Dynamic Minimum Service Level of Demand–Responsive Transit: A Prospect Theory Approach

Abstract

Demand–responsive transit (DRT) provides flexible, user-centric services and is gaining attention as a solution to modern transportation challenges. Establishing a minimum service level is crucial for its effectiveness, yet existing methods rely on supplier-centric indicators that fail to reflect user psychology and the flexible nature of DRT. To address this, this study applied a prospect theory from behavioral economics and used logistic regression analysis of stated preference survey data to determine minimum service levels based on user perceptions. To account for regional variations, we classified user groups based on primary transportation mode, travel purpose, and age, proposing dynamic minimum service levels tailored to each group. Additionally, using the maximum likelihood estimation method, we estimated value function parameters for the prospect theory, allowing us to analyze users’ loss aversion and sensitivity to DRT services. The findings indicated that users would accept higher fares for DRT than for conventional public transportation, provided it offers shorter travel times. Sensitivity to service levels varied across user groups, highlighting the need for differentiated policies. This study provides insights to optimize DRT operations, improve user satisfaction, and guide policies that reflect regional and demographic characteristics, enhancing the efficiency and effectiveness of DRT services.

1. Introduction

In modern society, the issue of underserved transportation areas is becoming increasingly severe. This is not only due to budget constraints for operating routes in remote areas and inadequate public transportation infrastructure but also because, even in large cities and newly developed urban areas, transportation infrastructure fails to keep pace with population growth. As a result, dependence on private vehicles continues to rise. Urbanization and the increasing reliance on private vehicles have made this a global transportation challenge.

To alleviate road congestion, a modal shift from private vehicles to public transportation is essential [1]. However, conventional public transportation systems often prove inefficient due to transfer difficulties and first-mile/last-mile accessibility issues—key factors discouraging private vehicle users from making the switch. A 2023 survey by the Korea Transportation Safety Authority found that the average transit transfer time on weekdays (8.3 min per transfer) accounts for approximately 26.4% of the total average travel time (31.5 min per trip). Additionally, the average public transport access time in the Seoul region is 15.4 min per day, highlighting the inefficiency of public transportation. This issue presents a growing challenge for urban transportation systems worldwide as they strive to enhance accessibility and efficiency. At the same time, traditional fixed-route public transportation services are struggling to accommodate passengers’ increasingly personalized travel demands [2].

To overcome the inefficiencies of traditional public transportation, demand–responsive transport (DRT) has gained attention as an innovative public transport service [3,4,5]. Initially, DRT was considered a form of paratransit, providing access to mass transit networks such as train stations from low-density suburban areas [6,7]. It was also studied as a solution for transportation-disadvantaged groups, including individuals with disabilities, the elderly, and students [8].

Unlike traditional transit systems, DRT does not operate on fixed routes or schedules but dynamically adjusts routes and stops based on user requests. This door-to-door approach effectively addresses issues related to access time, waiting time, and transfers, positioning DRT as an intermediate solution between buses and taxis [9]. By offering flexible public transit, DRT presents a promising strategy to overcome the limitations of traditional public transport and reduce private vehicle use [10]. Its high adaptability contributes significantly to decreasing reliance on private vehicles [11,12].

For DRT to function effectively as public transportation, establishing a minimum service level is essential. The minimum service level (MSL) defines the baseline public transit service that must be provided, ensuring mobility rights in underserved areas, enhancing social equity, and promoting environmental sustainability. Additionally, it guarantees a basic quality of service that meets user expectations, ensuring a minimum level of satisfaction while supporting essential social functions. Setting a minimum service level is crucial for sustainable operations, as providing services below cost indefinitely is not feasible [13].

Methods for calculating the minimum service level for public transportation vary by country and region but are typically based on supplier-centric metrics, such as operating frequency, number of routes, stop spacing, operating hours, and stop accessibility, as presented in the Transit Capacity and Quality of Service Manual, Third Edition by the Transportation Research Board [14]. However, these methods fail to account for user-experienced factors such as travel cost, travel time, and access time. Additionally, metrics designed for fixed-route public transportation do not adequately capture the flexible nature of DRT, which allows for customizable stops and routes [15]. Furthermore, when introducing a new public transportation service, the lack of initial data and reliance on traditional demand–supply methods limit the ability to incorporate user experience and psychographic factors [16].

A review of previous studies on DRT services indicates that [16,17] analyzed service determinants affecting DRT users to assess its performance and suggest improvements, emphasizing the need for clear criteria to support DRT expansion. However, most studies focused on operational costs and environmental impacts, with limited systematic research on user psychology and service quality [18,19,20].

