect morning departure time choices, with individuals being less likely to alter the timing of non-work activities. Additionally, the duration of corresponding activities also affects travelers’ choices of departure time [21]. In leisure travel, Le et al. investigated the departure time choice behavior of travelers who travel for tourism purposes [22].

Regarding intracity traffic-related factors, studies have found that fare, travel time, and crowding can influence departure time choices [23,24,25]. However, the impact of crowding varies; for instance, Li et al. found that commuters were mainly influenced by fare and potential travel time savings, while the effect of underground congestion on departure time choice was not significant [26]. In contrast, the research conducted by Cheng et al. in the Shanghai metro context revealed that high crowding levels led to noticeable shifts in departure times, with individuals showing a stronger aversion to arriving late than to arriving early [27]. Singh et al. observed that rail travelers’ aversion to onboard crowding was inversely related to vaccination rates [28]. In addition, connecting transport may also affect residents’ choice of departure time, as Yu et al. found that reducing the number of shared bikes reduces the earliest departure time for metro commuters, prompting them to depart earlier [29]. Moreover, the type and quality of travel information services were also identified as important factors affecting departure time choices [30,31].

In modeling departure time choice, most researchers employ discrete choice models, including multinomial logit models (MNL) [3], nested logit models (NL) [32], cross-nested models (CNL) [33], mixed logit models (ML) [26,27], and latent class models (LCM) [34]. Traditional generalized extreme value models (i.e., MNL, NL, and CNL) assume that different choice sets are independent. In contrast, both ML and LCM address this limitation by capturing individual preference heterogeneity. LCM accommodates parameter variability among individuals using discrete distributions, unlike the continuous random variation assumed in mixed logit models. Consequently, LCM is statistically more adequate at explaining observed behavioral patterns and phenomena than ML [35].

The literature suggests that current research primarily focuses on departure time choice behavior for intracity commuting, particularly concerning private vehicles, buses, and urban rail systems. Studies on high-speed rail (HSR) departure time choices are very limited. Unlike intracity travel, the choice behavior of PDRV for HSR passengers is very different. It can be impacted by many unique HSR-related factors, such as journey duration, frequency of the train to the destination, the number of companions, etc. Further, as travelers’ preferences are different, it is also important to model the heterogeneity of PDRV for different groups of travelers.

In China, high-speed rail services are distinguished from regular railway services by factors such as ticket pricing, schedule frequency, and operational velocity. HSR services typically feature higher ticket prices, more frequent schedules, and quicker travel times. These attributes make HSR a preferred choice for more affluent travelers who require punctual arrival at their destinations and are more sensitive to time constraints, potentially influencing their travel planning and PDRV. In contrast, regular rail passengers often exhibit greater flexibility and tolerance for uncertainties and delays, placing a lower premium on optimizing travel efficiency than HSR users. Given these considerations, this study selected HSR passengers as the primary research object.

To address this problem, this study uses Nanjingnan Station as a case study to explore the factors influencing the PDRV of HSR passengers from three impact factor categories: individual socioeconomic characteristics, intracity transport-related attributes, and HSR-related attributes. Initially, the LCM is employed to segment the dataset based on passenger attributes, followed by the application of the MNL model to investigate the choice behavior of different passenger subsets regarding PDRVs. Integrating LCM with MNL models provides a more flexible approach to identifying and interpreting different subgroups within the data. This integration also allows for comparisons between various choices, enhancing the model’s interpretability and potentially uncovering choice characteristics not captured by the overall dataset. The findings reveal that variables such as travel purpose, frequency of HSR trips from Nanjingnan Rail Station in the previous year, HSR travel time, number of companions, feeder trip duration, and peak hour departures significantly impact pre-departure reserved time choices. Notably, there is choice heterogeneity between the segmented dataset and the overall dataset.

The remainder of the paper is structured as follows: The next section explicitly discusses the data collected for the survey and the design of the variables. Following that, the methodology used in this study is introduced, including latent class analysis and the MNL model. The penultimate section presents the estimation results and discussion, and the final section concludes the research.

