# Enhancing Simulation and Analysis of Aircraft Operational Scenarios via SysML Activity Diagram to BPMN Transformation

Mihal Brumbulli, Fabien Bouffaron, Emmanuel Gaudin, Frederique Populus, Fatima-Ez-Zahra Asli

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Mihal Brumbulli, Fabien Bouffaron, Emmanuel Gaudin, Frederique Populus, Fatima-Ez-Zahra Asli. Enhancing Simulation and Analysis of Aircraft Operational Scenarios via SysML Activity Diagram to BPMN Transformation. 13th European Congress of Embedded Real Time Systems (ERTS), Feb 2026, Toulouse, France. 10.82331/ERTS.2026.9. hal-05513255

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# Enhancing Simulation and Analysis of Aircraft Operational Scenarios via SysML Activity Diagram to BPMN Transformation

Mihal Brumbulli¹, Fabien Bouffaron², Emmanuel Gaudin¹, Frederique Populus³, and Fatima-Ez-Zahra Asli³

¹ PragmaDev, Paris, France
mihal.brumbulli@pragmadev.com
emmanuel.gaudin@pragmadev.com

² Airbus SAS, Blagnac, France
fabien.bouffaron@airbus.com

³ Airbus Operations, Toulouse, France
frederique.populus@airbus.com
fatima-ez-zahra.asli@airbus.com

## ABSTRACT

The aerospace industry is faced with highly complex and critical operational scenarios, exemplified by aircraft ground handling, where efficiency and safety are paramount. Simulation has become crucial for managing this complexity, allowing for analysis and optimization. A key technique for such time-sensitive projects is Critical Path Analysis (CPA), which identifies the sequence of tasks determining the overall duration. Given the intricate dependencies in aircraft ground operations, CPA is vital for minimizing turnaround time. While Model-Based Systems Engineering (MBSE) tools utilizing SysML Activity Diagrams (AD) offer simulation capabilities, they often lack sophisticated CPA, and provide limited integrated formal verification. Standard SysML simulation engines primarily focus on execution flow rather than the advanced analytical techniques required for rigorous analysis. This requires exploring alternative approaches for conducting in-depth analysis and formal verification on MBSE models. To address these limitations, this paper proposes a model transformation approach for converting SysML ADs into Business Process Model and Notation (BPMN) diagrams. BPMN's strengths in process modeling and the availability of specialized tools, which offer advanced simulation (including stochastic CPA) and formal verification capabilities, provide a pathway to overcome the analytical shortcomings of standard MBSE simulation. This transformation aims to leverage BPMN's richer semantics and dedicated analysis features to gain deeper insights into complex operational scenarios. The contributions of this paper include defining mapping rules for transforming relevant SysML AD constructs to BPMN and demonstrating this transformation's feasibility using an aircraft standing phase case study. The results show that this approach enables advanced analysis, such as stochastic CPA and formal verification, which are challenging to perform directly within the original SysML modeling environment.

## 1. INTRODUCTION

The aerospace domain is characterized by systems of immense complexity and operational scenarios where efficiency, punctuality, and safety are paramount [26]. Aircraft ground handling and turnaround operations, occurring between arrival and departure, exemplify this complexity. These operations involve orchestrating numerous interdependent activities within confined spaces and tight timeframes, directly impacting airline performance, resource utilization, and passenger satisfaction [26]. Delays during turnaround can propagate through airline networks, leading to significant operational costs and disruptions [24]. Consequently, effective planning, analysis, and optimization of these scenarios are critical [4].

### 1.1. Motivation

Simulation has emerged as an indispensable tool for managing the complexity in the aerospace industry [24]. It allows engineers and operators to model, visualize, and analyze system behavior under various conditions, facilitating performance evaluation, risk reduction, design optimization, and cost savings compared to physical testing alone. Specifically for operational scenarios like aircraft turnaround, simulation enables the study of process dynamics, resource allocation strategies, and the impact of uncertainties [24]. A key analytical technique often required for managing such complex and time-sensitive projects is Critical Path Analysis (CPA). CPA is a method focused on identifying the sequence of dependent tasks that determines the overall scenario duration. By mapping out tasks, their dependencies, and estimated durations, CPA identifies the "critical path" – the longest path through the project network. Tasks on the critical path have zero slack or float, meaning any delay in these tasks directly delays the entire scenario completion. CPA helps in setting realistic deadlines, prioritizing tasks, allocating resources effectively, and monitoring progress. Given the intricate dependencies and stringent time constraints in aircraft ground operations, CPA is crucial for identifying potential bottlenecks and minimizing turnaround time [26].

