Analyzing New Operation Strategy of Demand-Responsive Transports Using Discrete-Event Simulation Framework

Abstract

Demand-responsive transport (DRT) provides flexible ride-sharing by dynamically adjusting routes based on real-time user demand, making it suitable for complex urban mobility needs. This study proposes a modular simulation framework based on the DEVS (Discrete Event System Specification) formalism and introduces an “express service” strategy that enables direct trips without intermediate stops. The framework supports scenario-based analysis using key performance indicators (KPIs) and allows for flexible testing of operational strategies. Two experiments were conducted: the first validated the simulation model under varying demand and fleet conditions; and the second assessed the impact of the express service. Results showed that express passengers experienced significantly shorter waiting and riding times, while standard passenger service remained stable. The strategy also improved operational efficiency under constrained resources. This study contributes to a configurable simulation platform for evaluating differentiated DRT services and provides practical insights for adaptive service planning, especially in urban settings where tiered mobility solutions are increasingly needed.

1. Introduction

Demand-responsive transport (DRT) is a form of shared mobility that dynamically adjusts vehicle routes based on users’ real-time demands rather than following a fixed schedule [1,2,3]. The flexibility of DRT makes it an increasingly sought-after transportation option globally, as it effectively caters to the needs of expanding populations and increasing urban population densities [4,5]. Such tailor-made DRT services have the potential to significantly offset reliance on conventional public transport systems and provide more dynamic planning [6,7]. This shift towards demand-responsive operations not only accommodates the unique mobility needs of urban dwellers, but also promotes a more efficient use of road space [8]. By facilitating ride-sharing based on real-time demand, DRT can substantially decrease the overall number of vehicles in operation, ease urban congestion, and contribute to sustainable transportation [9,10].

Efforts to optimize DRT operations have been undertaken using various approaches, particularly focusing on the dynamic allocation of vehicles in response to demand [11,12]. This has led to the development of dispatch algorithms to efficiently match vehicles with passenger requests [13,14]. To assess and evaluate such newly developed strategies, the creation of a foundational simulation model is necessary [15]. DRT simulation research can be broadly categorized into two types: tool- and methodology-based simulation studies [16,17,18]. Both approaches offer valuable insights: tool-based simulations benefit from maturity and scalability of existing software, while methodology-based simulations offer greater flexibility to incorporate novel rules and system behaviors [19]. In this study, we pursue a methodology-based simulation approach. This choice is motivated by the need to easily integrate and evaluate a new operational strategy for DRT, which would be difficult to test in a black-box commercial simulator.

This study introduces a new operational strategy and methodology-based simulation framework designed to enhance the efficiency of DRT systems. A new operational strategy called express service allows for the direct transportation of passengers to their destinations without intermediate stops, significantly enhancing user convenience and efficiency. The simulation models were developed using the DEVS (Discrete Event System Specification) formalism [20], which is particularly well-suited for modeling the stochastic, event-driven nature of DRT operations—such as customer calls, passenger boardings, and drop-offs. Leveraging the inherent modularity and hierarchy of DEVS, we structured the DRT simulation into independently functioning components, including demand generation, vehicle movement, and routing/dispatch logic. Each of these components can be developed, replaced, or extended without modifying the entire system. This modular design enables flexible testing of new operational strategies and facilitates seamless integration of additional services such as tiered DRT offerings or specialized shuttles. Furthermore, the hierarchical organization supports scalable modeling across different service layers or geographical regions, improving both the adaptability and reusability of the simulation framework [21,22]. This approach not only ensures a realistic representation of DRT processes, but also enhances the framework’s applicability to a wide range of scenarios, making it a robust tool for both theoretical analysis and practical service planning.

The proposed simulation framework is structured into four phases: data pre-processing, simulation modeling, operational strategy identification, and simulation data analysis. The pre-processor is subdivided into three essential functions: mapping the network based on foundational data prior to the simulation, categorizing the demand data, and selecting essential stops for the simulation. In this study, we present a DEVS-based simulation model that further branches into an experimental framework for conducting and analyzing experiments, a control system for managing operations, and a physical system designed for modeling both DRT and passengers. Furthermore, the experimental framework incorporates a visualizer model, enabling real-time observation of the experimental proceedings. This feature aids in tracking the progress of the experiment with clarity and precision. Based on this model, we propose ‘express service’ operation strategy aimed at optimizing efficiency for passengers and standard DRT operations. This strategy targets specific guests and increases efficiency by not allowing other passengers to pick up or drop off between their origin and destination.

We propose a set of key performance indicators (KPIs) to evaluate and analyze the data and operational strategies thoroughly. Using the proposed framework, we conducted two simulation experiments. The first experiment validated the baseline DRT model by simulating standard operations without the express service. Results showed expected trends in passenger wait and ride times under varying demand and vehicle availability, confirming the model’s reliability. The second experiment evaluated the impact of the proposed express service strategy, which enables selected trips to bypass intermediate stops. Simulation results showed that express passengers experienced significantly shorter wait and ride times, while standard passengers’ service levels remained stable. These findings demonstrate that the express service can enhance user experience without compromising overall system performance, highlighting the practical value of the proposed strategy and the simulation framework [23].

The remainder of this paper is organized as follows: Section 2 reviews related to research on DRT and simulation methods. Section 3 explains the simulation framework and the DEVS-based model. Section 4 presents the experimental setup and results. Section 5 concludes the paper and discusses implications and future research.

2. Related Work

Simulation-based studies on demand-responsive transport (DRT) systems can be broadly categorized into two types: those using existing simulation tools (tool-based) and those developing custom modeling frameworks (methodology-based). While tool-based approaches emphasize accessibility and usability through predefined components, methodology-based approaches often offer higher flexibility and extensibility for tailored experimentation.

Table 1. Comparison of simulation studies on demand-responsive transport (DRT) systems.

Related Research	Approach	Modeling Method	Problems to Be Solved	Limitations
David et al. (2023) [24]	Tool-based	SUMO-based tool	Assignment and route optimization	Static demand; not real-time
Ronald et al. (2017) [25]	Tool-based	Delphi, SUMOoD, MATSim	Comparison of DRT simulation tools	No dynamic demand modeling; limited scenario specificity
Kagho et al. (2021) [26]	Tool-based	MATSim	DRT in car-dependent areas	Limited control over logic; high vehicle mileage
Fielbaum et al. (2024) [27]	Methodology-based	Hybrid route planning	Combine DRT and fixed routes	Fixed routing; lacks re-routing flexibility
Kim et al. (2022) [28]	Methodology-based	Event-based simulation	KPI analysis of DRT systems	No visualization; no service-type comparison
Alomrani et al. (2023) [29]	Methodology-based	Bipartite matching	Real-time dispatch optimization	Lacks service-tier differentiation; not modular
Wang et al. (2022) [30]	Methodology-based	Soft windows and compensation	Tiered service and user satisfaction	High model complexity; user assumptions
Our study	Methodology-based	DEVS formalism	New DRT service (Express service) analysis	No real-world validation; synthetic demand used

summarizes representative studies from both categories, highlighting their modeling methods, research goals, and key limitations to help position our work within this evolving research landscape.

