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Owing to increasingly important drivers for change, such as automation, digitisation, and dynamic demand patterns, simulation models of production systems become outdated rapidly. At the same time, building simulation models often requires much time, cost, and expertise, especially when dealing with complex job shop production systems. To address these challenges, an automated simulation model generation (ASMG) framework for material flow simulation of production systems is presented. This framework contains multiple approaches to infer routeing, control and temporal aspects from event-based data. To achieve this, methods from process mining (PM) and machine learning (ML) are applied. Additionally, the suitability of Coloured Petri Nets (CPNs) to serve as conceptual and operational simulation models is examined. The inferred simulation models have high validity when compared to the real system concerning the KPIs machine utilisation, throughput, and work in process. It is shown, that most model elements can be inferred very well, in particular process routes, processing times, and resource selection rules. This proof of concept serves as a foundation for research on detection approaches inferring further model elements such as setup times accurately. [ABSTRACT FROM AUTHOR]

Intrusion Detection Systems (IDSs) are a crucial component of modern corporate firewalls. The ability of IDS to identify malicious traffic is a powerful tool to prevent potential attacks and keep a corporate network secure. In this context, Machine Learning (ML)-based methods have proven to be very effective for attack identification. However, traditional approaches are not always applicable in a real-time environment as they do not integrate concrete traffic management after a malicious packet pattern has been identified. In this paper, a novel combined approach to both identify and discard potential malicious traffic in a real-time fashion is proposed. In detail, a Long Short-Term Memory (LSTM) supervised artificial neural network model is provided in which consecutive packet groups are considered as they flow through the corporate network. Moreover, the whole IDS architecture is modeled by a Petri Net (PN) that either blocks or allows packet flow throughout the network based on the LSTM model output. The novel hybrid approach combining LSTM with Petri Nets achieves a 99.71% detection accuracy—a notable improvement over traditional LSTM-only methods, which averaged around 97%. The LSTM–Petri Net approach is an innovative solution combining machine learning with formal network modeling for enhanced threat detection, offering improved accuracy and real-time adaptability to meet the rapid security needs of virtual environments and CPS. Moreover, the approach emphasizes the innovative role of the Intrusion Detection System (IDS) and Intrusion Prevention System (IPS) as a form of "virtual sensing technology" applied to advanced network security. An extensive case study with promising results is provided by training the model with the popular IDS 2018 dataset. [ABSTRACT FROM AUTHOR]

Ventricular assist devices (VADs) are designed to provide sufficient blood flow to patients with severe heart failure. Once implanted, the patient becomes dependent on the VAD, making it essential to prevent situations that could harm the patient while receiving circulatory support. VADs are classified as critical systems (CS), and adverse events (AEs) can lead to serious consequences, including hospitalization or even death. At present, patient care is provided through in-person consultations, with incidents reported via medical device reports (MDRs) to the Food and Drug Administration (FDA). However, there is no real-time monitoring of AEs or oversight of these events. In response to this gap, a system for supervising critical adverse processes in patients with implanted VADs (SCVAD) is proposed, based on horizontally and vertically integrated architecture. This system aims to address the complexity of AEs by considering multiple domains of operation: the device, the patient, and the medical team, as well as the interactions between these entities. In this context, the formalism of Petri nets (PN) is used to develop models that represent adverse processes based on the actions recommended by the medical team. These models allow for the mapping of events with the potential to cause harm to the patient. Therefore, the medical team will be able to monitor adverse processes, as the models in interpreted PN can be isomorphically transcribed into computable algorithms that can be processed on compatible devices, enabling the tracking of complications caused by adverse processes. [ABSTRACT FROM AUTHOR]

The article "Viscous Marangoni migration of an inviscid bubble by surfactant spreading: an exactly solvable model" in the Journal of Fluid Mechanics explores the movement of an inviscid bubble in a viscous fluid due to surfactant spreading. The study analyzes the bubble's speed and displacement based on initial surfactant distribution, identifying a weak finite-time singularity. An exact solution is derived for infinite surface Péclet number using the method of characteristics, with special initial conditions leading to explicit solutions in terms of the Lambert W-function. The research delves into the viscous Marangoni migration of a two-dimensional bubble, offering insights into the dynamics of Marangoni flows and potential advancements in the field. [Extracted from the article]