<footnote>Mihal Brumbulli et al.. This is an open-access article distributed under the terms of the Creative Commons Attribution 4.0 License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.</footnote>
## 1.2. Problem Statement

Model-Based Systems Engineering (MBSE) promotes the use of models over documents for system specification, design, analysis, and verification. The Systems Modeling Language (SysML) [18], an extension of the Unified Modeling Language (UML) [17], provides a standardized graphical notation for representing system requirements, structure, behavior, and para-metrics, facilitating communication and integration across engineering disciplines. MBSE tools, such as Cameo Systems Modeler [14], offer environments for creating and managing these SysML models. These tools often include simulation capabilities, allowing engineers to execute behavioral models like SysML Activity Diagrams (AD). Cameo Simulation Toolkit [15], for instance, supports executing activity models and simulating activity durations based on specified constraints, offering modes like minimum, maximum, average, or random duration sampling. This allows for dynamic execution tracing and basic performance estimation. However, standard SysML AD simulation engines within MBSE tools often exhibit limitations when faced with the rigorous analysis demands of complex operational scenarios like aircraft turnaround:

*   **Lack of Sophisticated Critical Path Analysis:** While tools like Cameo can simulate durations, they often lack built-in, advanced CPA capabilities specifically designed for activity diagrams. Calculating the total duration is different from dynamically identifying the sequence of activities that constitutes the critical path, especially when activity durations are stochastic. The documentation for typical SysML simulation engines focuses on execution flow and time accumulation, not the specific algorithms and statistical reporting needed for robust CPA. This gap is significant because CPA is a primary analysis required for optimizing time-critical operations [26].

*   **Challenges with Variability and Reproducibility:** Real-world operations are subject to inherent variability and uncertainty in task durations due to weather conditions, equipment issues, or human factors [26]. Simulation tools attempt to model this using random durations or statistical distributions. However, this inherent stochasticity means that simulation results can be variable or non-deterministic. Identifying the critical path becomes complex, as different paths may become critical under different sampled durations. Relying solely on basic simulation runs with random elements can make rigorous analysis and result reproducibility difficult. Advanced techniques are needed to perform probabilistic CPA and understand the statistical likelihood of different paths being critical [26].

*   **Limited Integrated Formal Verification:** SysML AD, while useful for describing flow, may lack the formal semantic rigor required for certain types of verification, such as deadlock detection or automated property checking [7]. Standard simulation toolkits may not integrate these formal methods directly with activity diagram execution. System simulation tools often struggle in performing exhaustive state-space analysis efficiently, which are necessary for proving properties like the absence of deadlocks [7].

These limitations highlight a critical challenge: the need often arises to perform specific, rigorous analysis (CPA, formal

verification) on system behavior defined within MBSE models, but the standard simulation capabilities of the MBSE tools themselves may be insufficient for these specialized tasks. The focus of many MBSE tools is on broad modeling capabilities across the system lifecycle, rather than providing deep, specialized analysis engines for behavioral diagrams. This necessitates exploring alternative approaches to enable the required analysis.

## 1.3. Proposed Solution

To address the identified limitations, this paper proposes a model transformation approach. Specifically, it details a method for transforming SysML ADs, as modeled within the Cameo Systems Modeler environment, into Business Process Model and Notation (BPMN) diagrams [16]. The rationale for choosing BPMN as the target language stems from its strengths in process modeling, particularly for simulation and analysis [9]. BPMN offers a richer, more standardized notation specifically designed for representing business processes with greater semantic precision, especially regarding control flow, events, and collaboration. Crucially, BPMN is widely supported by specialized tools that offer advanced simulation and analysis capabilities often lacking in general-purpose MBSE environments. The target tool selected for this work is PragmaDev Process [20]. This tool is specifically designed for BPMN modeling, execution, verification, and optimization. It provides features directly relevant to overcoming the limitations of standard SysML simulation, including:

*   Simulation based on the BPSim standard [31], allowing detailed modeling of time, cost, and resources using statistical distributions.

*   Formal verification capabilities, including exhaustive state-space exploration, automatic deadlock detection, and property checking using Property Sequence Charts (PSC) [20].

*   Explicit support for performance analysis, including the generation of CPA statistics [20].

By transforming the SysML AD representing the aircraft operational scenario into a BPMN model, the aim is to leverage the specialized analysis capabilities of PragmaDev Process to perform CPA and formal verification that are not readily available or easily achievable within the original Cameo environment.

## 1.4. Contributions

The main contributions of this paper are:

1.  The definition of a structured set of mapping rules for transforming SysML AD constructs (within the scope relevant to operational scenarios) into semantically equivalent or approximate BPMN constructs.

2.  A demonstration of the feasibility and practical application of this transformation using a relevant aerospace case study: the aircraft standing phase.

3.  Evidence that the transformation enables advanced analysis, specifically stochastic Critical Path Analysis and formal verification (e.g., deadlock detection), which address key limitations of simulating the original SysML model in a standard MBSE tool.
## 2. RELATED WORK

This study encompasses multiple research domains relevant to aircraft operational scenario modeling. Specifically, it employs MBSE for the specification of operational scenarios, utilizes simulation techniques for analytical evaluation and verification, applies CPA to support optimization efforts, and integrates model transformation methodologies to enable a cohesive and interoperable toolchain across these components.