2. Survey Design and Data Collection

Considering that the revealed preference (RP) survey can reflect the actual situation of passengers on the current trip, a preliminary RP survey was developed, which included the socioeconomic and travel attributes of HSR passengers. The survey was conducted in two phases: the initial phase took place on 15 January and 20 January 2024, and the subsequent phase occurred from 11–15 November 2024. Both instances of data collection were carried out at Nanjingnan Station. Nanjingnan Station is the largest transport hub in East China, with a considerable volume of passenger traffic and many railway lines converging at the station.

The scope of the survey respondents was set as the HSR travelers whose origin location is within the administrative division of Nanjing. To ensure that respondents met the specified criteria, the survey questionnaire requested the departure point of each respondent, and questionnaires that met the specified criteria would be retained. Furthermore, to accommodate the schedules of passengers pressed for time, a digital questionnaire was also developed, and a QR code was generated for passengers to scan and complete. A total of 525 questionnaires were collected, out of which 436 were valid, resulting in a validity rate of 83%. The individual and trip attributes of the passengers obtained through the survey and the distribution of their departure points are shown in

Table 1. Descriptive Statistics of the Survey Data.

Attributes	Levels	Proportion (%)
Gender	Male	41.51
	Female	58.49
Age	18–30	26.37
	31–40	29.60
	41–50	24.08
	>51	19.95
Education	High school and below	4.82
	Undergraduate	63.99
	Postgraduate and above	31.19
Occupation	Public department/Enterprise employee	49.08
	Others	50.92
Purpose	Work	23.85
	Leisure	48.62
	Education	16.28
	Others	8.26
Monthly Income	<3000¥	12.16
	3001–5000¥	24.77
	5001–8000¥	23.39
	8001–10,000¥	19.72
	>10,001¥	19.95
Times of taking HSR in last year	<3 times	38.80
	4–6 times	31.05
	7–9 times	16.14
	>10 times	13.02
Departure Time Period	Peak (7:00–9:30, 17:00–19:30)	36.93
	Flat (Other)	55.05
	Night (22:00–6:00 the next day)	8.02
Travel Mode	Private car	8.32
	Taxi	18.34
	Metro	73.34
In-Vehicle Time (Time spent on transportation during the feeder trip)	Mean: 48.64 min
Number of companions	Travel alone	42.43
	Trave with one person	31.19
	Travel with two people or more	26.38
On Board Time	<3 h	55.28
	4–6 h	31.13
	7–9 h	12.21
	>10 h	1.38

and Figure 1, respectively.

As illustrated in Table 1, in terms of socioeconomic characteristics, most of the respondents are women, and there is a high number of individuals aged between 18 and 40. Nearly 75% of the sample population has achieved a college or bachelor’s degree, and the distribution of income levels is relatively even. Moreover, most travelers have taken the HSR train from the Nanjingnan Railway Station less than six times in the past year. Regarding travel attributes, most travelers leave at off-peak times and use public transportation as the main mode for intra-city connections. The onboard time of passengers is often less than 6 h. In addition, as can be observed in Figure 1, most travelers’ origin locations are within a 40 km range from Nanjingnan Railway Station. The distribution of PDRV is classified into four categories: T1 for pre-departure reserved time within 1 h, T2 for 1 to 1.5 h, T3 for 1.5 to 2 h, and T4 for above 2 h.

3. Methodology

3.1. Latent Class Analysis

Latent class analysis (LCA) is a statistical model-based approach that can classify datasets into homogeneous subsets by maximizing the heterogeneity between classes [36]. We suppose that the total number of variables used for latent class segmentation is $J$, where $1\le j\le J$. All categorical variables are used to classify the entire dataset into $Q$ categories. Then the probability of complete response to each categorical variable when individual $i$ belongs to potential category $q\left(q\in Q\right)$ can be calculated as:

$$\mathrm{P}\left(Y_i|class=q\right)={\displaystyle \prod }_{j=1}^J\mathrm{P}\left(y_{ij}|class=q\right)={\displaystyle \prod }_{j=1}^J{\displaystyle \prod }_{r_j=1}^{R_j}{\theta }_{qjr}^{f\left(y_{ij}=r_j\right)}$$

(1)

where, $Y_i$ is the set of categorical variables for individual $i$. $r_j$ denotes the level value of each categorical variable $j\left(r_j=1,2,3,\dots ,R_j\right)$. ${\theta }_{qjr}$ represents the conditional probability that the value of the $j$th categorical variable for individual $i$ belonging to latent class $q$ is $r_j$. $f\left(y_{ij}=r_j\right)$ denotes the indicator function that equals 1 when $y_{ij}=r_j$, and 0 otherwise.

