2.1. State of the art (available modeling methods)

Our research approach established a solid foundation for identifying and examining existing modeling methods and approaches. Table 1 presents a comprehensive overview of approaches for modeling complex, data-driven networks. Each approach is briefly described, with the key findings highlighted, and example real-world scenarios for practical applications are illustrated. In subsequent sections of this paper, we will delve into a more detailed analysis of these modeling methods, examining their strengths, limitations, and specific contexts where they provide optimal value.

Table 1. Modeling methods retrieved from literature

2.2. Definition of requirements for the modeling method

After finding multiple modeling methods in the literature, their suitability must be evaluated in detail. To do so, specific requirements for the data communication model must be defined stem from a comprehensive review spanning various fields relevant to complex systems analysis, smart systems modeling, and adjacent developmental methodologies. This foundation integrates insights drawn from an extensive literature survey that includes significant contributions as well as established demands identified by Langner et al. (Reference Langner, Rehberg, Tüzün, Roth and Kreimeyer2024) and Paliyenko et al. (Reference Paliyenko, Tüzün, Roth and Kreimeyer2022) within design disciplines. The derived requirements synthesize distinctive needs for both modeling approaches and methods, drawing on established and rigorously tested requirement definitions for modeling methods and languages.

Three key publications are instrumental in shaping these requirements due to their grounded and systematic approach to defining needs within developmental processes, modeling languages, and smart system design. Keller & Binz (Reference Keller and Binz2009) defined requirements for supportive methods in development processes through a comprehensive meta-analysis. Frank & Laak (Reference Frank and van Laak2003) derived requirements for modeling languages, emphasizing process description through their meta-analytical approach. Paliyenko et al. (Reference Paliyenko, Heinz, Schiller, Tüzün, Roth and Kreimeyer2023a) complement this foundation by detailing requirements derived from extensive industrial surveys, which articulate specific needs in the development of smart systems.

In order to undertake this research endeavor, a synthesized model that bridges these three essential domains is required. The envisioned model for data communication is designed to functionally integrate key insights from developmental processes, process modeling languages, and smart system requirements, ensuring that it is capable of capturing the nuanced demands of each. The synthesis juxtaposes challenges identified within the public transportation sector with those in adjacent fields, extracting and aligning specific requirements to ensure that the model is sufficiently robust, adaptable, and sensitive to complex, real-world data flows. By synthesizing the requirements as shown in Table 2, the proposed model for data communication in complex stakeholder networks is positioned to serve as a robust analytical and descriptive tool.

Table 2. Requirements for a suitable modeling approach

3.1. Investigation of available modeling methods

To select a suitable modeling approach, the presented models in Table 1 are evaluated by assessing their fitness to fulfill the requirements posed in Table 2. Table 3 shows the evaluation conducted by the authors who are experts in the research field and have extensive project experience in the industry. A three-step scale is applied: “3” indicates fully fit to meet the requirement, “2” means only a partial fit, and “1” signifies a lack of fitness for this purpose. Each author evaluated the models independently, and the outcomes were discussed in a workshop to derive the final established evaluation.

Table 3. Evaluation of the fitness of the investigated models for the given requirements