### 2.1. MBSE with SysML

An integrated approach combining SysML with formal model checking to enhance safety analysis of complex systems is presented in [30]. The authors introduce a transformation framework that converts SysML models into formal NuSMV [8] representations. This enables automated verification of safety properties using temporal logic.

The authors in [1] explore the application of SysML to model-based engineering of safety-critical avionics systems. The paper proposes a domain-specific avionics application concept leveraging SysML standardized API and server-based architecture to enable tool integration, CI/CD pipelines, and collaborative modeling.

A SysML-driven model-based development approach for avionics is evaluated in [12]. It integrates a domain-specific SysML profile, a formal semantic foundation, and an automated verification toolchain. Applied to a wireless avionics data link case study, the method demonstrates improvements in precision, consistency, verifiability, and modifiability of models.

The preceding discussion underscores the relevance of MBSE, with SysML serving as a foundational element in frameworks designed for system analysis, verification, and toolchain integration. While existing methodologies predominantly target safety-critical avionics applications, the present work shifts focus toward operational scenarios. Accordingly, beyond conventional verification tasks, our approach emphasizes the integration of CPA as a key mechanism for optimizing these operational workflows.

### 2.2. Micro- vs Macro-level analysis

The authors in [25] introduce a stochastic simulation framework designed to investigate aircraft boarding as a pivotal element within the overall turnaround process. Their methodology employs a microscopic modeling paradigm grounded in the asymmetric simple exclusion process to capture individual passenger dynamics. This approach enables the comparative assessment of boarding strategies across diverse aircraft configurations and operational scenarios.

A related study presented in [13] examines the influence of passenger boarding within the aircraft turnaround process, with particular focus on its consistent positioning along the critical path. Through simulation-based analysis conducted across various aircraft configurations, the findings indicate that boarding often represents a time-intensive phase of the turnaround.

While both approaches employ microscopic analysis centered on boarding strategies, the present work adopts a macroscopic perspective, emphasizing the optimization of broader operational scenarios in which boarding may represent just one

component. In this context, such approaches are complementary to our methodology, offering value when detailed optimization of specific elements is required following a macro-level analysis. Moreover, as these methods target isolated aspects of the operational framework, they do not inherently engage with MBSE.

### 2.3. CPA

A fuzzy critical path method to estimate aircraft turnaround times under uncertainty is proposed in [3]. The approach addresses scheduling uncertainty by transforming probabilistic distributions of sub-process durations into fuzzy membership functions. It enables modeling of stochastic ground operations by evaluating multiple potential paths and their likelihoods.

In [2] CPA is applied to composite structure repairs in aviation, revealing that 40% of turnaround time stems from waiting for approvals and materials. By modeling the process in ARIS using Event-driven Process Chain (EPC), they identify these delays on the critical path and propose digital interventions—automated documentation, predictive approval, and pre-arrival damage assessment—to shift them off it. These changes could reduce total process time by over 50%, demonstrating CPA’s value in optimizing workflows.

CPA is a key technique for workflow optimization, particularly in complex systems contexts. As such systems comprise numerous interdependent activities whose durations are more accurately represented by probabilistic distributions rather than deterministic estimates, addressing uncertainty becomes essential. While the approach in [3] employed fuzzy logic-based CPA to manage uncertainty, the methodology presented here adopts a simulation-driven strategy. By aggregating results from multiple replications, we construct a stochastic representation of the critical path, visualized as a heat map that highlights regions of temporal sensitivity and process bottlenecks.

## 2.4. Model Transformation

Several formalization strategies have been proposed to define the semantics of UML ADs and enable their transformation into analyzable models. The work in [28] adopts a rule-based model transformation approach to formalize UML AD semantics, targeting project management applications to facilitate scheduling, cost estimation, and resource allocation. The framework in [22] enables the transformation of UML ADs into Petri Nets (PN), facilitating formal verification via the INA model checker. The method employs meta-modeling and graph grammars to automate the transformation process. In [29], UML ADs are translated into Coloured Petri Nets (CPNs), demonstrating the ability to detect behavioral anomalies including inconsistencies, deadlocks, and livelocks. A formal verification technique that converts UML/SysML ADs into equivalent PN models is also presented in [11]. The methodology formalizes token-based execution semantics through a set-theoretic framework and derives systematic mapping rules to translate AD constructs into corresponding PN components.

The authors in [21] present a framework that automatically transforms BPMN models into UML activity diagrams. They adopt a model-driven engineering approach that leverages meta-modeling and graph transformation techniques. Initially, they
define two meta-models—one for BPMN (focusing on events, activities, gateways, and data objects) and another for UML activity diagrams. These meta-models form the backbone of the approach and are used to automatically generate visual modeling environments for both notations.