To address this limitation, a user-centric calculation method that applies a behavioral economics approach to setting a minimum service level for DRT is needed. Behavioral economics provides a valuable framework for understanding user psychology and decision-making processes, enabling the design of policies that effectively guide user behavior [21]. As behavioral economics has gained recognition as a key tool in policy design, incorporating user psychology has become increasingly important in the transportation field [22].

Among the major theories in behavioral economics, prospect theory has been particularly successful in explaining bounded rationality and user attitudes [23]. It has been widely applied to modeling travel route and transport mode selection [24,25,26,27]. For instance, ref. [28] conducted an empirical study on user psychology by applying prospect theory to route selection decision-making. However, most transportation studies using prospect theory focus on route and mode selection, with limited research on its application to DRT and minimum service level calculation.

Therefore, this study aimed to identify the factors that users consider most important when using DRT, establishing criteria for determining the minimum service level, and proposed a user-centric minimum service level based on prospect theory from behavioral economics. Additionally, we analyzed sensitivity to service level changes and loss aversion, providing insights into prioritizing DRT policy making.

Since DRT operations and effectiveness vary based on local characteristics, demand patterns, and traffic environments, it is essential to calculate a minimum service level that accounts for group-specific characteristics [29]. While several studies have examined DRT in rural and urban areas—emphasizing the need to consider local conditions and regulations for successful implementation [30]—few have focused on dynamic transport mode selection tailored to different user groups [31]. Therefore, this study proposed a dynamic minimum service level customized for each user group within each region, ensuring that local resident characteristics are adequately reflected in the service level calculations.

This study differentiates itself from previous research by analyzing sensitivity to service changes and identifying priority improvement factors. Additionally, it addresses the limitations of conventional infrastructure-based estimation methods by incorporating user psychology to propose a user-centered minimum service level. By introducing a dynamic minimum service level tailored to each group based on local characteristics, this study overcomes the shortcomings of prior studies and provides practical contributions to policy development.

2. Materials and Methods

2.1. Prospect Theory

Prospect theory, as proposed by Daniel Kahneman and Amos Tversky in 1979 [32], is a foundational theory in behavioral economics and is widely regarded as one of the most influential models of human decision-making [33,34,35]. This theory posits that people experience losses more intensely than equivalent gains and that decision-making is based on changes in value relative to a reference point rather than absolute valuations [36,37,38]. Unlike traditional expected utility theory, which assumes that individuals make rational choices, prospect theory acknowledges that people are influenced by psychological biases and do not always act rationally. These deviations from rationality have been applied in consensus-reaching processes (CRPs) and various decision-making models [39,40,41,42,43], offering a rational framework for understanding decision-making behavior under uncertainty [44].

Reference Dependence: People evaluate gains and losses relative to a specific reference point rather than in absolute terms [45]. For example, users may perceive a new public transportation service as a gain or loss based on their expected level of service.

Diminishing Sensitivity: The perceived impact of a change is stronger initially but decreases as the magnitude of the change increases [46]. This phenomenon explains how the perceived differences in gains and losses diminish over time. For example, in stock investing, a 5% loss in Stock A on the first day may feel significant. However, if an investor experiences an additional 5% loss in Stock B, which is already down 50%, they are likely to perceive it with less concern.

Loss Aversion: People are more sensitive to losses than to equivalent gains, meaning the psychological impact of a loss is greater than that of a comparable gain. For example, the anxiety and stress from a 5% loss in a stock investment are typically more intense than the satisfaction from a 5% gain.

According to Tversky and Kahneman [47], a value function can be used to represent the psychological evaluation of gains and losses based on these three principles (Figure 1).

According to prospect theory, $\nu \left(x\right)$ represents the psychological value of $x$ relative to a reference point, while $\lambda$ is the loss aversion coefficient. For losses and gains of the same value, losses are perceived as $\lambda$ times more sensitive than gains, explaining loss aversion—a key principle of prospect theory. The parameters $\alpha ,\beta$ represent sensitivity to outcomes in the gain and loss regions, respectively. Typically 0 $<\alpha , \beta <1$, indicating that the perceived sensitivity to additional losses or gains diminishes as their magnitude increases.

Tversky and Kahneman, who proposed the prospect theory, estimated the parameter values in a typical setting to be $\alpha ,\beta =0.88$, $\lambda =2.25$, which means that people are about 2.25 times more sensitive to losses than to gains, and that the sensitivities to losses and gains are roughly similar [47].