This study addresses the problem of attack identification in discrete event systems modeled with Petri nets, focusing specifically on sensor attacks that mislead observers to making incorrect decisions. Insertion attacks are one of the sensor attacks that are considered in this work. First, we formulate a novel observation structure to systematically model insertion attacks within the Petri net framework. Second, by generating an extended reachability graph that incorporates the observation structure, we can find a special class of markings whose components can have negative markings. Third, an observation place is computed by formulating an integer linear programming problem, enabling precise detection of attack occurrences. The occurrence of an attack can be identified by the number of tokens in the designed observation place. Finally, examples are provided to verify the proposed approach. Comparative analysis with existing techniques demonstrates that the reported approach offers enhanced detection accuracy and robustness, making it a significant advancement in the field of secure discrete event systems. [ABSTRACT FROM AUTHOR]

The NC-Link protocol, as an integrated communication protocol in the Computerized Numerical Control (CNC) machine tool industry, has drawn significant attention regarding its security since its inception. Although there have been studies proposing improvements to address security issues related to key management and message transmission, systematic security analysis of the protocol remains relatively weak. To better investigate and enhance the security of the NC-Link protocol, our research introduces a formal modeling and analysis method based on Colored Petri Nets (CPN). By establishing a CPN model of the protocol, we analyze the security issues present during communication and propose improvement measures for verification and analysis. First, we developed a CPN model for the NC-Link protocol and verified the model's feasibility through simulation analysis. Subsequently, we introduced an attacker model to analyze the protocol's authentication interaction process, revealing security issues, such as authentication vulnerabilities and key management flaws. Finally, we proposed an improved scheme addressing these issues and conducted a security validation and cost analysis of this scheme. The results show that the improved protocol reduces the computational overhead by 75% during the connection and interaction phases. This indicates that the improved protocol can achieve interactions at a faster speed while maintaining higher security and reliability. The implementation of this scheme provides new reference ideas for related research. [ABSTRACT FROM AUTHOR]

Cybersecurity is an urgent concern. Cybersecurity simulation is an important part of the response to it. This article describes a research program consisting of several interconnected cybersecurity simulation research projects. Cyberattacks are modeled using Petri nets extended with features designed for modeling cyberattacks, including representations of the attacker's and defender's strategies, their actions, and their actions' cost. A database of known attack patterns is automatically processed to generate cyberattack component models, one for each attack pattern. The models are verified and validated using multiple application-relevant methods that consider both Petri nets' theoretical properties and cyberattacks' practical characteristics. Because the source attack pattern database is attacker-centric, the cyberattack component models are enhanced to include defender actions and responses, as well as representations of normal user activities on the computer system being attacked. Cyberattack component models stored in a repository are selected and composed into complete models of target computer systems. Metadata associated with each model guides the selection and composition. The cyberattack models are executed to simulate cyberattacks. Multiple simulation iterations are used to train reinforcement learning algorithms that automatically learn improved attacker or defender strategies. [ABSTRACT FROM AUTHOR]

A dynamical system is considered such that, in this system, particles move on a toroidal lattice of the dimension N1×N2$$ {N}_1\times {N}_2 $$ according to a version of the rule of particle movement in Biham–Middleton–Levine traffic model. We introduce a stochastic case with direction choice for particles. Particles of the first type move along rows, and the particles of the second type move along columns. The goal is to find conditions of self‐organization system for any lattice dimension. We have proved that the BML model as a dynamical system is a special case of Buslaev nets. This equivalence allows us to use of Buslaev net analysis techniques to investigate the BML model. In Buslaev nets conception, the self‐organization property of the system corresponds to the existence of velocity single point spectrum equal to 1. In the paper, we consider the model version when one notable aspect is that a particle may change its type. Exactly, we assume a constant probability q$$ q $$ that a particle changes type at each step. In the case where q=0$$ q=0 $$, the system corresponds to the classical version of the BML model. We define a state of the system where all particles continue to move indefinitely, in both the present and the future, as a state of free movement. A sufficient condition for the system to result in a state of free movement from any initial state (condition for self‐organization) has been found. This condition is that the number of particles be not greater than half the greatest common divisor of the numbers N1,N2,...,Nn$$ {N}_1,{N}_2,\dots, {N}_n $$. It has been proved that, if n=2$$ n=2 $$, and whether 0