Reviewed literature indicates that the predominant focus of model transformation techniques is on PN. This emphasis is justified, given that PN represents a well-established formalism that facilitates the rigorous analysis and verification of discrete event dynamic systems. However, the analytical advantages provided by PN come at the expense of domain-specific expressiveness. While PN is a formally sound and computationally powerful notation, its capacity to explicitly represent domain concepts is constrained by its inherently limited set of modeling primitives (only places, transitions, and arcs are available). Consequently, it is essential to ensure that insights derived from PN-based analysis are systematically mapped back to the original model, thereby enhancing their interpretability and usability for domain experts.

The approach presented in this paper targets BPMN 2.0 to facilitate analysis and verification without sacrificing domain-specific conceptual integrity or necessitating a feedback loop to the original model. The analytical processes can be conducted entirely within the BPMN framework, as its structural and semantic similarities to SysML ADs [19, 5] enable seamless representation and evaluation.

# 3. BACKGROUND

## 3.1. Modeling Operational Scenarios

Modeling the behavior of complex operational scenarios requires notations capable of representing sequences of actions, control flow logic, data flow, and potentially resource allocation and timing. Two prominent notations often considered are SysML ADs and BPMN.

### 3.1.1. SysML Activity Diagrams

SysML ADs extend UML ADs to model the flow-based behavior of systems. They depict the sequence of actions, decisions, parallel flows (forks/joins), and the flow of data or objects between actions using pins and object nodes. A key strength of SysML ADs is their integration within a comprehensive SysML model, allowing direct traceability to system requirements, structural elements (Blocks, Parts), and other behavioral views (e.g., State Machines, Sequence Diagrams). They offer flexibility in modeling various types of flows, from high-level operational workflows to detailed software logic. However, SysML ADs can sometimes suffer from semantic ambiguities, particularly concerning complex control flows or precise execution semantics, as the standard allows for interpretation [27, 23]. While powerful for design description, their semantics are not always directly geared towards rigorous, unambiguous execution or formal analysis compared to more specialized notations [11].

### 3.1.2. Business Process Model and Notation (BPMN)

BPMN is an OMG standard specifically designed for modeling business processes. Its primary goal is to provide a notation that is readily understandable by business stakeholders

(analysts, managers) while being precise enough for technical implementation and execution. BPMN features a richer palette of graphical elements compared to UML/SysML ADs, including specific types of start, intermediate, and end events (e.g., message, timer, error events), different task types (e.g., service, user, script), explicit gateway types (exclusive, inclusive, parallel, event-based) for precise control flow logic, and constructs for modeling collaboration between participants and message flows. BPMN 2.0 includes formal execution semantics, which enable simulation, automation via process engines, and rigorous analysis [9]. Its strengths lie in its expressiveness for complex process logic, clarity in representing collaborations, and strong tool support for simulation and analysis. Potential weaknesses include the risk of creating overly complex diagrams if not managed carefully [10] and a less inherent integration with structural system models compared to SysML ADs within an MBSE environment.

### 3.1.3. Comparative Analysis

SysML AD and BPMN offer similar levels of readability and understanding [19, 5]. The choice depends heavily on the modeling context and the primary goal. SysML ADs are advantageous when the behavioral model needs to be tightly integrated with the overall system architecture and requirements within an MBSE framework. They provide a unified language for various system aspects. However, when the primary goal is detailed process analysis, simulation with precise semantics, formal verification, or communication with business stakeholders about operational workflows, BPMN often proves superior due to its specialized constructs, richer notation, and clearer execution semantics. For tasks requiring CPA or deadlock detection on complex workflows, BPMN's provides a more robust foundation for analysis tools. This distinction motivates the transformation from SysML AD (for system context) to BPMN (for specialized analysis). Table 1 summarizes the key differences.

## 3.2. Simulation and Analysis Tools

The choice of modeling notation is often intertwined with the capabilities of the supporting tools for simulation and analysis.