The prior probability that passenger $i$ belongs to latent class $q$ is as follows:

$${\pi }_{iq}={\displaystyle \frac{\exp \left({\theta }_q^T{\mathit{z}}_i\right)}{{\sum }_{q=1}^Q\exp \left({\theta }_q^T{\mathit{z}}_i\right)}}$$

(2)

where, ${\mathit{z}}_i$ denotes the attribute variable with homogeneity among different individuals in class $q$, and its corresponding parameter vector is ${\theta }_q$.

According to Bayesian theory, the probability of response to $Y_i$ is:

$$\mathrm{P}\left(Y_i\right)={\displaystyle \sum }_{q=1}^Q{\pi }_{iq}\times \mathrm{P}\left(Y_i=j|class=q\right)$$

(3)

Akaike Information Criterion (AIC) and Bayesian Information Criteria (BIC) are used to determine the best number of classes, their respective functions are as follows:

$$AIC=-2\mathsf{\Lambda }+2K$$

(4)

$$BIC=-2\mathsf{\Lambda }+\left(\ln \left(N\right)\right)\times K$$

(5)

where $\mathsf{\Lambda }$ is the maximum log-likelihood of the model, $K$ denotes the number of parameters in the model, and $N$ refers to the sample size.

3.2. Ordered Probit Model

The analysis above indicated that the PDRV is an ordinal variable, hence an ordered probit model can be employed to analyze the factors influencing the passengers’ choice behavior of PDRV and their heterogeneity. The Ordered Probit Model is derived by defining an unobserved variable, $Z_n$, that is used as a basis for modeling the ordinal ranking of data. This unobserved variable is typically specified as the linear combination of the vector of independent variables $X_n$ that affect the decision of passenger $n$ and the error disturbance term ${\epsilon }_n$, as shown in Equation (6):

$$Z_n=\beta X_n+{\epsilon }_n$$

(6)

where, $\beta$ is the matrix of parameter estimates corresponding to the vector of independent variables $X_n$, and ${\epsilon }_n$ follows a standard normal distribution.

Then, convert $y$, the ordinal variable representing the duration of passengers’ early departure, from text to numerical form to represent the degree of time length, as shown in

Table 2. Variable Transformation Table.

PDRV Levels	Time Interval
1	T1: Less than 1 h
2	T2: 1–1.5 h
3	T3: 1.5–2 h
4	T4: More than 2 h

.

Using Equation (6), observed ordinal data, $y$, for each observation are defined as:

$$y=\left\{\begin{array}{c}1,Z_n⩽{\mu }_1\hfill \\ 2,{\mu }_1<Z_n⩽{\mu }_2\hfill \\ 3,{\mu }_2<Z_n⩽{\mu }_3\hfill \\ 4,Z_n>{\mu }_3\hfill \end{array}\right.$$

(7)

where, ${\mu }_1,{\mu }_2,{\mu }_3$ are the estimated parameters for the cut-off points that determine the passengers’ pre-departure reserved time.

Then, the probability $P_y$ that passenger $n$ chooses a certain level of PDRV $y$ is as follows:

$$P_y=\left\{\begin{array}{cc}\mathsf{\Phi }\left({\mu }_1-\beta X_n\right),\hfill & y=1 \hfill \\ \mathsf{\Phi }\left({\mu }_2-\beta X_n\right)-\mathsf{\Phi }\left({\mu }_1-\beta X_n\right),\hfill & y=2\hfill \\ \mathsf{\Phi }\left({\mu }_3-\beta X_n\right)-\mathsf{\Phi }\left({\mu }_2-\beta X_n\right),\hfill & y=3\hfill \\ 1-\mathsf{\Phi }\left({\mu }_3-\beta X_n\right),\hfill & y=4\hfill \end{array}\right.$$

(8)

where, $\mathsf{\Phi }$ represents the cumulative distribution function of the standard normal distribution.