2.2. Research Procedure

To estimate the minimum service level of DRT and analyze user loss aversion and sensitivity, this study employed a two-step analysis.

First, a Stated Preference (SP) survey was conducted to assess the importance of various DRT service attributes and user acceptance of service changes. SP surveys guide respondents’ choices based on hypothetical scenarios, which may lead to discrepancies between stated and actual behavior. In real-world settings, external factors such as traffic conditions, unexpected delays, and habitual travel patterns can influence decision-making, which may not be fully reflected in SP survey responses. Nevertheless, SP surveys remain a valuable method as they allow for the controlled analysis of various factors individually, making them useful for assessing the relative importance of DRT service attributes and user acceptance. Based on these data, the criteria for calculating the minimum service level were reviewed, and a logistic regression analysis was performed to determine the reference point for the minimum service level using prospect theory.

Next, based on the findings from the first analysis, a second SP survey was designed to estimate the value function parameters of prospect theory using the Maximum Likelihood Estimation (MLE) method. This survey also evaluated user loss aversion and sensitivity to changes relative to the reference point using the derived parameter values.

Finally, the general minimum service level, loss aversion, and sensitivity were estimated for the entire sample. A comparative analysis was then conducted to examine variations in the minimum service level, loss aversion, and sensitivity across different user groups based on their primary transportation mode, travel purpose, and age. The overall research procedure is outlined in Figure 2.

As for the data collection method, this study employed an SP survey, which presents respondents with hypothetical scenarios and asks for their preferences. The survey targeted residents in areas where DRT services are in operation. A total of 600 questionnaires were distributed, and after removing irrational or contradictory responses, data from 504 participants were used for analysis. The adequacy of the sample size (n = 504) was confirmed based on statistical guidelines, ensuring reliable estimations and generalizability.

To determine the minimum service level items, we identified the service factors users consider most important and selected three key items: in-vehicle time, off-vehicle time, and travel cost (fare). The baseline values for evaluating the minimum service level (reference point) were set at 30 min for in-vehicle time, 20 min for off-vehicle time, and KRW 1300 (0.89 USD) for travel cost—reflecting the national public transportation averages in South Korea from the previous year. These values were derived from the 2023 public transportation status survey conducted by the Korea Transportation Safety Authority.

Considering the asymmetric perception of gains and losses suggested by prospect theory, the survey included scenarios where each item was increased or decreased by a specific percentage to assess user acceptance of service level changes. Travel cost was set to increase in 20% increments from 0% to a maximum of +100%, while in-vehicle and off-vehicle times were set to vary in 20% increments from −60% to +60%. Based on these scenarios, we examined whether users accepted the service changes and analyzed the minimum service level (reference point).

To further investigate sensitivity and loss aversion, a second survey was conducted, asking users to rate their satisfaction on a scale of 1 to 10 when travel cost, in-vehicle time, and off-vehicle time changed in 20% increments from −60% to +60% relative to the reference point. This approach accounted for the tendency of users to perceive losses more strongly than equivalent gains. The results were used to quantitatively analyze user loss aversion and sensitivity to service changes.

2.3. Minimum Service Level Calculation Method

In this study, the reference point represents the threshold users use when evaluating a given service level and serves as a critical decision-making factor in prospect theory. Since users perceive changes beyond this point as losses, the reference point defines the lowest acceptable service level, which we identify as the minimum service level.

To estimate this threshold, we conducted a logistic regression analysis using data from the first SP survey to predict the probability of user acceptance of service level changes. The logistic function used is as follows:

$$P\left(Acceptance=1|ServiceLevelChangeRate={\displaystyle \frac{1}{1+e^{-\left({\beta }_0+{\beta }_1·Service Level Change Rate\right)}}}\right)$$

(1)

$P$ represents the probability that users will accept the service at a given change rate. ${\beta }_0$ is the intercept, indicating the initial probability of acceptance when the service level change rate is zero. ${\beta }_1$ represents the change in acceptance probability for each unit increase in the service level change rate. We used a logistic regression model to derive the user acceptance probability curve as a function of the service level change rate (Figure 3). As suggested by prospect theory [33], the slope of this curve changes sharply near the reference point. Therefore, we defined the reference point as the point on the curve where the slope (rate of change in acceptance probability) increases most rapidly. This threshold represents the limit at which users are willing to accept service changes and serves as the criterion for determining the minimum service level. Based on this analysis, we derived a minimum service level that incorporates users’ psychological reactions and acceptance limits, ensuring a more user-centered evaluation of DRT service thresholds.