### 3.2.1. Cameo Simulation Toolkit

Integrated within the Cameo Systems Modeler MBSE suite, the toolkit provides execution capabilities for various SysML diagrams, including Activity Diagrams, State Machines, and Parametric Diagrams [15]. Its primary focus is on model execution for validation and basic behavioral analysis. For Activity Diagrams, it supports step-by-step execution, breakpoint debugging, and duration simulation based on constraints applied to actions, using modes like minimum, maximum, average, or random time values [15]. While valuable for understanding model behavior and estimating timelines, it generally lacks sophisticated, built-in features for advanced analysis like stochastic CPA or formal verification methods such as automated deadlock detection or temporal logic property checking directly on the activity diagram. The emphasis is on simulating the defined flow and timing, rather than exhaustively analyzing all possible behaviors or identifying specific critical sequences under uncertainty.
<table><caption>Table 1. SysML AD vs. BPMN comparison.</caption><thead><tr><td>Feature</td><td>SysML AD</td><td>BPMN</td></tr></thead><tbody><tr><td>Purpose</td><td>Model flow-based behavior within a system (software, hardware, process)</td><td>Model business processes end-to-end</td></tr><tr><td>Primary Audience</td><td>Systems Engineers, Software Developers</td><td>Business Analysts, Technical Developers, Managers</td></tr><tr><td>Notation Elements</td><td>Actions, Control/Object Flows, Pins, Decisions, Merges, Forks, Joins, Partitions</td><td>Tasks, Sequence Flows, Gateways (Exclusive, Parallel, Inclusive, Event-Based), Events (Start, Intermediate, End - various types), Pools, Lanes, Data Objects, Message Flows</td></tr><tr><td>Control Flow Semantics</td><td>Can be less precise; relies on Decision/Fork nodes</td><td>More precise; explicit Gateway types (Exclusive, Parallel, Inclusive, Event-Based)</td></tr><tr><td>Data Flow Modeling</td><td>Object Flows, Pins, Activity Parameters</td><td>Data Objects, Data Inputs/Outputs, Data Stores, Data Associations</td></tr><tr><td>Event Modeling</td><td>Basic AcceptEventAction, Time Events</td><td>Rich set of specific event types (Message, Timer, Error, Signal, etc.)</td></tr><tr><td>Collaboration Modeling</td><td>Activity Partitions (Swimlanes)</td><td>Pools and Lanes for participants/roles, Message Flows for inter-pool communication</td></tr><tr><td>Execution Semantics</td><td>Can be ambiguous; less defined for execution [27, 23]</td><td>Defined execution semantics [16]</td></tr><tr><td>CPA / Verification</td><td>Limited built-in support in standard tools [15]</td><td>Stronger foundation for analysis due to precise semantics; supported by specialized tools [20]</td></tr><tr><td>Integration with System Structure</td><td>Tightly integrated within SysML/UML model</td><td>Less direct integration with system structural models</td></tr></tbody></table>

### 3.2.2. PragmaDev Process

This tool is specifically dedicated to the BPMN standard, with a strong focus on process verification and optimization [20]. Its execution engine strictly follows BPMN semantics, allowing for step-by-step animation and trace generation. Critically, the tool incorporates advanced analysis features:

*   **Formal Verification:** It employs exhaustive state-space exploration techniques to automatically detect unreachable paths and potential deadlocks. It also allows users to define behavioral properties using Property Sequence Charts (PSC) and automatically verifies them using an integrated prover (OBP), generating counter-example traces for violations [6].

*   **Performance Simulation:** It implements the BPSim standard, enabling detailed simulation scenarios with stochastic timing (various distributions), costs, resource definitions (availability, roles, performance, cost), and probabilities for gateway branches [20], while ensuring reproducibility of results.

*   **Critical Path Analysis:** Based on the BPSim simulation results, it explicitly calculates and provides statistics on the critical path(s), identifying activities that most frequently impact the overall process duration [20].

### 3.2.3. Comparative Analysis

The two tools represent different philosophies. Cameo Simulation Toolkit provides broad simulation support across various SysML diagram types within an integrated MBSE environment, suitable for general behavioral validation. Pragmadev Process offers deep, specialized analysis capabilities (formal verification, BPSim simulation, CPA) specifically tailored for the BPMN standard. For the specific needs of analyzing complex operational scenarios involving uncertainty, requiring rigorous CPA and verification against potential deadlocks or behavioral errors, Pragmadev Process offers features

that directly address the limitations identified in SysML simulation tools like Cameo. This difference in tool focus justifies the transformation effort: moving the behavioral model from the general MBSE environment to a specialized analysis tool unlocks deeper insights. Table 2 summarizes the comparison.

## 4. SysML AD to BPMN TRANSFORMATION

The transformation approach is structured around a set of translation rules designed to systematically map SysML AD elements to their corresponding BPMN counterparts. It exploits the standardized XML-based representations of both notations not only as a foundation for model transformation, but also as a mechanism for preliminary validation through the XSD Schemas specified by the OMG. Semantic conformance is verified during transformation using the PragmaDev Process tool, which enforces compliance with the rule set defined in the BPMN 2.0 specification [16].

Rather than aiming to establish an exhaustive catalog of transformation rules, the focus is on key and particularly complex mappings, selected based on the specific case study under examination. Additionally, the proposed rules exhibit similarities to those formulated in [21], albeit in reverse; whereas previous work addressed the conversion from BPMN to SysML AD, this study focus is on the opposite direction. The complete list of supported rules is discussed in the following paragraphs.