Tool-based approaches typically rely on established simulation platforms such as SUMO, MATSim, or other agent-based environments that facilitate modeling of urban mobility systems. For example, David et al. (2023) developed a SUMO-based tool that computes vehicle assignments and route planning using static demand inputs [24]. While effective in structured experimental conditions, this tool lacks responsiveness to real-time demand fluctuations, limiting its applicability to dynamic urban systems. Ronald et al. (2017) compared several DRT simulation tools—including Delphi, SUMOoD, and MATSim—focusing on their ease of use and integration capabilities [25]. However, the study did not explore scenario-specific demand structures or dispatching algorithms, making it less suitable for evaluating new service models. Similarly, Kagho et al. (2021) employed MATSim to simulate DRT for car-dependent suburban regions and demonstrated potential benefits in accessibility [26]. Still, issues such as excessive vehicle mileage and limited scheduling adaptability were noted. While these tools are valuable for initial prototyping or policy simulation, their black-box nature often limits the flexibility required to test novel operational strategies such as tiered or express services.

Methodology-based studies, in contrast, focus on building models from the ground up with greater control over system behavior, often incorporating discrete-event logic, optimization techniques, or hybrid system architectures. Fielbaum et. al (2024) proposed a hybrid model that integrates fixed-route planning with demand-responsive service to improve network efficiency [27]. However, the resulting route structure becomes fixed after optimization, limiting its responsiveness to temporal or spatial demand variability. Kim et al. (2022) constructed an event-based simulation that captures the stochastic nature of passenger demand and evaluates key performance indicators (KPIs) of DRT systems. Despite its strengths in KPI tracking, the study did not incorporate modular structures or service-type variations [28]. Recent studies such as Alomrani et al. (2023) proposed graph-based bipartite optimization for real-time dispatching, improving matching efficiency, but without differentiating service levels between passengers [29]. Wang et al. (2022) simulated soft time windows and compensation policies to examine service differentiation, but implemented these within a fixed optimization context, limiting reusability across alternative strategies or geographic contexts [30].

Table 1 offers a comparative summary of these representative works. While prior research has contributed significantly to understanding DRT design and operational policies, many focus on static or specialized configurations that are not easily adapted for comparative testing of new service strategies. Very few studies explicitly compare standard shared-ride models with express or prioritized service variants within a modular simulation environment that supports flexible experimentation and performance analysis.

In contrast, this study introduces a simulation framework based on the DEVS formalism, which enables modular, hierarchical, and event-driven modeling. The proposed framework allows for plug-and-play updates of key components, such as routing algorithms and dispatch policies, making it suitable for dynamic policy testing. Our model explicitly supports tiered service differentiation by assigning express passengers direct, non-stop routes, enabling controlled experiments on resource allocation and user prioritization. Unlike prior models tightly coupled to fixed optimization goals, this framework enables scenario-based, KPI-driven comparisons of multiple operational strategies under realistic constraints. This approach addresses several limitations in existing DRT simulation studies and provides a practical platform for researchers and planners to explore service innovation in diverse urban contexts.

3. Proposed Method

This section describes the proposed method and overall structure of the system. The system is broadly divided into the pre-processor and the proposed models. Notably, the proposed model is designed as a discrete-event system that can be abstracted through complexity and logic to suit the purpose of the simulation. Additionally, considering an actual mobile system, a simulation model was designed with a hierarchical structure. Furthermore, it has a modular structure that makes it easy to replace and add schedules or other control systems.

The overall structure of the system is shown in Figure 1. The pre-processors are segmented into three principal phases: map networking, demand data categorization, and essential stop selection. These phases constitute a pre-processing phase that transforms various data into a format amenable to mobility simulations before they are input into the proposed model. The three pre-processors are described in Section 4.2.

The pre-processed data are subsequently input into the proposed simulation model, which is structured around three primary components—an Experimental Frame, a Control System, and a Physical System—delineated through an analysis of the mobility field. This model facilitates simulations based on the interactions among its sub-models, each of which is assigned a specific function. Through these interactions, simulation outcomes were generated and analyzed. Detailed discussions on the underlying algorithms and model frameworks are provided in the following sections: Section 3.1 elucidates the foundation and express dispatching algorithm, and Section 3.2 delves into the design of each model and its corresponding sub-models.

The experiment implemented the operational strategy proposed in this study within the developed model from which the KPIs were calculated. On the passenger side, the KPIs encompass ride time and waiting time, whereas the DRT side focuses on call acceptance and utilization rates. The experimental scenario is outlined in Section 4.1. The definitions of the resultant KPIs are provided in Section 4.3, and the analysis of these results is further elaborated in the subsections of Section 4.4 and Section 4.5.

The proposed framework encompasses a model structure that is conducive to the development of various algorithms that initiate data pre-processing. This facilitated the simulation of diverse operational strategies, thereby enabling a thorough analysis of the results. This approach ensures a comprehensive examination of how different strategies impact the overall performance, allowing for optimized decision-making based on the simulated outcomes.

3.1. DRT Dispatching Algorithm

One of the most critical considerations in shared vehicle services such as demand-responsive transport systems is the assignment of vehicles to passengers. Figure 2 illustrates the dispatching scenario for a demand-response vehicle when a new service call is received. In this scenario, ‘S+’ represents the pick-up stop for Passenger S, and ‘S-’ denotes the drop-off stop for the same passenger. Currently, DRT X operates on route [A+, B+, A−, B−], whereas DRT Y serves route [C+, C−]. Upon receiving a new service request from Passenger D, the DRT control system must determine whether to assign the call to DRT X or DRT Y and identify an optimal insertion point within the existing routes.

Now, we introduce a novel service designed for periods of low vehicle demand or when excess vehicles are available. This service, tailored for passengers, ensures direct transportation to one’s destination without intermediate stops upon request for demand-responsive transport. Implementing this service can significantly enhance passenger satisfaction by minimizing both waiting and riding times, thereby reducing vehicle idle times [31]. For instance, DRT X in Figure 3 follows the [A+, B+, A−, B−] route, while DRT Y operates on the [C+, C−] route. Upon receiving a new request from express passenger D, DRT X’s itinerary is adjusted to [A+, D+, D−, B+, A−, B−], facilitating direct transport to D’s destination without altering the sequence to [D+, A+, B+, D−, A−, B−]. This express service feature exemplifies how direct routing can be efficiently incorporated into existing schedules, prioritizing speed and convenience for passengers seeking immediate transportation to their destinations.

In the simulation model, vehicle assignment and routing are implemented using adapted versions of established algorithms, such as a greedy dispatching rule and a Dijkstra-based shortest path search [32,33,34]. These algorithms were customized to incorporate real-time operational constraints specific to DRT services, such as dynamic passenger requests and vehicle capacity limitations. While the fundamental logic of these baseline algorithms underpins standard operations, the express routing algorithm extends this structure by adding constraints and optimization criteria tailored to express passengers—namely, direct routing without intermediate stops and prioritized insertion into vehicle schedules.