3.3. Variable Design

Most of the independent variables in the model were discrete variables. To ensure the interpretability of the results, the discrete variables in the independent variables were processed and transformed into dummy variables in this paper. For ordinal categorical variables, values were assigned to distinct categories based on their classification level. When dealing with unordered categorical variables, each category in the independent variables was set as a dummy variable, with the values of each dummy variable set to 1 and 0. Then, a category would be chosen from all the categories as the reference group. The ultimate arrangement of the model variable list is presented in

Table 3. Variable Design Results.

Attribute	Variable	Description
Gender	Gend	Male = 1, Female = 0
Age	Age	Marked as 1–4 based on the levels in Table 1
Education	Edu	Marked as 1–3 based on the levels in Table 1
Occupation	Occu	Public department/Enterprise employee = 1, Others = 0
Purpose		Reference = Education and Others
Work	Work	Purpa = 1 if the purpose is work, and 0 otherwise.
Leisure	Leisure	Purpb = 1 if the purpose is leisure, and 0 otherwise.
Education	Education
Others	Others
Monthly Income	Inc	Marked as 1–5 based on the levels in Table 1
Times of taking HSR in last year	Tts	Marked as 1–4 based on the levels in Table 1
Departure Time Period		Reference = Others
Peak	Peak	Peak = 1 if the departure moment is during the peak hours, and 0 otherwise.
Travel Mode		Reference = Taxi
Private car	Private car	Privatecar = 1 if traveling by private car and 0 otherwise
Taxi	Taxi
Metro	Metro	Metro = 1 if traveling by metro and 0 otherwise
In-Vehicle Time	Invt	Continuous variable
Number of companions	Partner	Marked as 1–3 based on the levels in Table 1
On Board Time	Obt	Marked as 1–3 based on the levels in Table 1

.

To avoid multicollinearity, a correlation analysis was performed, and the results were visualized in a heat map. As shown in Figure 2, all correlation coefficients between variables are below 0.7. Therefore, all variables can be retained for the modeling process.

4. Results and Discussion

4.1. Latent Class Analysis Results

This paper selected personal attributes such as age, education level, monthly income, occupation, and the number of times passengers used HSR at Nanjingnan Rail Station last year as categorical variables for latent class analysis. To determine the optimal number of latent classes, models with 1 to 5 classes were tested. The Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) for each model were calculated and compared, as shown in

Table 4. Indicators for Different Number of Classes.

Number of Classes	1	2	3	4	5
AIC	5100.89	4751.60	4607.87	4562.18	4558.21
BIC	5157.98	4860.55	4903.69	4954.85	5006.75

.

Based on the results in Table 3, the model with the lowest BIC value was selected as the best model. Therefore, this paper adopts the two-latent-class model for further analysis. The classification results of passengers and the characteristics of the different latent classes are presented in

Table 5. Distribution of Categorical Variables in Each Class.

Variables	Levels	Class 1	Class 2
Age	18–30	0.07	0.60
	31–40	0.36	0.19
	41–50	0.31	0.12
	>51	0.26	0.09
Edu	High school and below	0	0.13
	Undergraduate	0.56	0.78
	Postgraduate and above	0.44	0.09
Occu	Public department/Enterprise employee	0.58	0.34
	Others	0.42	0.66
Inc	<3000¥	0	0.33
	3001–5000¥	0.22	0.30
	5001–8000¥	0.23	0.24
	8001–10,000¥	0.24	0.11
	>10,001¥	0.31	0.01
Tts	<3 times	0.01	0.48
	4–6 times	0.34	0.32
	7–9 times	0.32	0.12
	>10 times	0.19	0.08
Number of observations		278	158

.

The distribution of categorical variables was used to define and characterize each class:

Class 1: Passengers in this group are predominantly over 30 years old, with the majority holding at least an undergraduate degree. Over 50% earn a monthly income exceeding 8000¥, and half traveled by HSR at Nanjingnan Station more than seven times last year. Therefore, Class 1 can be labeled as a high-income group with high travel frequency.

Class 2: In this group, 40% of passengers are under 30. Most have an undergraduate degree or lower and earn a monthly income of less than 5000¥. Furthermore, 48% of passengers used HSR at Nanjingnan Railway Station fewer than three times last year. Thus, Class 2 can be labeled as a low-income group with low travel frequency.