### 4.1. Translation rules

The majority of translation rules exhibit a straightforward mapping, further emphasising the similarities between the two notations. These rules are presented in Table 3. Certain fundamental translation rules are deliberately omitted from the table due to the inherent complexity of these cases. Rather than employing a direct mapping approach, a pattern-based translation methodology is deemed more appropriate. The complex-
<table><caption>Table 2. Cameo Simulation Toolkit vs. PragmaDev Process.</caption><thead><tr><td>Feature</td><td>Cameo Simulation Toolkit</td><td>PlagmaDev Process</td></tr></thead><tbody><tr><td>Primary Modeling Standard</td><td>SysML (Activities, State Machines, Parametrics, etc.)</td><td>BPMN 2.0</td></tr><tr><td>Main Purpose General</td><td>MBSE model execution and validation</td><td>BPMN model verification, simulation, and optimization</td></tr><tr><td>Simulation Engine</td><td>Proprietary execution engine for SysML semantics</td><td>BPMN 2.0 standard semantics and BPSim for performance</td></tr><tr><td>Time/Duration Modeling</td><td>Duration constraints (min, max, avg, random) on actions</td><td>BPSim standard: fixed values, statistical distributions, costs, resources</td></tr><tr><td>Formal Verification Support</td><td>Limited built-in support for Activity Diagrams</td><td>Exhaustive exploration, deadlock detection, unreachable paths, property checking</td></tr><tr><td>Critical Path Analysis</td><td>Not explicitly mentioned as a feature</td><td>Explicit CPA statistics based on BPSim simulation</td></tr><tr><td>Strengths for Operational Analysis</td><td>Integration with full SysML model supporting various diagrams</td><td>Deep analysis (CPA/Verification), BPSim standard, clear semantics</td></tr><tr><td>Weaknesses for Operational Analysis</td><td>Lacks advanced CPA/Verification; potential ambiguity/non-determinism</td><td>Focused only on BPMN; less integration with system structure</td></tr></tbody></table>

<table><caption>Table 3. SysML AD to BPMN basic translation rules.</caption><thead><tr><th>SysML AD</th><th>BPMN</th></tr></thead><tbody><tr><td>Initial Node</td><td>Start Event</td></tr><tr><td>Flow Final Node</td><td>End Event</td></tr><tr><td>Activity Final Node</td><td>Terminate End Event</td></tr><tr><td>Action</td><td>Task</td></tr><tr><td>Call Behavior Action</td><td>Call Activity</td></tr><tr><td>Timer Event</td><td>Intermediate Timer Event</td></tr><tr><td>Decision Node</td><td>Exclusive Gateway</td></tr><tr><td>Merge Node</td><td>Exclusive Gateway</td></tr><tr><td>Fork Node</td><td>Inclusive Gateway</td></tr><tr><td>Join Node</td><td>Inclusive Gateway</td></tr><tr><td>Control Flow</td><td>Sequence Flow</td></tr></tbody></table>

ity arises primarily from the intricacies of SysML AD Object Flow semantics. To better illustrate this challenge, we examine a representative example in Figure 1. In this scenario, an intuitive translation into BPMN can be achieved through the use of a Data Object. It is feasible for Object Flows to traverse Decision, Merge, Fork, and Join nodes. However, this introduces a fundamental bottleneck in the translation process, as the only BPMN construct capable of propagating through gateways is the Sequence Flow. BPMN Data Associations linked to a Data Object do not adhere to this semantic behavior.

<figure><img src="image_2.png" /><figcaption>Figure 1. Translation of SysML AD Object Flow using BPMN Data Object.</figcaption></figure>

To mitigate this issue, a transformation mechanism is required to convert Data Flow into Sequence Flow and subsequently revert it back to Data Flow. Notably, there exists no direct translation pathway from a Data Association to a Sequence Flow. An effective solution to this problem involves leveraging BPMN Message Flows, as shown in Figure 2.

<figure><img src="image_3.png" /><figcaption>Figure 2. Translation of SysML AD Object Flow using BPMN Message Flow pattern.</figcaption></figure>

This is possible because:
* A Message can encapsulate data, thereby serving as a representation of the Object Flow.

* A Message has the capability to initiate a Message Start Event, which enables the generation of Sequence Flows.

* All Sequence Flows can subsequently converge at a Message End Event, triggering the regeneration of the original Message along with its associated data, thereby preserving continuity.

The same pattern can be applied while defining SysML AD Call Behavior Action as shown in Figure 3.

<figure><img src="image_4.png" /><figcaption>Figure 3. Translation of the definition of a SysML AD Call Behavior Action using BPMN Call Activity with the Message Flow pattern.</figcaption></figure>

The Message Flow pattern offers a viable solution to the Object Flow translation challenge. However, despite its applicability, the approach is not without limitations. Specifically, Message Flows are not allowed within the same BPMN Pool or Participant. For instance, while the example in Figure 3b adheres to BPMN 2.0 rules, the construct in Figure 2b does not comply. Any BPMN 2.0 tool will flag this issue and prevent the implementation of such a pattern.