The easy-to-comprehend architecture of DSM makes it possible to include any type of entity and domain (Reference Eppinger and BrowningEppinger & Browning, 2012), and be extensible to other parameters of interest. It applies to numerous complexity issues and is adaptable to specific conditions. By dividing into domains, it allows to reduce the complexity, also showing its flexibility: while one domain can be described in detail, others can be summarized, still, a certain depth is required to enable useful analysis. DSM has proven useful in various applications, such as identifying important stakeholders and patterns of interactions (Reference Eppinger and BrowningEppinger & Browning, 2012). However, objectivity concerns arise as interpretation can vary based on the user. SysML comprises various diagrams to comprehensively model any aspects of a system, making it both extensible and adaptive to specific conditions. This also enables its vast applicability. By dividing sub-diagrams of the overall system, it reduces complexity and gives room for flexibility, but still requires that modeling is performed with a certain consistency across the levels under consideration. Numerous case studies show the usefulness of analyzing systems with a SysML-based model, e.g., Orellano (Reference Orellano, Medini, Lambey-Checchin and Neubert2019). Compared to the DSM methods, the strict modeling rules give it an advantage in terms of objectivity, but simultaneously make it more complicated for new users to comprehend. BPMN is primarily suited for business processes and struggles with technical representations. While it simplifies business processes effectively, its comprehensibility and applicability beyond this context are limited. Its extensibility and adaptability are also constrained, reducing its usefulness. The GEMINI Method focuses on stakeholder interdependencies and system interactions, making it highly applicable in multi-domain settings. While adaptable and flexible, it is more complex to use than DSM or SysML and may require training to be fully understood. Its extensibility is moderate, and some subjectivity remains in how dependencies and relationships are assessed. The CPPSS Meta Model is specialized for analyzing cyber-physical product-service systems, offering strong insights into these domains but limiting broader applicability. While it is adaptable and extensible within its domain, comprehensibility is a challenge due to its specialized focus, and complexity reduction is not as effective compared to other modeling techniques. KMDL is comprehensively able to represent stakeholders and data flows within a system (Reference Bastos, Moreira, Bruno, Filho and de Farias FilhoBastos et al., 2014), due to its focus on modeling knowledge-intensive problems, but has limited applicability in multi-domain engineering. It enforces objectivity through strict modeling rules and can simplify knowledge-related systems, but it may not be as effective in reducing complexity in other types of systems. SVN integrates DSM and Graph Theory to model stakeholder relationships and interdependencies effectively. It is highly applicable and flexible, allowing for detailed system representations. However, its comprehensibility is lower due to the need to understand both DSM and Graph Theory, and extensibility to new domains such as IT systems requires considerable customization and effort. Graph Theory mathematically underpins DSM through adjacency matrices, allowing powerful analyses like clustering and centrality measures. It is highly flexible and applicable across domains, though multi-domain representations can become complex. While comprehensible at a basic level, interpreting results objectively still depends on user expertise.

Resulting, both DSM and SysML seem to pose promising approaches. A combined holistic approach comprising both methods could provide promising outputs for modeling data flows in a complex stakeholder network. To investigate this, both are applied to a case study presented in the next section.

3.2. Example application of selected methods

Autonomous buses play an essential role in advances toward more efficient transportation solutions, since they provide the possibility of extending the transportation offering without needing to combat the general shortage of bus drivers. Previous work has identified the need to conceptualize the data communication systems needed for the operation of these smart PSS, since there are numerous interdependent stakeholders in a complex network (Reference Langner, Rehberg, Tüzün, Roth and KreimeyerLangner et al., 2024; Reference Paliyenko, Tüzün, Roth and KreimeyerPaliyenko et al., 2022). To derive recommendations for action, the data-related links in this complex stakeholder network must be analyzed - making this a suitable case study for the research question at hand.

As described, industry workshops were conducted in order to collect the necessary data input. At first, the lifecycle of the autonomous bus is used as a guiding framework to identify all relevant stakeholders in the smart PSS. The necessary data input for the stakeholders and the related data source are then discussed. Further input from discussions with other stakeholders in the system is also considered.

The data available for each information exchange is therefore as follows: information/data, sending stakeholder, and receiving stakeholder. This input is used to create a network model utilizing both a DSM and a SysML approach. Figure 1 shows the structured DSM, which is built with the Lattix software tool for working on DSM-based projects. The stakeholders are shown in the first row and column of the symmetric matrix. The dependency between each other, marked with an entry in the related cell, represents a data/information exchange. All entries in rows represent the input received by this stakeholder, whereas the entries in the column indicate the output generated by the respective stakeholder. The value in the cells is generated by adding the relevant numbers pertaining to the data/information flow: if one item of information is exchanged, “1” is entered, “2” if two, and so on.