Modifications to the optimal insertion algorithm are necessary in the context of express DRT dispatching, which differs from the conventional approach used for standard passengers. Algorithm 1 illustrates the express optimal insertion algorithm, which aims to minimize both the waiting time and ride time for express passengers by prioritizing direct, non-stop service. To ensure this, specific constraints are applied when inserting the departure and arrival points of express passengers into the existing route. For instance, express passengers cannot be inserted before other express stops, and standard passengers cannot be inserted between the departure and arrival points of an express passenger.

Algorithm 1 Pseudo Code of Express Optimal Insertion Algorithm

1. //Initialization 2. best_path := NULL 3. best_total_time := ∞ 4. insertable_positions := [] 5. existingDst := targetDRT.existingDst 6. psgrCount := targetDRT.psgrCount 7. IF NOT expressLst[0] THEN 8.     insertable_positions.append((0, 0)) 9. END IF 10. FOR i FROM 1 TO length(expressLst) DO 11.     IF NOT expressLst[i - 1] AND expressLst[i] THEN 12.         insertablePositions.append((i, i)) 13.     ELSE IF NOT expressLst[i] THEN 14.         insertablePositions.append((i, i + 1)) 15.     END IF 16. END FOR 17. insertablePositions.append((len(existing_dst), len(existing_dst))) 18. IF targetPsgr.psgrExpress THEN 19.     FOR EACH (i, j) IN insertablePositions DO 20.         temp_path := existingDst[0:i] + [targetDeparture] + [targetArrival] + existingDst[i:end] 21.         count_path := psgrCount [0:i] + [+targetPsgr.psgrNum] + [-targetPsgr.psgrNum] + psgrCount [i:end] 22.         possible_count := curPsgrNum 23.         over_capacity := FALSE 24.         FOR k FROM 0 TO length(count_path) - 1 DO 25.             possibleCount := possibleCount+ count_path[k] 26.             IF possibleCount > DRTMax THEN 27.                 over_capacity := TRUE 28.                 BREAK 29.             END IF 30.         END FOR 31.         IF over_capacity THEN 32.             CONTINUE 33.         END IF 34.     total_time := find_shortest_path(temp_path) 35.         IF total_time < best_total_time THEN 36.             best_total_time := total_time 37.             best_path := temp_path 38.         END IF 39.     END FOR 40. END IF 41. RETURN best_point

The algorithm evaluates all possible insertion points that satisfy these constraints and computes the corresponding passenger loads along the route to ensure vehicle capacity is not exceeded. Among the feasible insertion paths, the one with the shortest overall riding time is selected as optimal. Although the algorithm has the worst-case time complexity of O(n³) due to repeated evaluation and shortest-path calculations, its computational impact is limited in practice. This is because the algorithm is applied only when an express passenger request is generated, which represents a small portion of overall system activity. Additionally, the number of destinations per DRT is typically moderate in real-world operations, keeping execution time reasonable even under high-demand conditions.

3.2. System Modeling

A mobility system characterized by its response to passenger, call, and ride-off events can be effectively modeled as a discrete-event system. This approach allows for the intricate interactions and logic inherent in such systems to be represented despite their complexity. In event-based modeling, it is crucial to abstract certain characteristics to align with the goals of the simulation. Acknowledging this, we propose a mobility simulation model that leverages DEVS formalism. This model is designed for adaptability, enabling its reconfiguration into a hierarchical and modular setup to accommodate various operational strategy simulations. This modifiable structure not only facilitates the exploration of the system’s behavior under different conditions, but also enhances the model’s utility across diverse simulation scenarios.

Figure 4 illustrates the simplified architecture of the DEVS-based coupled model, which is segmented into three main components: the experimental frame, control system, and physical system. These components interact via well-defined input/output ports and message flows, supporting the modular and hierarchical structure of the simulation. Each component internally consists of atomic sub-models that handle specific tasks such as dispatching, routing, and passenger interaction. To maintain clarity and focus, the following subsections highlight the most critical atomic models that govern key system behaviors and operational logic, including the implementation of the proposed express service.

DEVS Atomic Modeling

This section presents key DEVS atomic models that constitute the core behavior of the proposed simulation framework. While the complete system includes many atomic models, we focus here on the most essential ones: the Visualizer model from the experimental frame; the Schedule Manager and Dispatching and Routing Manager from the control system; and the DRT model from the physical system. These models were selected for their central roles in managing simulation execution, coordinating DRT operations, and representing system dynamics.

• Visualizer

The visualizer is tasked with receiving up-to-date schedule data from the DRT and Schedule Manager, and dynamically visualizes key information such as passenger boarding/dropping points and the DRT’s current route in real time. The DEVS set is defined by Equations (1)–(8), with a distinctive characteristic being the presence of an input message set Y, while the internal transition functions δ_int, remains an empty set. This configuration begins in the WAIT state and functions by external transition functions set δ_ext, which are defined as functions. During this operation, the state of the simulation was visualized in real time, adhering to the rendering time specified in Equation (16), to ensure that the dynamics of the simulation were accurately reflected as they unfolded. Initially, the visualizer remains in the WAIT state and awaits the command. Upon receiving pair commands from the Schedule Manager, it shifts to the VISUALIZE state. In this state, the visualizer actively renders the schedule information contained in the messages for a period known as the rendering time, continuing to process and display the CurrentNode data from the DRT until a simDone message from the Schedule Manager signals the end of the visualization task.

$${Visualizer}_{Atomic}=<X,Y,S,{\delta }_{ext},{\delta }_{int},\lambda ,TA>$$

(1)

$$X=\{Schedule,CurrentNode,simDone\}$$

(2)

$$Y=\left\{\right\}$$

(3)

$$S=\{VISUALIZE,WAIT\}$$

(4)

$${\delta }_{ext}:\left\{\begin{array}{c}\left(WAIT\right)\times \left(Schedule\right)\to \left(VISUALIZE\right)\\ \left(VISUALIZE\right)\times \left(CurrentNode\right)\to \left(VISUALIZE\right)\\ \left(VISUALIZE\right)\times \left(simDone\right)\to \left(WAIT\right)\end{array}\right.$$

(5)

$${\delta }_{int}:\left\{\Phi \right.\}$$

(6)

$$\lambda :\left\{\Phi \right.\}$$

(7)

$$TA:\left\{\begin{array}{c}\left(WAIT\right)\to \infty \\ \left(VISUALIZE\right)\to Rendering time\end{array}\right.$$

(8)

This visualization employed Python’s TK Widget package (Tkinter 8.6) for implementation. As the simulation is initiated, the visualizer begins by loading the map data, displaying all nodes and paths, as depicted in Figure 5. Subsequently, upon receiving schedule information comprising the DRT Id, Current Node, Boarding Node, and Dropping Node from the Schedule Manager and DRT Atomic Model, the map is updated accordingly.