4.2. Ordered Probit Model Results

Based on the results of the latent class analysis, three OPM models were developed to explore further the heterogeneity within the entire dataset: Class 1, and Class 2. The estimation results for all models are presented in

Table 6. Estimation results.

Variable	Overall Dataset		Class 1		Class 2
	Coef.	Z-Value	Coef.	Z-Value	Coef.	Z-Value
Gend	−0.087	−0.77	−0.02	−0.13	−0.092	−0.44
Age	0.054	0.89	0.122	1.36	−0.131	−1.04
Edu	−0.086	−0.77	−0.068	−0.46	0.184	0.71
Occu	−0.063	−0.54	0.019	0.12	−0.621 **	−2.42
Purpose
Work	−0.507 ***	−3.07	−0.886 ***	−4.18	−4.286	−0.03
Lesiure	0.744 ***	5.45	0.503 **	2.45	0.949 ***	4.22
Inc	0.036	0.74	0.028	0.42	0.321 **	2.54
Tts	−0.353 ***	−5.95	−0.261 ***	−3.19	−0.548 ***	−4.34
Peak hours	0.391 ***	3.39	0.272 *	1.86	1.272 ***	5.07
Travel Mode
Private car	0.164	1.11	0.227	1.31	−0.181	−0.36
Metro	−0.021	−0.14	−0.095	−0.45	−0.037	−0.15
Invt	0.029 ***	9.29	0.045 ***	9.66	0.017 ***	3.36
Partner	0.447 ***	5.92	0.381 ***	4.06	1.058 ***	5.73
Obt	0.234 ***	3.2	0.097 ***	2.82	0.705 ***	4.36
${\mu }_1$	0.567		1.335		1.791
${\mu }_2$	2.174		3.407		3.148
${\mu }_3$	3.66		5.657		4.322
Pseudo R2	0.232		0.311		0.315

***, **, and * indicate significance levels less than 0.01, 0.05, and 0.1, respectively.

.

The results presented in Table 5 show that the signs and significance of parameter estimates for the variables Leisure, Times of taking HSR in last year (Tts), Peak Hours, In-vehicle time (Invt), Partner and Obt are consistent across the overall dataset, Class 1, and Class 2, indicating that the individual impact of these variables on passengers’ choice of PDRV is similar across different segmentations, although the specific influence exerted by each variable may vary. In contrast, the variables Work, Occupation, and Income exhibit different effects on PDRV selection across the two latent classes, suggesting that the latent class model effectively uncovers the underlying patterns in passengers’ PDRV behavior. Additionally, compared to the overall dataset, the Pseudo R² values for the post-classification models are higher, indicating that the latent class model with OPM better fits the data.

The Work variable shows significant negative coefficients in both the overall dataset and Class 1. This suggests that an increase in Purpa tends to push the dependent variable towards selecting lower categories (such as PDRV = 1 or PDRV = 2). This indicates that passengers traveling for work are more likely to opt for shorter PDRVs because they prioritize efficiency and are more experienced with HSR travel. However, in class 2, the work variable does not have a significant impact on the choice of PDRV. This indicates that for individuals with low income and low travel frequency, travel for work does not significantly affect the time they reserve before departure. Conversely, the Leisure variable (leisure travel) consistently shows significant positive coefficients, implying that leisure travelers are more likely to allocate extra time before departure to enhance the comfort and enjoyment of their journey. Another possible reason is that leisure travelers may wish to engage in activities such as shopping and dining at HSR stations. Consequently, they reserve more time before departure to ensure they have ample opportunity to partake in various activities in the station.

The Obt (Time required for HSR travel) variable consistently exhibits significant positive parameter estimates across all models, indicating that as the travel time for HSR increases, passengers are more likely to allocate additional time for their journey. Longer HSR travel durations are often associated with greater distances between the train station and the destination, which means fewer train services are available. Consequently, in the event of a missed train, the probability of obtaining a substitute service is lower, thereby rendering the consequences of missing the train difficult to remedy. To mitigate these risks, passengers are inclined to reserve more time. The absolute value of the coefficient for the Obt variable among passengers in Class 2 (0.705) is much larger than that for Class 1 and the overall group. This suggests that Class 2 travelers are more risk-averse and are willing to allocate significantly more time to account for potential delays or uncertainties.