As a workaround, Message Flows can be omitted, and simple Tasks can be transformed into Send/Receive tasks. These tasks can be then internally linked via the corresponding Message associated with the Start and End Event. This approach

ensures BPMN 2.0 compliance; however, it reduces readability, as flows appear disconnected.

Given this limitation, a specific option has been added into the tool to allow this construct. This decision is justified by the fact that it does not alter execution semantics while significantly enhancing the readability of the model.

## 4.2. Duration and resource properties

Temporal and resource-related data extracted from activity diagrams are mapped to BPSim, extending the BPMN representation. Figure 4 illustrates this transformation.

<figure><img src="image_5.png" /><figcaption>Figure 4. Translation of duration and resource allocation.</figcaption></figure>

However, there exist constraints pertaining to both duration and resource allocation methodologies. SysML ADs, along with the tooling environment, exhibit limitations in their ability to represent complex temporal distributions and intricate resource allocations. Specifically, in Figure 4a, the execution of "Action" necessitates "Resource"; yet, there is no formal mechanism to quantify the amount of "Resource". Additionally, duration is defined using minimum and maximum values, but no capability exists to specify the probabilistic distribution of valid temporal values.
To address this, all durations expressed in (min, max) format are converted to a *triangular distribution* with the *mode* defined as the arithmetic mean: $mode = (min + max) / 2$. Notably, these restrictions are absent in the target language (BPSim), which offers comprehensive tooling support for such specifications.

## 5. CASE STUDY: AIRCRAFT STANDING PHASE

This use-case demonstrates the proposed SysML AD to BPMN transformation framework using a realistic aerospace operational scenario: the aircraft standing phase (turnaround). This critical phase occurs between the aircraft arrival at the parking stand and its departure from it. It has been chosen because of its complexity in order to really challenge the capability and performance of the tool (the associated activity diagram is far from being a simple sequence of a couple of boxes). It involves a coordinated sequence of interdependent and parallel activities that directly impact airline punctuality and airport efficiency, while considering the variability of the operations.

The aircraft standing phase encompasses activities from aircraft securing upon arrival to being ready for departure. Key activities include aircraft securing, ground power/air conditioning connection, passenger deplaning / boarding, baggage / cargo unloading / loading, cabin cleaning, catering / lavatory / water servicing, refueling and associated Ground Support Equipment (GSE) positioning and removal, cockpit preparation, line maintenance and other checks. These activities exhibit various dependencies (e.g., cabin cleaning can start only after passengers deplaning is complete) and opportunities for parallelism (e.g., refueling and baggage handling). On top of that, the sequence is highly dependent on the operational context, such as: Is it the first flight of the day? Do we consider a typical low-cost airline, or an airline for which the quality of service is of high importance? Are some maintenance tasks required? The case study focuses on a typical scenario for a short-haul aircraft, such as an Airbus A320, operating at a moderately busy airport hub. Identifying the activities belonging to the critical path helps to focus the effort on time and robustness where it will bring most value. A graphical representation allows us to visually identify dependencies and the sequence of these critical activities. This directly facilitates the optimization of the turnaround process in several ways: by pinpointing the critical path, efforts can be concentrated on shortening the duration of these specific activities; the graphical representation clearly highlights bottlenecks, allowing for targeted improvements; visualizing the sequence and dependencies can reveal opportunities to re-arrange tasks for parallel execution; knowing the critical path allows for better resource allocation; and it aids in identifying activities where delays would yield the highest operational impact.

To ensure the resulting SysML model faithfully represents the intended operational logic and resource interactions of the aircraft turnaround, rigorous model simulation and debugging are essential. This model debugging capability enables the identification and correction of modeling errors, ensuring the resulting SysML model accurately reflects the intended operational logic and resource interactions of the aircraft turnaround.

The execution of these activities relies on numerous resources, including ground handling and flight crews, and various GSE.

The availability and allocation of these resources significantly influence the overall turnaround time.

### 5.1. The model

The aircraft standing phase model is depicted in Figure 5. While specific details remain undisclosed, the figure offers an overview of the structural complexity inherent to the top-level diagram of the system. The model contains 33 call behavior actions, 363 distinct activities, 162 decision / merge nodes, 110 fork / join nodes, and over 1600 simulation parameters (e.g., activity duration, branch condition, resource requirement, etc.). To enhance clarity and manage the complexity arising from a high number of activities, the model has been structured into two distinct levels. The upper level, as illustrated in Figure 5, exclusively comprises Call Behavior Actions, whereas the lower level encompasses the detailed definitions of these Call Behavior Actions.

### 5.2. Debugging Deadlocks

Prior to conducting performance analysis, a verification procedure is applied to the translated model in BPMN using PragmaDev Process. This step is essential for detecting potential issues that could hinder subsequent analysis. Through this verification, six deadlocks were identified, necessitating resolution. The tool facilitates the retrieval of the execution state at the precise moment a deadlock occurs, enabling targeted debugging and refinement. Figure 6 illustrates an example of a deadlock scenario identified through this process.