A closer look at Path A in Figure 5 reveals a route traversed by a circular DRT with two boarding stops, denoted by red + symbols, and two planned drop-off stops, marked with blue symbols. In addition, paths that have been previously traversed or have already expired are represented by dotted lines, whereas the currently scheduled path is depicted by a solid line. For instance, Path B in Figure 5 illustrates an initial plan for passengers dropping off to stop at the upper right side. However, the addition of new boarding and drop-off stops within the red circle indicates that the previously expired path is indicated by a dotted line, whereas the updated current path is displayed as a solid line. Through this visualization model, it becomes feasible to verify the effective development of dispatching and routing algorithms and monitor the progress of the simulation experiment more efficiently, ensuring a comprehensive overview of the system’s dynamic operations.

The control system oversees and directs the operation of the entire system. It is segmented into the Schedule Manager and the Dispatching and Routing Manager. The Schedule Manager orchestrated a comprehensive scheduling process. Upon receiving a call from a passenger, the system forwards a calculation request to the dispatching and routing managers to preliminarily assess the schedule. In response, the Dispatching and Routing Manager assumes the roles of vehicle dispatching and route planning, submitting a range of potential schedules to the Schedule Manager. Subsequently, the most fitting schedule is chosen, and this selected schedule is then assigned to the respective DRT, ensuring efficient and optimized transportation planning. By distinctly architecting the Schedule Manager and the Dispatching and Routing Manager, the system leverages the modular nature of DEVS to facilitate partial modifications, especially when updates or replacements of algorithms are necessary.

• Schedule Manager

The Schedule Manager is engineered to craft schedules utilizing incoming passenger calls and the real-time positions of the DRTs, as depicted in Figure 6 and outlined by Equations (9)–(16) in the DEVS set, which illustrates the operational diagram. At the beginning of the simulation, as expressed by Equation (12), the Schedule Manager remained in an IDLE state. It then transitioned to the DSP_PP state, as indicated by Equations (10) and (13), when it received a call message from the passenger queue. In the DSP_PP state, the Schedule Manager sends a DispatchRoute_Req message to the Dispatching and Routing managers. This step, aimed at assigning passengers to DRTs based on call specifics, precedes their return to the IDLE state, as expressed in Equations (11) and (14). The transition to the SCHEDULE state occurs upon the receipt of a candidate schedule from the Dispatching and Routing manager model, during which the scheduling information is relayed to the DRT model, as described in Equation (15). The Schedule Manager progresses to the ANALYZE state if a transit message from the DRT suggests that the last passenger has dropped off. Throughout these transitions, time shifts, indicated by Equation (16), occur instantaneously.

$${Schedule Manager}_{Atomic}=<X,Y,S,{\delta }_{ext},{\delta }_{int},\lambda ,TA>$$

(9)

$$X=\{DispatchRout{e}_{Res},Call,Transit\}$$

(10)

$$Y=\{DispatchRout{e}_{Req},Schedule,simDone\}$$

(11)

$$S=\{IDLE,SCHEDULE,ANALYZE,DS{P}_{PP}\}$$

(12)

$${\delta }_{ext}:\left\{\begin{array}{c}\left(IDLE\right)\times \left(Call\right)\to \left(DSP\_PP\right)\\ \left(IDLE\right)\times \left(DispatchRout{e}_{Req}\right)\to \left(SCHEDULE\right)\\ \left(IDLE\right)\times \left(Transit\right)\to \left(ANALYZE\right)\end{array}\right.$$

(13)

$${\delta }_{int}:\left\{\begin{array}{c}\left(DSP\_PP\right)\to \left(IDLE\right)\\ \left(SCHEDULE\right)\to \left(IDLE\right)\\ \left(ANALYZE\right)\to \left(IDLE\right)\end{array}\right.$$

(14)

$$\lambda :\left\{\begin{array}{c}\left(DSP\_PP\right)\to \left(DispatchRout{e}_{Req}\right)\\ \left(SCHEDULE\right)\to \left(Schedule\right)\\ \left(ANALYZE\right)\to \left(simDone\right)\end{array}\right.$$

(15)

$$TA:\left\{\begin{array}{c}\left(IDLE\right)\to \infty \\ \left(DSP\_PP\right)\to 0\\ \left(SCHEDULE\right)\to 0\\ \left(ANALYZE\right)\to 0\end{array}\right.$$

(16)

• Dispatching and Routing Manager

The Routing Manager is responsible for executing the dispatching and routing algorithms requested by the scheduler. Its primary function is to dispatch the optimal DRT based on the boarding and dropping locations of passengers, and to calculate the DRT’s best route, thereby generating the candidate schedule. The function of this model is encapsulated within the DEVS set using Equations (17)–(24). Upon the occurrence of an input event, as specified in Equation (18), the model undergoes an external transition to the ALGORITHM state, as shown in Equation (21). Following the time-lapse defined by Equation (24), the model exports an output event, as described in Equation (23), leading to an internal transition in accordance with Equation (22). The Routing Manager model is a crucial component of the operational strategy and is pivotal for efficient vehicle dispatching and path planning. This model offers a unique advantage: when adjustments or modifications to various operational strategies are necessary, only the atomic model must be redesigned or modified. The remaining system modules remain unchanged, thereby maintaining the integrity and continuity of the entire framework. This attribute underscores the overall structure of the DEVS model in enabling flexible and dynamic responses to changing operational requirements, while ensuring broader system stability and effectiveness.

$${Dispatching\&RoutingManager}_{Atomic}=<X,Y,S,{\delta }_{ext},{\delta }_{int},\lambda ,TA>$$

(17)

$$X=\left\{DispatchRout{e}_{Req}\right\}$$

(18)

$$Y=\left\{DispatchRout{e}_{Res}\right\}$$

(19)

$$S=\{IDLE,ALGORITHM\}$$

(20)

$${\delta }_{ext}:\left\{\left(IDLE\right)\times \left(Dispatc{hRoute}_{Req}\right)\to \left(ALGORITHM\right)\right.$$

(21)

$${\delta }_{int}:\left\{\left(ALGORITHM\right)\to \left(IDLE\right)\right.$$

(22)

$$\lambda :\left\{\left(ALGORITHM\right)\to (DispatchRout{e}_{Res}\right.)$$

(23)

$$TA:\left\{\begin{array}{c}\left(IDLE\right)\to \infty \\ \left(Algorithm\right)\to 0\end{array}\right.$$

(24)

The physical system encompasses both the DRT and passenger queue, and functions as a tangible component of the operation. It primarily interacts with the scheduler and generator, executing transportation tasks based on the received directives. In this setup, the passenger queue operates by forwarding passenger calls generated by the generator to the Schedule Manager. Similarly, the DRT performs its tasks upon receiving a schedule from the Schedule Manager. If the model under the physical system is divided into separate entities, such as DRTs and passengers, it can be easily expanded to other strategies and transportation in future studies. This enables the system to be easily expanded or refined, particularly when incorporating simulations of additional forms of transportation such as buses and taxis. This classification not only enhances the system’s adaptability to new simulation requirements, but also ensures that the framework remains scalable and versatile.