Figure 1. Structured DSM built with Lattix showing possible analysis approaches

Lattix enables users to conduct analysis with pre-implemented algorithms for clustering and sequencing. After being applied, the resulting DSM model shows numerous possibilities for analysis. As shown in Figure 1, clusters of closely intertwined stakeholders were identified by clustering. But since these clusters are also interrelated, strict separation is unsuitable. Furthermore, a group of stakeholders with no required input is identified by sequencing. This forms the basis for more detailed analysis: do these stakeholders really need no input, or is data input for the model missing? In this case, this reflects the group of mainly legal authorities and political entities that were not represented in the workshops.

In addition, the DSM model allows for easy identification of the links between certain stakeholders. For example, the bus driver as a currently important stakeholder will be replaced by the autonomous bus. Two views could be of interest: the first is analyzing the information flows coming from the driver and investigating if those need to be replaced, while the second is retrieving the necessary interfaces of the autonomous bus by looking into the flow of information both received and sent. Overall, the DSM model provided a good understanding of the overall system and showed the autonomous bus as a core stakeholder in the closely intertwined stakeholder group related to its operation. This is used as the basis for modeling the data flows between those stakeholders in more detail with SysML.

Both DSM and SysML are modeling techniques used to represent relationships between entities. DSM matrices can be converted into SysML-based models and vice versa. When an autonomous bus network is modeled using SysML, it enables a higher level of detail and information density. This facilitates the breakdown of DSM clusters and the organization and visualization of underlying information or data flows, along with their corresponding sources and sinks. However, as the granularity of content increases, the model’s clarity tends to decrease, primarily due to the overlapping edges between blocks in the two-dimensional representation. To address this limitation, the proposed approach allows for the coexistence of both DSM matrices and SysML models, offering complementary perspectives by utilizing existing software solutions. In the subsequent section, the same network depicted in Figure 1 is modeled using SysML, specifically through an internal block diagram created as a “logical architecture diagram” with the widely used Arcadia Capella software. Capella employs a SysML-like modeling logic, that utilizes modeling principles from UML, SysML and NAF, thus ensuring a high interoperability with other MBSE tools. Figure 2 presents an excerpt from the stakeholder analysis, focusing on data flows, with the autonomous bus as the central point of analysis. The SysML model comprises multiple domains that are divided into subsystems (dark blue) or sub-actors (light blue). Within these subsystems, functions (green) depict how data is processed by the entities. Different types of data and information are transferred between these elements to fulfill the functions of the systems.

Figure 2. Internal block diagram for the stakeholder network around the autonomous bus (excerpt)

The autonomous bus, characterized as a smart product, integrates key components such as sensors, actuators, software, and a human-machine interface (HMI) to enable autonomous operation and user interaction. Sensors on board the bus collect data about its internal state and external environment, such as passenger occupancy, route conditions, and traffic patterns. This data is processed by an onboard controller, which analyzes it to generate control signals for actuators, enabling real-time decision-making for navigation, safety, and operational adjustments. The bus’s behavior can be adapted dynamically through configurable settings that consider factors such as usage patterns, passenger preferences, data insights, and optimization goals. Service providers or data-driven services can implement these changes, ensuring the system evolves with operations and user requirements.

A communication infrastructure supports the autonomous bus network by facilitating seamless data transfer between the smart bus, central systems, and external stakeholders. Pre-processing and filtering of sensor data occur on board the bus to ensure relevance and reduce the volume of raw data transmitted to the cloud. This minimizes communication overhead while maintaining high-quality data for further analysis. The processed and raw data is stored in a service platform where it is enriched with contextual external data, either in a data lake for unprocessed formats or a data warehouse for structured insights.

Customers, as key stakeholders, interact with the autonomous bus network through intuitive interfaces, including the bus’s HMI and an integrated service platform accessible via mobile apps or web portals. These interfaces allow passengers to view real-time bus information, request services, customize preferences, and receive data-driven insights such as route recommendations or delay alerts. Additionally, APIs enable integration with external systems, such as city traffic management or other transportation networks, fostering a cohesive and interconnected public transportation ecosystem.