2.4. Methods of Examining Sensitivity and Loss Aversion

Examining sensitivity to gains and losses, as well as loss aversion, is essential for understanding user psychology and quantitatively assessing the relative importance of service attributes. This process plays a key role in setting priorities for policy design. To achieve this, this study aimed to analyze users’ sensitivity to service changes and their degree of loss aversion using the value function from prospect theory.

Data from the second SP survey were used to estimate the key parameters of the value function—specifically, gain and loss sensitivity and the loss aversion coefficient—to assess how service level changes influence users’ subjective value perceptions. Maximum likelihood estimation was employed to estimate the parameters of the prospect theory value function. The function is as follows:

$$i\left(\alpha ,\beta ,\lambda ,\sigma \right)=-{\displaystyle \frac{n}{2}}\log \left(2\pi {\sigma }^2\right)-{\displaystyle \frac{1}{2{\sigma }^2}}{{\displaystyle \sum }}_{i=1}^n({\left(y_i-v\left(x_i\right)\right)}^2$$

(2)

The equation above represents the log-likelihood function of maximum likelihood estimation (MLE) and is used to estimate the parameters that best describe the observed data. The parameters $\alpha ,\beta ,\lambda$ are derived from the value function of prospect theory, while $\sigma$ is the standard deviation of the error, representing data variability. Here, $x_i$ denotes the predicted value of the model and $y_i$ represents the observed data. Using this equation, we quantitatively measured users’ psychological reactions to service changes and assessed loss aversion by comparing sensitivity to gains and losses. Specifically, we considered the shape of the prospect theory value function to capture the tendency of users to react more strongly to losses than to gains (Figure 4). Through this process, we analyzed how changes in each DRT service attribute influenced user acceptance, identified differences in responses, and derived the optimal service level along with policy implications.

3. Results

3.1. Aggregated Results

To examine the minimum service level criteria in a general context, we analyzed the minimum service level of DRT using the entire dataset without classifying user groups (Figure 5). The results indicate that travel costs are acceptable up to a maximum increase of 57.0% compared to conventional public transportation, while in-vehicle time and off-vehicle time are acceptable up to a decrease of 5.1% and 29.7%, respectively, as shown in

Table 1. Results of reviewing the MSL of demand–responsive transport (aggregated).

Classification	MSL (Allowable Increase/Decrease (%))	Assessment Metrics in Logistic Regression Analysis
		$\mathbf{Pseudo}{\mathit{R}}^2$	Coefficient	ROC-AUC
Travel Cost	$\le +57.0\%$	0.39	−0.057	0.88
In-vehicle Time	$\le -5.1\%$	0.40	−0.050	0.88
Off-vehicle Time	$\le -29.7\%$	0.36	−0.036	0.92

.

The logistic regression model used for the analysis demonstrated strong classification performance, with pseudo-R² values ranging from 0.36 to 0.40 and receiver operating characteristic area under the curve (ROC-AUC) values between 0.88 and 0.92. All variables were statistically significant, with p-values less than 0.001.

Across all service items, users were more sensitive to losses than to gains. As shown in

Table 2. Results of reviewing the sensitivity to the minimum service review items and the loss aversion (aggregated).

Classification	Gain Sensitivity	Loss Sensitivity	Loss Aversion Coefficient	Assessment Metrics of MLE
				$\mathbf{Pseudo}{\mathit{R}}^2$	Log-Likelihood
Travel Cost	0.58	0.73	2.18	0.40	−701
In-vehicle Time	0.46	0.71	1.98	0.43	−661
Off-vehicle Time	0.43	0.85	2.31	0.38	−772

, the loss sensitivity of off-vehicle time (0.85) is nearly double its gain sensitivity (0.43), indicating that users are most affected by increases in off-vehicle time.

A comparison of loss aversion coefficients revealed that off-vehicle time (2.31) had the highest coefficient, followed by travel cost (2.18) and in-vehicle time (1.98) (Figure 6). This suggests that an increase in off-vehicle time has the greatest negative impact on user satisfaction. Compared to the typical gain sensitivity (0.88) and loss aversion coefficient (2.25) reported by Tversky and Kahneman [32], most DRT service items in this study exhibited lower gain sensitivity and loss aversion coefficients.