The variable Partner shows significant positive coefficients for both the overall sample, Class 1 and Class 2, indicating that passengers are more likely to allocate additional time before departure as the number of companions increases. This could be due to the complexities of coordinating multiple individuals, the increased likelihood of delays caused by latecomers, or heightened anxiety about ensuring all companions are ready to depart on time. Social activities, such as conversations or taking photos, may also extend the overall transition time, making passengers more inclined to choose longer PDRVs when traveling with others.

The coefficient for Tts (Times traveled on HSR in the last year) shows a consistent and significant negative trend across all models. This suggests that passengers with more frequent HSR travel experience tend to allocate shorter PDRVs. As travelers become more familiar with the intercity travel process, they feel more confident in managing the time required for boarding and station procedures, which leads them to reserve less time in advance.

The coefficient for Peak (Peak travel times) indicates that passengers departing during peak hours are more sensitive to PDRV and are more inclined to allocate more time for their travel, regardless of their income level and travel frequency category. This is understandable, as peak-hour travel typically involves longer intra-city transit times and higher uncertainty regarding urban transfer times, prompting passengers to allocate more time to ensure they can catch their train. Class 2 passengers show even higher coefficients for Peak (1.272). This suggests that low-income, infrequent travelers are particularly cautious during peak periods and are more likely to extend their reserved time to account for potential delays.

The variable Invt (In-vehicle time) positively impacts the choice of longer PDRVs. This can be attributed to two factors: (1) the time spent traveling to the HSR station contributes to the overall trip duration, and (2) as in-vehicle time increases, passengers experience more uncertainty about the duration of their feeder trips. Consequently, they tend to leave earlier to ensure sufficient time to catch their train. This reflects the risk-averse behavior of passengers when faced with longer or more unpredictable journeys.

In summary, these findings highlight the diverse factors influencing passengers’ PDRV choices and underscore the effectiveness of the latent class model in revealing the distinct preferences of different passenger groups.

4.3. Suggestions for Minimizing Travelers’ Pre-Departure Reserved Time

The research findings reveal that various factors have a substantial impact on travelers’ pre-departure reserved time (PDRV). This paper, therefore, provides a set of detailed recommendations to reduce the time allocated for pre-departure activities and to improve the convenience of accessing high-speed rail (HSR) services.

• Purpose of Travel: Occupational vs. Leisure

Occupational travelers typically allocate less time before departure compared to leisure travelers, who tend to reserve more time. Based on these characteristics, it is suggested that major cities and tourist hotspots implement real-time passenger flow monitoring systems at high volumes of critical bus and subway stations. Strategic adjustments to bus routes, schedules, or the provision of direct transit services could alleviate pressure on urban transport systems and decrease PDRV.

2.

HSR Travel Frequency and Station Familiarity

Frequent HSR travelers exhibit a higher familiarity with HSR stations. Conversely, unfamiliarity with station layouts and procedures can lead to extended PDRVs. Based on this finding, three feasible recommendations are proposed. Firstly, mobile assistance personnel should be deployed at HSR stations to guide passengers, particularly those unfamiliar with the layout of the station, in navigating the station more efficiently. Secondly, optimize security procedures and the inbound flow to reduce the time spent at checkpoints, which is a significant factor contributing to PDRV for first-time travelers. Thirdly, collaboration with navigation apps to provide detailed routes and walking directions is recommended for large stations with complex routes to help passengers reduce navigational uncertainty and better understand their connection routes.

3.

In-Vehicle Time and Public Transport Efficiency

In-vehicle time is the most influential factor on PDRV. For smaller cities, increasing the efficiency of public transport by adjusting service frequency and reducing transfer requirements can decrease PDRV. In larger cities, where service improvements are more complex, providing accurate travel time estimates can help manage passenger expectations and reduce uncertainty, thereby aiding in trip planning and mitigating concerns about delays. Additionally, implementing on-demand public bus services within a geo-fenced area, allowing commuters to book rides through a mobile application, can reduce PDRV by offering more direct and personalized connections to HSR stations.

By focusing on these critical areas—travel purpose, station familiarity, and in-vehicle time—HSR operators and urban planners can enhance travel process efficiency, minimize pre-departure time, and improve the overall convenience and experience of HSR connectivity.