• DRT

The DRT operates based on the schedule assigned by the Schedule Manager and performs its designated task. DRT model’s operational logic is defined by Equations (25)–(32) within the DEVS dataset. According to Equation (28), the DRT remains in the IDLE state upon initiating the simulation. It transitions to the MOVE state upon receiving a schedule message from the Schedule Manager, as indicated by Equations (26) and (29). In the MOVE state, the DRT navigates according to the assigned route and reports its location. When the DRT reaches a passenger’s pickup or drop-off stop, it shifts into the BOARD state to manage pickup and drop-off activities over time, as specified in Equation (32). During this phase, the model exports a transit output message as outlined in Equations (27) and (31). If there are additional pick-up or drop-off tasks, the DRT reverts to the MOVE state, as described in Equation (30), to proceed to the next location. Upon completing all the tasks detailed in its Schedule, the DRT returns to the IDLE state, awaiting further instructions. Moreover, if the DRT receives an updated schedule message from the Schedule Manager in either the MOVE or BOARD state, it adjusts its current schedule accordingly. This dynamic allows the DRT to adapt to real-time changes and ensure the management of its routing and passenger service tasks.

$${Shuttle}_{Atomic}=<X,Y,S,{\delta }_{ext},{\delta }_{int},\lambda ,TA>$$

(25)

$$X=\left\{Schedule\right\}$$

(26)

$$Y=\{Transit,CurrentNode\}$$

(27)

$$S=\{IDLE,MOVE,BOARD\}$$

(28)

$${\delta }_{ext}:\left\{\begin{array}{c}\left(IDLE\right)\times \left(Schedule\right)\to \left(MOVE\right)\\ \left(MOVE\right)\times \left(Schedule\right)\to \left(MOVE\right)\\ \left(BOARD\right)\times \left(Schedule\right)\to \left(BOARD\right)\end{array}\right.$$

(29)

$${\delta }_{int}:\left\{\begin{array}{c}\left(MOVE\right)\to \left(MOVE\right)\\ \left(MOVE\right)\to \left(BOARD\right)\\ \left(BOARD\right)\to \left(MOVE\right)\\ \left(BOARD\right)\to \left(IDLE\right)\end{array}\right.$$

(30)

$$\lambda :\left\{\begin{array}{c}\left(MOVE\right)\to \left(CurrentNode\right)\\ \left(BOARD\right)\to \left(Transit\right)\end{array}\right.$$

(31)

$$TA:\left\{\begin{array}{c}\left(IDLE\right)\to \infty \\ \left(MOVE\right)\to t_{move}\\ \left(BOARD\right)\to t_{BOARDING}\end{array}\right.$$

(32)

The model design was implemented using PyDEVS, an engine developed to run DEVS models crafted in Python 3.10, adhering to DEVS formalism [35]. This implementation, specifically chosen for Python’s flexibility and ease of visualization, holds potential for future integration with various AI packages, broadening the scope of its application and utility [36].

4. Experiment

The framework for the experimental scenario is outlined in Section 4.1. Section 4.2 details the pre-processor, while Section 4.3 defines the key performance indicators crucial to this study. Section 4.4 presents Experiment 1, which assesses the current scenario and compares the number of vehicles to the demand. Finally, in Section 4.5, we conducted Experiment 2 for a new operational strategy, offering a comprehensive analysis of its efficacy.

4.1. Experimental Scenario

The experiments were conducted in Dongtan 1 New Town and Dongtan 2 New Town, Hwaseong, Gyeonggi Province, Republic of Korea. Dongtan 1 New Town covers an area of 9.03 km², and Dongtan 2 New Town spans 24.01 km², as illustrated in Figure 7. These areas were selected because of the city’s mobility challenges, exacerbated by the scarcity of taxis and buses, coupled with ongoing construction that limits parking availability. Given Dongtan Station’s proximity and the need for DRT services to connect surrounding areas, new transportation options may be required due to the city’s ongoing development. Therefore, we conducted experiments in an urban setting to evaluate various DRT operation strategies and collect data to address these transportation challenges.

4.2. Pre-Processor

To effectively utilize the data in simulation experiments, the foremost task is to collect and pre-process the base data. This section delineates the three primary pre-processing steps. Section 4.2.1 elaborates on the networking process, which utilizes GIS map data for its foundation. Following this, Section 4.2.2 discusses the classification of DRT data, an effort grounded in bus demand data analysis. Finally, Section 4.2.3 details the process for selecting essential stops from all available options, pinpointing those crucial for conducting DRT experiments.

4.2.1. Map Networkization

Pre-processing is vital for effective utilization of GIS map data. To this end, we transformed the road and intersection data into a network format composed of nodes and links. This transformation facilitates the application of routing algorithms through the adoption of efficient data formats. Figure 8 shows the transformation, or ‘networkization’, using GIS data from Dongtan New Town. The network consisted of 1088 nodes representing intersections or destinations, connected by 3166 links. Each node includes details on adjacent nodes and links, including x- and y-coordinates. Links provide essential details, such as the link length, start and end nodes, and maximum allowable speed on that road segment, all of which are crucial for optimizing routing algorithms.

4.2.2. Demand Data Categorization

Given the practical challenges of gathering real DRT demand data, we chose an alternative approach. We collected bus stop data for Dongtan New Town in March 2024, using the Republic of Korea’s Transportation Card Big Data System [37]. To estimate the DRT demand from the bus data, we applied the public transportation share ratio provided by the Ministry of Land, Infrastructure, and Transport of the Republic of Korea [38]. As illustrated in Figure 9, the share of public transport varies annually, and based on this data,

Table 2. Yearly demand rate for taxis compared to bus demand.

Taxi/Bus	2018	2019	2020	2021
Rate (%)	10.7	12.1	18	19.5

summarizes national taxi usage rates ranging from 10.7% to 19.5%. Reflecting these values and following practices in early-stage DRT planning, we assumed DRT demand to be 5% (low) and 10% (moderate) of existing bus demand. Passenger requests were generated dynamically using probabilistic distributions to simulate time-varying demand, and multiple simulation runs were performed for each scenario to ensure robustness in the evaluation of key performance indicators (KPIs).

4.2.3. Essential Stop Selection

Given that bus stops are overly abundant for DRT services, strategic selection of essential stops is necessary. By leveraging bus stop data, we applied specific criteria to identify these pivotal stops. The area of interest was divided into eighty-one zones, arranged on a 9 × 9 grid. The essential stops were identified within each zone based on the following five weighting criteria:

• The presence of more than one elementary, middle, or high school within a 10-m radius;
• The proximity to an industrial complex or distribution center within 10 m;
• The existence of two or more apartment complexes or residential buildings within the same distance;
• The availability of cultural and essential living facilities such as hospitals and parks within 10 m;
• The location being within twenty meters of a busy street, restaurant street, or subway station.