3.2. Analysis Results by Group

For public transportation services, user demand and sensitivity vary based on primary transportation mode, travel purpose, and age. Relying on a singular average without considering these factors risks overlooking the distinct characteristics and preferences of different user groups across regions. Therefore, a group-based analysis is essential for a more detailed understanding of user psychology, enabling more effective policy design and service delivery.

In this study, which applied prospect theory, it is particularly important to examine differences in sensitivity to gains and losses as well as loss aversion across user groups. This approach allows for the development of tailored policies and service improvements that reflect the specific needs of each group. To achieve this, we categorized users based on their primary transportation mode, main travel purpose, and age. By doing so, we aimed to determine minimum service levels for DRT for each group, compare sensitivity to gains and losses, assess loss aversion, and provide insights for setting policy priorities.

3.2.1. Main Transportation Mode

This study analyzed the minimum service levels of DRT and user sensitivities based on their primary mode of transportation. The acceptable service levels and loss aversion tendencies varied depending on the transportation mode. Notably, private vehicle users exhibited higher loss aversion than public transport users, showing greater resistance to service changes and stronger sensitivity to fluctuations.

Private vehicle users prioritize personal convenience and freedom of movement, making them more likely to perceive service level changes as losses. As shown in

Table 3. Results of reviewing the minimum service levels of DRT (main transportation mode).

Classification		MSL (%)	Assessment Metrics in Logistic Regression Analysis
			$\mathbf{Pseudo}{\mathit{R}}^2$	Coefficient	ROC-AUC
Private Vehicle	Travel Cost	$\le +49.5\%$	0.40	−0.061	0.91
	In-vehicle Time	$\le -13.1\%$	0.37	−0.042	0.89
	Off-vehicle Time	$\le -37.3\%$	0.41	−0.028	0.87
Bus	Travel Cost	$\le +59.6\%$	0.35	−0.058	0.89
	In-vehicle Time	$\le +0.3\%$	0.40	−0.051	0.83
	Off-vehicle Time	$\le -30.8\%$	0.39	−0.033	0.90
Subway	Travel Cost	$\le +64.6\%$	0.37	−0.050	0.92
	In-vehicle Time	$\le -4.2\%$	0.38	−0.045	0.90
	Off-vehicle Time	$\le -27.9\%$	0.36	−0.035	0.85
DRT	Travel Cost	$\le +56.7\%$	0.36	−0.056	0.90
	In-vehicle Time	$\le -2.7\%$	0.40	−0.049	0.87
	Off-vehicle Time	$\le -10.9\%$	0.37	−0.042	0.84

DRT = demand-responsive transport; ROC-AUC = receiver operating characteristic area under the curve.

, they consider reducing off-vehicle time their top priority, with an acceptable reduction of up to 37.3%. However, as indicated in

Table 4. Results of reviewing sensitivity and loss aversion (main transportation mode).

Classification		Private Vehicle	Bus	Subway	DRT
Travel Cost	α (Gain Sensitivity)	0.43	0.56	0.62	0.69
	$\beta$ (Loss Sensitivity)	0.56	0.70	0.73	0.82
	λ (Loss Aversion Coefficient)	2.24	2.17	1.99	2.19
In-vehicle Time	α (Gain Sensitivity)	0.42	0.48	0.57	0.52
	$\beta$ (Loss Sensitivity)	0.61	0.68	0.82	0.79
	λ (Loss Aversion Coefficient)	2.28	1.83	2.07	2.06
Off-vehicle Time	α (Gain Sensitivity)	0.44	0.62	0.53	0.47
	$\beta$ (Loss Sensitivity)	0.63	0.89	0.79	0.65
	λ (Loss Aversion Coefficient)	2.39	2.31	1.98	1.75

, they have the highest loss aversion coefficient (2.39), suggesting that any increase in off-vehicle time would significantly reduce their satisfaction.

In contrast, private vehicle users demonstrate a relatively flexible attitude toward costs, accepting fare increases of up to 49.5%. Car drivers have already accepted higher costs in advance, so an increase in ticket prices does not concern them at all. This likely reflects the characteristics of this group, which includes a higher proportion of high-income individuals. These findings suggest that improvements in off-vehicle time and accessibility are more critical in encouraging private vehicle users to switch to DRT than fare adjustments.

Bus users prioritize off-vehicle time, accepting a reduction of up to 30.8%. Their loss aversion coefficient is also high at 2.31, indicating that longer waiting times and accessibility issues significantly reduce service satisfaction. However, they show relatively high tolerance for fare changes, accepting an increase of up to 59.6%. This suggests that bus users prioritize accessibility and ease of use over punctuality.