During real turnaround operations, the cabin crew starts to prepare the cabin for the passenger boarding of the next flight (e.g., safety and security checks, inventory of food and drinks) only after everyone else (e.g., passengers, catering staff) has left the aircraft, that is to say when the cabin is vacated. However Figure 6a shows that the execution of the call-activity (call behavior action) "Perform pre-flight cabin preparation" is halted due to the absence of the "Cabin Vacated" message. This is clearly an error in the initial SysML model. This message is typically received via either branch (1) or branch (2) of the merging exclusive gateway. However, as illustrated in the figure, branch (1) is unavailable since the execution path diverts through branch (3) instead. Consequently, branch (2) remains the sole pathway for unblocking the call-activity. Tracing branch (2) enables identification of the message source, which is similarly labeled (2) in Figure 6b. The figure demonstrates that branch (1) is selected during execution, thereby bypassing the activity "Exit the A/C (Catering staff)", which is responsible for transmitting the "Cabin Vacated" message. The obvious correction in this case is to make sure the message is sent even when branch (1) is taken.

The corrections implemented during the verification phase enabled the model to execute successfully through completion during simulation.

### 5.3. Critical Path

The simulation scenario is characterized by fixed activity durations, with each activity requiring a single resource for execution. Additionally, the resource allocation is constrained to one unit per resource type, which is clearly a simplification of
<figure><img src="image_6.png" /><figcaption>Figure 5. SysML AD of the aircraft standing phase.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Figure 6. Deadlock scenario.</figcaption></figure>

the reality of the operations.

During each simulation replication, the tool automatically determines the critical path. The resulting critical path heatmap is presented in Figure 7. Given the fixed nature of activity durations, the critical path remains invariant across replications, leading to a superposition of all paths and yielding a concentrated heatmap along the same trajectory (indicated in red in the figure).

Typically, the critical path exhibits greater distribution, resulting in more varied and colorful heatmaps. Each color represents a probability value (ranging from 0% to 100%) indicating the likelihood of an activity appearing within the critical path. This variation arises from modeling activity duration as a distribution rather than a fixed parameter. This would

be more representative of the real operations duration which varies depending on the current specific context, e.g., passenger boarding efficiency, fatigue of the cargo staff, availability of the ground support equipment. However, for the current scenarios, durations remain fixed, leading to a uniform critical path representation in the heatmap. Despite this constraint, the initial results are very promising, demonstrating the effectiveness of the approach in identifying and resolving model inconsistencies while accurately determining the critical path for further analysis.

As a next step, additional simulations could be performed to enhance the analysis of aircraft turnaround efficiency. One approach involves incorporating real duration distributions as inputs to evaluate the sensitivity of the total turnaround duration. Another key objective is to determine the optimal allocation of resources—both human personnel and ground support equipment—to either minimize the overall turnaround time or ensure that it remains within acceptable variations.

## 6. CONCLUSION AND FUTURE WORK

This study has demonstrated the feasibility of transforming SysML ADs into BPMN models to enhance the simulation and analysis of complex operational scenarios, particularly in aircraft turnaround processes. By leveraging BPMN's richer semantics and specialized tools, we have addressed limitations inherent in SysML AD-based simulation, enabling more rigorous CPA and formal verification. The transformation framework proposed in this work offers a structured mapping of SysML constructs to BPMN elements, facilitating advanced performance analysis and process optimization. The case study on aircraft standing phase has illustrated the effectiveness of this approach in identifying bottlenecks and improving operational efficiency.

However, the current work has limitations that should be acknowledged. First, the approach has been validated through a single, albeit representative, case study. Preliminary observations indicate its capacity to manage relatively large-scale
<figure><img src="image_8.png" /><figcaption>Figure 7. BPMN of the aircraft standing phase with the Critical Path.</figcaption></figure>

models, suggesting promising scalability characteristics. Still, issues might occur due to the structural complexity of the model (e.g., more than two levels), and the introduction of activity durations based on distributions. Hence, comprehensive validation across diverse scenarios and application domains remains necessary to draw definitive conclusions regarding its scalability and robustness. Second, the current research framework concentrates on analyzing process flow within a single operational phase. However, many real-world systems, such as aircraft operations, involve transitions between multiple distinct phases modeled effectively using SysML State Machines. A crucial direction for future work is to expand the current approach to analyze these cross-phase scenarios. This would involve integrating the analysis of process flows (using Activity Diagrams) with state-based behavior (using State Machines). The aim is to enable the simulation and analysis of the entire operational life-cycle, understanding how inter-phase transitions occur due to events and conditions and how these state changes impact the processes within each phase, including their initiation, execution, and potential interruptions.

Another direction for future work is to incorporate advanced visualization techniques that will enhance the clarity and usability of simulation results. For example, by leveraging Gantt charts, analysts could track execution timelines with greater precision, facilitating improved planning and resource allocation.

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