Through this refinement process, the number of available stops was reduced from 282 to 188—a 33% reduction—as shown in Figure 10. The resulting list of essential stops was then utilized in the simulation experiments to establish a more focused and operationally realistic environment for evaluating the proposed DRT system. This selection not only enhances simulation efficiency, but also reflects the practical constraints of deploying DRT services in high-density urban settings.

4.3. Key Performance Indicator

Defining the KPIs is crucial for testing new operational strategies and evaluating algorithms.

Table 3. Summary of KPIs within an experiment.

Perspective of KPI	KPI Name	KPI Description
Passenger	AWm	Average waiting time to board a vehicle with m passengers
Passenger	ARm	Average ride time in a vehicle with m passengers
Passenger	AΔWm	Average of the difference between expected and actual waiting times for m passengers
Passenger	AΔRm	Average of the difference between expected and actual boarding time for m passengers
DRT	AURn	Average utilization rate for DRT n
DRT	APLn	Average ridership within the operating hours of DRT n
DRT	AAR	Average acceptance rate for calls from DRT n

lists the four essential KPIs from the passenger perspective and three key KPIs from the DRT perspective that we identified for evaluating our strategies. These KPIs are instrumental in assessing the system’s performance and capturing data for subsequent analyses, ensuring a comprehensive evaluation of operational efficacy and strategic outcomes. More information to derive the KPIs is provided in Appendix A.1 and Appendix A.2.

4.4. Experiment 1

In Experiment 1, the number of vehicles varied from 1 to 10 in the current map, and the KPIs for the DRT operation were analyzed across two distinct demand stages: low and high. This strategic approach allows for an understanding of the optimal number of DRTs required prior to service deployment, thereby facilitating the acquisition of anticipatory data. Such a methodical analysis not only underscores the scalability of DRT operations, but also aids in forecasting the system’s efficiency and effectiveness under varying demand conditions.

4.4.1. Experiment 1 Parameter

The setup parameters for Experiment 1 are outlined in

Table 4. Input parameters for Experiment 1.

Parameter Name	Parameter Level	Parameter Description
City	Dongtan 1 and 2 New Town	The city that is the subject of the simulation
City area	33.04 km2 for combined area	The area of the city that is the subject of the simulation
Map node	1088 nodes	The number of nodes in the simulation map
Map link	3136 links	The number of links in the simulation map
Number of DRTs	1~10 (incrementing by 1)	The number of operational DRTs
Number of bus stops	188 stops	The number of bus stops on the map where boarding is possible
Passenger demand	5%, 10%	Passenger demand compared to bus demand
Passenger boarding time	5 s	The time it takes for passengers to board and alight
Passenger call Acceptance time	10 min	The maximum waiting time after calling for a DRT is set at a threshold beyond which passengers may decline the call
DRT speed	Each maximum road speed—5 km/h	The maximum speed that the DRT can travel on each road
DRT capacity	Nine passengers	The maximum number of passengers that can simultaneously be aboard the DRT
Monte Carlo simulations	Thirty simulations	The number of Monte Carlo simulations conducted

, with Dongtan 1 and 2 New Towns as the primary areas of study, covering a total area of 33.04 km². The map incorporates 1088 nodes representing intersections or stops connected by 3136 links that form a road network. In this experimental framework, the number of DRTs varied from one to ten, with 188 designated stops for boarding and alighting. Passenger demand was segmented into two categories, low and high, corresponding to 5% and 10% of the bus demand in Dongtan, respectively.

The key operational parameters include a boarding time of 5 s per group of passengers and a maximum waiting time threshold of 10 min, beyond which passengers may decline calls. The DRT speed was set to 5 km/h below the maximum speed limit of each road; for instance, on a road with a speed limit of 60 km/h, the DRT operated at 55 km/h. DRT can accommodate up to nine passengers simultaneously. To ensure the reliability of the results, the Monte Carlo method was employed, averaging the outcomes over 30 trials.

4.4.2. Experiment 1 Results

The results of the experiment were categorized based on the DRT demand levels of 5% (low) and 10% (high), with subsequent analysis of these outcomes. As discussed in Section 4.3, the analysis of the KPIs for passengers includes the average waiting time, average ride time, deviation in waiting time, and deviation in ride time. Meanwhile, the DRT KPIs focus on the average call acceptance rate, utilization rate, and passenger load per DRT.

In scenarios of low demand, the variations in the average waiting time for DRTs and passenger ride time in relation to the change in the number of vehicles are depicted in Figure 11. For instance, with the operation of six DRTs, passengers experienced an average waiting time of 4.48 min (268.9 s) from the moment the DRT was called for boarding. Furthermore, the journey to their destination post-boarding took an average of 7.76 min (465.8 s). This indicates a clear trend in which an increase in the number of DRTs leads to a reduction in both waiting and ride times for passengers.

The proposed DRT dynamic routing, which allows ride-sharing, leads to potential variations in both waiting and ride times beyond the initial estimates. These deviations are depicted in Figure 11 for both waiting time and ride time. For instance, with six DRTs in operation, the waiting time deviation was observed to be 1.56 min (94.1 s). Comparatively, based on the waiting time results, if a DRT had been able to proceed directly to a called passenger, the waiting could have been 2.92 min shorter (4.48 min–1.56 min deviation), indicating that the actual waiting time extended to 4.48 min due to mid route alterations. Similarly, the ride time deviation was recorded at 2.37 min (142.4 s), suggesting that a direct route to the destination post-boarding might have taken 5.39 min (7.76 min–2.37 min deviation). However, the necessity of adjusting dynamic routes for picking up or dropping off other passengers has led to increased ride times.

When a passenger call predicts a basic waiting time of approximately 10 min, such calls are automatically set for rejection. Figure 12 illustrates the effects on passenger request acceptance rate, DRT utilization rate, and DRT passenger load when the number of available DRTs is changed. Acceptance rates started at a significantly low level, with only one or two available DRTs. Nonetheless, this rate improved noticeably once the availability increased to four DRTs, with almost every call being accepted. When the availability reached six or more DRTs, the average acceptance rate was 100%. Regarding DRT utilization, when only one DRT was in operation, the average utilization rate was 85%; however, this rate decreased to 56% with four available DRTs. This pattern indicates that while more available DRTs lead to higher call acceptance rates, they also result in an increase in idle DRTs. Additionally, an analysis of DRT passenger load revealed that when only one to two DRTs were available, each DRT carried an average of five passengers. However, when the number of available DRTs increased from four to nine, the average number of passengers per DRT decreased to three.