Subway users place the highest value on punctuality and time efficiency. They are less sensitive to cost changes, tolerating an increase of up to 64.6%, but they accept only a 4.2% reduction in in-vehicle time and a 27.9% reduction in off-vehicle time. Their high loss aversion coefficients for time-related factors suggest that ensuring punctuality and minimizing travel time are essential. This aligns with the tendency of subway users to prioritize fast travel over cost.

Existing DRT users exhibit more sensitivity to service changes overall and have a lower tolerance for fare increases, accepting up to 56.7%. However, their off-vehicle time loss aversion coefficient is relatively low at 1.75, likely because the greater flexibility in waiting locations makes changes in off-vehicle time less burdensome.

3.2.2. Travel Purpose

This study analyzed the minimum service levels of DRT and user sensitivities based on their main travel purposes. The acceptable service levels and loss aversion tendencies varied depending on travel purpose. Essential trips, such as work commutes and business travel, showed higher sensitivity to losses, whereas optional trips, such as leisure and shopping, exhibited lower sensitivity.

As shown in

Table 5. Results of reviewing the minimum service levels of DRT (travel purpose).

Classification		MSL (%)	Assessment Metrics in Logistic Regression Analysis
			$\mathbf{Pseudo}{\mathit{R}}^2$	Coefficient	ROC-AUC
Work Commute	Travel Cost	$\le +63.3\%$	0.40	−0.051	0.82
	In-vehicle Time	$\le -8.9\%$	0.36	−0.043	0.90
	Off-vehicle Time	$\le -38.2\%$	0.38	−0.029	0.92
Business	Travel Cost	$\le +61.7\%$	0.36	−0.049	0.92
	In-vehicle Time	$\le -7.5\%$	0.38	−0.045	0.84
	Off-vehicle Time	$\le -36.2\%$	0.38	−0.031	0.88
School Commute	Travel Cost	$\le +44.1\%$	0.41	−0.041	0.87
	In-vehicle Time	$\le -0.6\%$	0.38	−0.053	0.91
	Off-vehicle Time	$\le -29.2\%$	0.36	−0.039	0.87
Leisure and Shopping	Travel Cost	$\le +50.4\%$	0.36	−0.053	0.93
	In-vehicle Time	$\le +9.7\%$	0.36	−0.057	0.90
	Off-vehicle Time	$\le -6.3\%$	0.40	−0.045	0.83

, work commuters prioritize waiting and access time, requiring a 38.2% reduction in off-vehicle time compared to conventional public transport for it to be acceptable.

Table 6. Results of reviewing sensitivity and loss aversion (travel purpose).

Classification		Work Commute	Business	School Commute	Leisure and Shopping
Travel Cost	α (Gain Sensitivity)	0.59	0.54	0.67	0.43
	$\beta$ (Loss Sensitivity)	0.74	0.67	0.81	0.52
	λ (Loss Aversion Coefficient)	2.21	1.98	2.67	1.64
In-vehicle Time	α (Gain Sensitivity)	0.49	0.47	0.42	0.37
	$\beta$ (Loss Sensitivity)	0.78	0.69	0.56	0.49
	λ (Loss Aversion Coefficient)	2.14	2.01	1.57	1.34
Off-vehicle Time	α (Gain Sensitivity)	0.46	0.46	0.41	0.31
	$\beta$ (Loss Sensitivity)	0.87	0.81	0.73	0.58
	λ (Loss Aversion Coefficient)	2.39	2.28	1.96	1.56

further indicates that their loss aversion coefficient is the highest (2.39), meaning service satisfaction is likely to drop sharply if waiting time increases. However, they are relatively flexible regarding cost, accepting fare increases of up to 63.3%, reflecting their preference for punctuality and accessibility over affordability.

For business travelers, reducing travel time is the top priority. They are willing to accept a 7.5% decrease in in-vehicle time and a 36.8% reduction in off-vehicle time. Additionally, they accept fare increases of up to 61.7%. Off-vehicle time has the highest loss aversion coefficient (2.28), suggesting that business travelers value not only punctuality but also travel convenience. While business travelers are slightly more flexible than work commuters, they strongly resist increases in travel time.

School commuters place the greatest emphasis on cost stability, accepting fare increases of up to 44.1%. However, they require a 29.6% reduction in off-vehicle time and accept only a minimal (0.6%) decrease in in-vehicle time. Their loss aversion coefficient for cost (2.67) is the highest among all groups, indicating that maintaining stable fares is crucial for increasing DRT acceptability among students.