5. Conclusions

This study aimed to identify the factors influencing high-speed rail (HSR) passengers’ pre-departure reserved time (PDRV) choices, using Nanjingnan Railway Station as a case study. A revealed preference survey was conducted with HSR passengers traveling from Nanjing to collect data on their socioeconomic characteristics, intra-city travel-related attributes, and HSR travel-related factors. Latent class analysis (LCA) was used to account for unobserved heterogeneity among passengers, dividing the dataset into two subgroups: one with high income and medium-high travel frequency, and another with low income and low travel frequency. Subsequently, ordered probit models (OPM) were developed for each latent class and the entire sample to further explore this heterogeneity. The main findings are as follows:

• Compared to the traditional OPM model, the combined LCA and OPM model demonstrated superior fit and highlighted heterogeneity in the choice behaviors of different traveler groups.
• The purpose of travel significantly influences PDRV choices. Travelers on business tend to opt for shorter PDRVs, while those traveling for leisure tend to prefer longer PDRVs. Additionally, lower-income, infrequent HSR travelers are less responsive to work-related travel demands.
• Among the passenger attributes, the frequency of HSR travel in the past year has a significant impact on PDRV choices. Experienced travelers who frequently use HSR tend to opt for shorter PDRVs, suggesting that familiarity with the station and processes leads to greater efficiency in time management.
• Among the intercity traffic-related variables, the duration of feeder trips significantly positively affects travelers’ PDRV choices. The longer it takes travelers to reach the high-speed rail station from their origins, the more likely they will choose a longer PDRV. Also, when travel occurs during peak periods, passengers allocate more time for pre-departure activities.
• Among the HSR travel-related variables, the time required for HSR travel significantly influences the selection of longer PDRVs. That is, the time travelers reserve before departure increases with the duration of the high-speed rail journey required for their trip. Furthermore, when multiple companions accompany travelers, they are more inclined to choose a longer PDRV.

Limitations and Future Research

One of the main limitations of this study is the survey design. While the revealed preference (RP) survey effectively reflects real-life choices, gathering a large sample requires considerable time and effort, which limits the sample size. Future research could explore combining mobile and internet-based survey methods, utilizing personal travel experience data as the baseline for experimental attributes. This approach could enhance both the efficiency and quality of data collection while also providing a more user-oriented, customized questionnaire scenario.

Additionally, this study primarily focuses on the impact of socioeconomic characteristics, intracity transport-related attributes, and HSR-related attributes on pre-departure reserved time choice. However, the analysis did not include psychological factors, such as passengers’ attitudes toward time management or their perceptions of connecting transportation and HSR services. Future research could incorporate these psychological factors, enabling a more comprehensive understanding of the multidimensional influences on PDRV choices.

Furthermore, this study lacks longitudinal data to analyze how passenger preferences evolve with infrastructure construction and the increasing familiarity of passengers with high-speed rail stations. Therefore, future work will involve collecting and analyzing longitudinal data to gain a deeper understanding of how passenger preferences change in response to infrastructure upgrades and as passengers become more familiar with the high-speed rail system. We plan to fill this research gap by conducting regular surveys or tracking the preference changes of the same group of passengers at different time points. This approach will help us more accurately predict future trends and provide data support for continuously improving high-speed rail services.

Finally, this paper lacked consideration of passenger expectations during the survey design process. Passengers’ expected travel time from their origin to the HSR station can reflect their aggressive or conservative personality. In addition, the gap between passengers’ expectations of their travel time and actual PDRV can also reflect the reliability of current urban connecting transportation. Therefore, in future research, we plan to include passengers’ expectations in the content of the questionnaire survey. This will provide a more comprehensive understanding of the decision-making process and help develop a more holistic approach to optimizing high-speed rail services.

The findings from this study contribute to a deeper understanding of HSR passengers’ departure time choices and provide valuable theoretical insights for optimizing the connection between high-speed rail and urban transportation systems. The study’s outcomes can help urban transport departments improve service levels based on the specific travel characteristics of HSR passengers, ultimately better meeting their needs.

To further enhance understanding of pre-departure reserved time behavior, future research should examine the interactions between different variables and consider the inclusion of additional factors such as psychological influences and perceptions of service quality. This would allow for a more nuanced, multidimensional analysis of the factors driving PDRV choices among HSR passengers.