As depicted in Figure 13, the high-demand scenario exhibited a trend similar to that of the low-demand scenario. However, the waiting and ride times observed at the sixth DRT iteration are notably longer, clocking in at 16.7 min (1001.1 s) and 16.5 min (995.2 s), respectively. This marks a significant increase from the low-demand scenario’s times of 4.48 min for waiting and 7.76 min for riding. Moreover, the deviations in waiting and ride times are 13.1 min (786.7 s) and 10.8 min (651.4 s), respectively. These deviations are higher than those recorded in the low demand scenario, which were 1.56 min for waiting and 2.37 min for riding, indicating a pronounced impact of demand levels on DRT service efficiency.

The DRT KPIs demonstrate a consistent trend across different demand scenarios. However, in the low-demand scenario, as shown in Figure 12, the call acceptance rate was 100% when the number of available DRTs reached four. Conversely, in a high-demand scenario, achieving a similar call acceptance rate requires more than six available DRTs, as shown in Figure 14. This finding contrasts with the low-demand condition in which a 56% DRT utilization rate was observed with four available DRTs. For the high-demand scenario, the utilization rate remains significantly higher at 76.2% with the same number of available DRTs. In addition, the analysis of the DRT passenger load shows its variability with the number of available DRTs. With one to three DRTs available, an average of six passengers was observed. This average decreases to five passengers with four to six available DRTs and further decreases to four passengers when the availability exceeds seven DRTs.

4.4.3. Experiment 1 Discussion

Across both low- and high-demand scenarios, the deviation in waiting time and ride time was observed to decrease as the number of vehicles increased, indicating greater service stability under larger fleets. However, at fixed fleet sizes, demand levels had a significant impact. For example, when demand increased from 10% to 20%, waiting times surged by 3.7 times, and ride times increased by 2.12 times, compared to low-demand conditions. This difference highlights the added strain on routing and scheduling in high-demand environments.

To isolate the core service delays, we subtracted the deviation factors and found that the base waiting time under low demand was 2.92 min (from 4.48 min), while under high demand it was 3.6 min (from 16.7 min). Similarly, the base ride time was 5.39 min under low demand and 5.7 min under high demand. These results suggest that the increased total times in high-demand scenarios primarily stem from additional intermediate stops and route adjustments, rather than changes in trip distance.

In terms of call acceptance rate, both demand scenarios showed improvement as vehicle numbers increased. However, when the fleet size exceeded four vehicles under low demand and eight under high demand, the utilization rate dropped significantly, indicating overprovision. Notably, for a fixed number of vehicles, high-demand conditions naturally resulted in a higher average passenger load per DRT, which improves utilization, but may reduce passenger satisfaction due to potential overcrowding.

This comparison underscores the inherent trade-offs between service accessibility (e.g., higher acceptance rates) and operational efficiency (e.g., vehicle utilization). It also emphasizes the importance of demand-aware planning to prevent vehicle underuse while maintaining acceptable service quality. These insights directly address the need for clearer interpretation of KPI dynamics, as emphasized in prior literature and noted in reviewer feedback.

4.5. Experiment 2

In this section, we explore and analyze a novel operation strategy known as the express dispatch service. As previously described, Express Dispatching is a service designed to transport express passengers directly from their pickup location to their destination without any intermediate stops, especially during periods when the number of vehicles exceeds the demand or when additional vehicles are available. This service offers express passenger convenience similar to that of a taxi, providing a more appealing option for those who may otherwise avoid shared rides owing to concerns over extended waiting or ride times.

4.5.1. Experiment 2 Parameter

Experiment 2 followed a structure similar to Experiment 1, as detailed in Section 4.4, but was conducted only for the high DRT demand category. The specific parameters for this experiment are listed in Table 4 and presented in Section 4.4.1. Unlike Experiment 1, this experiment introduced a new variable by varying the proportion of express passengers within the overall passenger pool. Three distinct scenarios were considered: (1) a baseline with no express passengers, identical to the setup in Experiment 1; (2) a case where express passengers accounted for 10% of all passengers; and (3) a case with a 20% express passenger share.

Accordingly, analysis and experimentation were conducted across three scenarios for high-demand situations: no express passengers, 10% express passengers, and 20% express passengers. When passengers are generated, express passengers appear with a random probability of 10% or 20% throughout the entire simulation period. The remaining 90% of passengers are standard passengers, following the same conditions as in Experiment 1. This approach allows a comprehensive examination of how varying levels of express passengers affect the dynamic operation and effectiveness of DRT services under different demand conditions.

4.5.2. Experiment 2 Result

The analysis initially focused on the relationship between the number of available DRTs and the ratio of express passengers under high demand conditions. In scenarios without express passengers, the average number of passengers per DRT is consistently the highest. This occurs because express passengers follow a boarding pattern where the DRT bypasses intermediate stops until reaching their destination, leading to an increased overall passenger count. Furthermore, similar to the observations in Experiment 1, the average passenger load per DRT decreased as more DRTs became available, demonstrating the trade-off between service efficiency and resource utilization.

Figure 15 and Figure 16 illustrate the effects of increasing the number of DRTs from five to ten on waiting and ride times. In these figures, the labels “Standard (10%)” and “Express (10%)” refer to standard and express passengers, respectively, when 10% of all DRT users are assigned to the express service. Similarly, “Standard (20%)” and “Express (20%)” represent the corresponding passenger groups when the express service adoption rate is 20%. Initially, with five DRTs available, the average waiting time stands at 21.71 min (1302.6 s). In a scenario with 10% express passengers, standard passengers have a waiting time of 19.76 min (1186 s), whereas express passengers have a waiting time of 11.85 min (711.1 s). In a 20% express scenario, standard passengers face a waiting time of 22.72 min (1363.4 s), whereas express passengers wait 12.04 min (722.6 s).

As the DRT count reaches nine, the waiting time for standard passengers drops to 6.49 min (389.5 s), 6.13 min (367.9 s), and 6.40 min (384.4 s), with express passengers experiencing times of 4.59 min (275.9 s) and 4.85 min (291.5 s). This trend demonstrates that as more DRTs become available, the gap in waiting times between standard and express passengers narrows, regardless of the express passenger ratio.

Ride times similarly exhibit disparities: 18.58 min (1115.2 s) without express service, 19.8 min (1188 s) in a 10% express scenario, and 19.27 min (1156.7 s) in a 20% express scenario with five DRTs available. However, these differences shrink to 11.17 min (670.2 s), 11.01 min (661.1 s), and 11.58 min (694.9 s) when the number of available DRTs is nine, indicating a convergence in travel durations as DRT availability increases. When there is a large number of available vehicles, accommodating the convenience of express passengers has minimal impact on the waiting and ride times of standard passengers.

Specifically, with five DRTs available and express passengers making up 10% of the total, it was observed that express passengers enjoy a waiting time that is 40% shorter and a ride time that is 72% shorter than standard passengers. Moreover, when the proportion of express passengers increases to 20%, express passengers experience a 47% reduction in waiting time and maintain a 72% shorter ride time relative to standard passengers, demonstrating the effectiveness of express services in optimizing passenger transit times without significantly affecting standard passenger experience.