Leisure and shopping travelers were less sensitive to service changes than those making essential trips. They accept fare increases of up to 50.4% and allow for a 9.7% increase in in-vehicle time and a 6.3% decrease in off-vehicle time. Their highest loss aversion coefficient is for travel cost (1.64), indicating that fare changes are more important to them than variations in travel time. Compared to essential travelers, they exhibit lower sensitivity to losses, meaning they are generally more adaptable to service changes.

3.2.3. Age

This study analyzed the minimum service levels of DRT and user sensitivities across different age groups. Tolerance levels and loss aversion to cost and time factors varied significantly among three age groups: those in their 20s and younger, those in their 30s to 50s, and those 60 and older.

The 20s and younger group, primarily composed of students and young adult workers with relatively low incomes, showed the highest sensitivity to cost changes. As shown in

Table 7. Results of reviewing the minimum service levels of DRT (age).

Classification		MSL (%)	Assessment Metrics in Logistic Regression Analysis
			$\mathbf{Pseudo}{\mathit{R}}^2$	Coefficient	ROC-AUC
20 y and Younger	Travel Cost	$\le +49.1\%$	0.40	−0.046	0.84
	In-vehicle Time	$\le +2.3\%$	0.41	−0.058	0.84
	Off-vehicle Time	$\le -19.5\%$	0.37	−0.043	0.83
30 y	Travel Cost	$\le +58.2\%$	0.38	−0.057	0.86
	In-vehicle Time	$\le -3.8\%$	0.39	−0.049	0.82
	Off-vehicle Time	$\le -30.1\%$	0.36	−0.038	0.85
40 y	Travel Cost	$\le +63.8\%$	0.38	−0.058	0.87
	In-vehicle Time	$\le -6.1\%$	0.38	−0.048	0.87
	Off-vehicle Time	$\le -33.7\%$	0.36	−0.037	0.86
50 y	Travel Cost	$\le +63.2\%$	0.38	−0.061	0.89
	In-vehicle Time	$\le -6.4\%$	0.36	−0.046	0.87
	Off-vehicle Time	$\le -33.8\%$	0.40	−0.037	0.89
60 y and Older	Travel Cost	$\le +52.3\%$	0.38	−0.052	0.87
	In-vehicle Time	$\le -0.2\%$	0.35	−0.054	0.85
	Off-vehicle Time	$\le -42.3\%$	0.40	−0.024	0.87

, they tolerate a fare increase of up to 49.1% over traditional public transportation, lower than that of other age groups.

Table 8. Results of reviewing sensitivity and loss aversion (age).

Classification		20 y and Younger	30 y	40 y	50 y	60 y and Older
Travel Cost	α (Gain Sensitivity)	0.62	0.60	0.54	0.41	0.54
	$\beta$ (Loss Sensitivity)	0.81	0.72	0.70	0.66	0.74
	λ (Loss Aversion Coefficient)	2.37	2.09	1.98	1.92	2.21
In-vehicle Time	α (Gain Sensitivity)	0.41	0.45	0.48	0.49	0.42
	$\beta$ (Loss Sensitivity)	0.59	0.71	0.74	0.75	0.63
	λ (Loss Aversion Coefficient)	1.74	2.01	2.09	2.09	1.62
Off-vehicle Time	α (Gain Sensitivity)	0.37	0.40	0.42	0.44	0.49
	$\beta$ (Loss Sensitivity)	0.64	0.80	0.83	0.85	0.92
	λ (Loss Aversion Coefficient)	1.99	2.24	2.28	2.29	2.65

further indicates that their loss aversion coefficient for travel cost is the highest (2.37), suggesting a strong resistance to fare increases. In contrast, they demand a 19.5% reduction in off-vehicle time, reinforcing their preference for cost stability over time-related factors. These findings suggest that financial burden is a key concern for students, making cost a more influential factor than travel time in their service choices.

The 30 to 50 year age group, which includes more affluent commuters and business travelers, demonstrated greater flexibility toward fare changes but higher sensitivity to travel time. Given the importance of commuting and business travel, this group places a strong emphasis on reducing travel time. They accept fare increases of up to 63.2%, with a relatively low loss aversion coefficient of 2.09. However, they demand a 6.4% reduction in in-vehicle time and a 33.8% reduction in off-vehicle time, with a loss aversion coefficient of 2.29. These findings highlight their prioritization of travel efficiency and punctuality, underscoring the need for service improvements that minimize commute times.

The 60 and older age group exhibited the highest sensitivity to off-vehicle time. They require a 42.3% reduction in off-vehicle time, and their loss aversion coefficient (2.65) is the highest among all age groups. In contrast, they are relatively less resistant to fare changes, tolerating an increase of up to 52.3%, which suggests that accessibility is a greater priority than cost. These results indicate that policies aimed at reducing off-vehicle time and improving waiting area accessibility are crucial for enhancing satisfaction among elderly users.

4. Discussion and Conclusions

Conventional methods for determining the minimum service level of public transportation do not fully account for the unique characteristics of DRT. These approaches are primarily supplier-centric and fail to adequately consider user psychology and travel behavior. To address this limitation, this study quantitatively analyzed and proposed minimum service levels for DRT based on user groups, using SP data and prospect theory.

Through this analysis, we identified variations in acceptable service levels for in-vehicle time, off-vehicle time, and travel cost across different user groups. Based on these findings, we proposed customized policy recommendations that reflect local characteristics and user preferences.

The results of this study indicate that the minimum service levels for DRT are as follows: a maximum travel cost increase of 57.0%, a 5.1% reduction in in-vehicle time, and a 29.7% reduction in off-vehicle time compared to conventional public transport. These findings suggest that users are willing to accept a higher fare than conventional public transportation, as long as both in-vehicle time and off-vehicle time are reduced, which is essential for DRT to become a regular mode of transportation.

Additionally, the sensitivity and loss aversion analysis showed that users are most sensitive to increases in off-vehicle time, perceiving it as a significant loss. This suggests that since DRT services may have higher travel costs than conventional public transport, shorter travel times may be necessary to enhance user acceptance.

Furthermore, the group-based analysis revealed that minimum service level criteria and sensitivity vary depending on primary transportation mode, travel purpose, and age group. This highlights the need for differentiated minimum service levels tailored to the characteristics of primary user groups in each region, along with policy considerations for effective DRT operation.

Preferences and minimum service level criteria for DRT service elements varied by primary transportation mode. Private vehicle users prioritized reducing off-vehicle time, subway users emphasized punctuality and shorter travel times, and existing DRT users considered travel cost the most important factor.

Notably, private vehicle users exhibited higher loss aversion than public transportation users, making them more resistant to service changes and more sensitive to fluctuations. As a result, their minimum service level requirements were higher. This suggests that in areas with high dependence on private vehicles, successful public transportation conversion to DRT requires strategies to reduce off-vehicle time, improve accessibility, and minimize waiting times. Given the high loss aversion of private vehicle users, strengthening accessibility to DRT services is crucial for increasing adoption.

The analysis of different travel purposes indicates that travelers on essential trips, such as work commutes and business trips, are most sensitive to reducing off-vehicle time and shortening travel time. In contrast, travelers on optional trips, such as leisure and shopping, are more sensitive to cost changes and generally more flexible toward service level adjustments.

As a result, minimum service level requirements for off-vehicle and in-vehicle time are higher for essential trips, whereas they are lower for optional trips. Therefore, in industrial park areas with a high concentration of essential travelers, policy measures should prioritize punctuality and time efficiency, with service improvements focused on optimizing travel efficiency and ensuring reliability. Conversely, in tourist areas with a high proportion of optional travelers, strategies that reduce cost burdens are likely to be more effective.

The analysis by age group shows that cost stability is the top priority for students and young adult workers, shorter travel time is most important for the economically active population (30 to 50 years), and reduced off-vehicle time is the primary concern for the elderly. Since different age groups have varying minimum service level requirements, it is essential to establish region-specific minimum service levels based on the primary user demographics.

In particular, the elderly are most sensitive to increases in off-vehicle time, suggesting that rural areas with a high proportion of older adults require policies and service standards that minimize waiting time and enhance travel convenience. Conversely, in newly developed urban areas with a large economically active population, strategies should focus on improving travel efficiency and punctuality.

The findings of this study provide a valuable foundation for policy design aimed at optimizing DRT operations and enhancing user satisfaction. Implementing customized policies that reflect regional characteristics and user needs is expected to encourage greater public transportation use and improve service efficiency. Notably, the minimum service level proposed in this study differs from previous research by incorporating users’ psychological characteristics and behavioral responses. Developing region-specific policies based on these insights is likely to further enhance user satisfaction.

A policy approach that considers the characteristics of key user groups is expected to improve DRT acceptance and support the long-term sustainability of transportation services. Additionally, this study contributes to improving the efficiency of DRT operations and provides guidance for user-centered policy design.