The deviations in the waiting and ride times followed a similar trend, as shown in the data depicted in Figure 17 for the waiting time and Figure 18 for the ride time deviation. With five vehicles available, the deviation in standard passenger waiting times registers at 17.70 min (1062.3 s), 15.61 min (937.1 s), and 18.43 min (1105.9 s), respectively. For express passengers, the waiting time deviation is significantly lower, at 2.21 min (132.8 s) and 7.40 min (444.4 s). Moreover, as the availability of DRTs increases to nine, the deviation decreases substantially for both standard and express passengers, falling to 3.75 min (225.2 s), 3.37 min (202.4 s), and 3.53 min (212 s) for standard passengers and to 1.53 min (92 s) and 1.8 min (108 s), respectively.

In the high-demand scenario concerning the DRT acceptance rate, as illustrated in Figure 19, the no-express scenario had an acceptance rate of 81.9%, whereas standard passengers in the 10% express scenario had an 80% acceptance rate, and those in the 20% express scenario had an 81.4% rate. However, the acceptance rates for express passengers were lower, at 75.5% and 77.6% in the 10% and 20% express scenarios, respectively. The primary reason for this difference is the challenge of consecutively integrating express passenger departures and destination points into the existing DRT route. This constraint often leads to call rejections for express passengers because of the difficulty in finding a suitable insertion point in the DRT journey. Furthermore, when the number of available vehicles increased to eight, the acceptance rates for all scenarios approached an average of approximately 100%.

The DRT utilization rate, as depicted in Figure 20, reveals that scenarios involving express passengers tend to exhibit slightly higher utilization rates than the no-express scenario, regardless of the number of vehicles. This increase is attributed to the incorporation of express passengers, which may have led to the creation of bypass routes. However, this trend shows that with five available vehicles, the utilization rates were 75.1%, 78.3%, and 75.3%; however, as the number of available vehicles increased to nine, the differences narrowed to 55.4%, 56.1%, and 56.3%, respectively.

Moreover, Figure 21 illustrates that the highest average number of passengers boarding the DRT occurred in the no-express scenario across all vehicle availabilities, and the lowest concurrent passenger numbers were observed in scenarios with 20% express. This is because passengers travel directly from their pickup locations to their destinations, bypassing other stops. In addition, the data indicate that as the number of available DRTs increases, passengers spread more across the fleet, leading to a decrease in the average passenger load per DRT. This dispersion effect underscores the impact of increased vehicle availability in reducing DRT crowding and optimizing passenger distribution.

4.5.3. Experiment 2 Discussion

In Experiment 2, we simulated a high-demand scenario and examined three DRT operation strategies: no express service, 10% express passenger ratio, and 20% express passenger ratio. When 20% of passengers used the express service, waiting times were reduced by 40%, and ride times decreased by 72%. These results indicate that express passengers consistently experienced improved KPIs compared to standard passengers, regardless of demand level, express ratio, or vehicle availability, demonstrating the efficiency of integrating express services into DRT operations.

Additionally, we analyzed the effect of express services on standard passengers’ KPIs. When the number of vehicles was limited, the gap between the KPIs of express and non-express operations was more pronounced. For example, in a high-demand setting with five vehicles, the average waiting times for standard passengers under each scenario were 21.71, 19.76, and 22.72 min, respectively. However, with nine vehicles, these values converged to 6.49, 6.13, and 6.40 min, showing that increasing vehicle availability reduces the disparity. These findings suggest that an optimal fleet size, combined with a balanced ratio of express passengers, can improve service quality for express users without adversely affecting standard passengers.

From an operational standpoint, adding express passengers tends to lower the call acceptance rate or increase the utilization rate compared with scenarios without express passengers. This suggests that more resources are allocated to efficiently transport express passengers. This pattern became more pronounced as the proportion of express passengers increased, regardless of the overall demand and number of vehicles available. If the proportion of express passengers becomes too high, it could negatively impact the KPIs for both standard passengers and overall vehicle operation. Therefore, when considering an increase in the ratio of express passengers, it is necessary to find a suitable balance to effectively manage the consumption of vehicle resources.

These results suggest that the express service is not merely a reclassification of passengers, but rather a strategic operational mechanism that enables differentiated service delivery within DRT systems. By prioritizing a subset of passengers for direct, uninterrupted service, this strategy supports flexible resource allocation aligned with service level expectations. While moderate adoption of express services can enhance performance for targeted users without significantly compromising standard service quality, excessive allocation may lead to system imbalance. Therefore, the express service should be regarded as a configurable operational tool that requires careful calibration. Its effectiveness lies not only in numerical improvements, but also in its potential to support tiered service models, optimize resource distribution, and enhance user satisfaction in capacity-constrained environments.

Furthermore, although express service inevitably introduces a degree of resource inclination by prioritizing specific passengers, our analysis shows that this effect can be mitigated through adequate fleet sizing and demand balancing. When appropriately configured, the express strategy improves overall system efficiency without significantly degrading the service experience for standard passengers. This highlights its potential as a robust and adaptable solution for tiered mobility services in real-world urban operations.

5. Conclusions

This study introduced a DEVS-based simulation framework to evaluate a novel operational strategy for demand-responsive transport (DRT), focusing on an express service model. The modular framework consists of four components—pre-processor, simulation model, operational strategy module, and result analysis—and was used to assess DRT performance across varying vehicle numbers and demand levels. Key performance indicators (KPIs) were analyzed from both the passenger and system perspectives, including wait time, ride time, call acceptance rate, and vehicle utilization.

Simulation experiments demonstrated the feasibility and effectiveness of the proposed strategy. Under high-demand conditions, limited fleet size increased waiting and ride times, whereas expanding the fleet improved call acceptance at the cost of reduced vehicle utilization. The express service strategy, in particular, yielded notable benefits: when 10–20% of passengers used the express option, their waiting and ride times decreased by up to 40% and 72%, respectively, without significantly degrading the experience of standard passengers. These findings indicate that selective integration of express services can improve both operational efficiency and user satisfaction, provided that vehicle allocation is appropriately managed.

This study primarily focused on operational-level modeling and simulation-based evaluation. While KPIs were designed to reflect system performance and user experience, cost-related indicators—such as total operating expenditure—were not explicitly modeled. We recognize that such metrics are essential for balancing service quality and financial sustainability, and we plan to integrate cost analysis modules in future extensions of the framework.

Furthermore, because real-world DRT data were unavailable for the study area, demand was estimated based on existing bus usage data, and model validation was conducted using simplified scenarios. Nevertheless, the proposed DEVS-based framework remains highly modular and adaptable, enabling integration of diverse services, dispatching logic, and regional contexts. Future research will focus on incorporating dynamic demand elements, advanced scheduling algorithms, and economic feasibility analyses, with the goal of supporting DRT deployment in rural and mixed-modal environments. This research offers a flexible and extensible simulation platform for evaluating innovative DRT strategies in evolving mobility systems