Studies in the area of mobile robotics have advanced in recent years, mainly due to the evolution of technology and the growing need for automated and dynamic solutions in sectors such as industry, transport, and agriculture. These devices are complex and the ideal method for localizing, mapping, and navigating autonomous mobile robots changes depending on the application. Thus, the general objective of this work is to propose a simultaneous localization and mapping method for autonomous mobile robots in indoor environments, using computer vision (CV) and Petri net (PN). A landmark was placed next to each door in the analyzed region and images were acquired as the rooms in the environment were explored. The algorithm processes the images to count and identify the doors. A transition is created in the PN for each door found and the rooms connected by these doors are represented by the places in the PN. Then, one of the doors is crossed, new images are obtained and the process is repeated until all rooms are explored. The algorithm generates a PN, which can be represented by an image file (.png) and a file with the extension.pnml. The results compare the layout of four environments with the respective generated PNs. Furthermore, six evaluation criteria are proposed for validating Petri nets as a topological map of environments. It is concluded that using PN for this purpose presents originality and potential innovation, being a SLAM technique for indoor environments, which demands low computational cost. [ABSTRACT FROM AUTHOR]

Hyperledger Fabric is a platform for permissioned blockchain networks that enables secure and auditable distributed data storage for enterprise applications. There is a growing interest in applications based on this platform, but its use requires the configuration of different blockchain parameters. Various configurations impact the system's non-functional qualities, especially performance and cost. In this article, we propose a Stochastic Petri Net to model the performance of the Hyperledger Fabric platform with different blockchain parameters, computer capacity, and transaction rates. We also present a set of case studies to demonstrate the feasibility of the proposed model. This model serves as a practical guide to help administrators of permissioned blockchain networks find the best performance for their applications. The proposed model allowed us to identify the block size that leads to a high mean response time (ranging from 1 to 25 seconds) caused by a change in the arrival rate. [ABSTRACT FROM AUTHOR]

Monitoring natural phenomena using a variety of methods to predict disasters is a trend that is growing over time. However, there is a great disunity among methods and means of data analysis, formats and interfaces of storing and providing data, and software and information systems for data processing. As part of a large project to create a planetary observatory that combines data from spatially distributed geosphere monitoring systems, the efforts of leading institutes of the Russian Academy of Sciences are also aimed at creating an information and computing ecosystem to unite researchers processing and analyzing the data obtained. This article provides a brief overview of the current state of publications on information ecosystems in various applied fields, and it also proposes a concept for an ecosystem on a multiagent basis with unique technical features. The concept of the ecosystem includes the following: the ability to function in a heterogeneous environment on federal principles, the parallelization of data processing between agents using Petri nets as a mechanism ensuring the correct execution of data processing scenarios, the concept of georeferenced alarm events requiring ecosystem reactions and possible notification of responsible persons, and multilevel information protection allowing data owners to control access at each stage of information processing. [ABSTRACT FROM AUTHOR]

This paper presents a simulation model to study the effect of the battery charging rate of Automated Guided Vehicles (AGVs) on the overall output of a toy car production environment. This paper uses Modular Petri Nets for modeling and the General Petri Net Simulator (GPenSIM) for model implementation on MATLAB and simulation. The main focus of this paper is to analyze the operational efficiency of AGVs under varying conditions, such as the impact of battery charge reduction rates and the strategic placement of Charging Stations within the production line. By employing Modular Petri Nets implemented with GPenSIM, this paper presents a detailed model that captures the dynamics (movements and interactions) of AGVs in a simulated manufacturing environment. The model is also extensible, as newer functionalities can be added to it as Petri Modules. This paper specifically focuses on two critical operational parameters: (a) the number of AGVs and their battery charge reduction rate; (b) the number of Charging Stations. In summary, the goal, aim, and novelty of this paper is to provide a simpler yet effective model to practitioners so that they can study and experiment without needing advanced mathematical skills. [ABSTRACT FROM AUTHOR]

Verifying industrial robotic systems is a complex task because those systems are distributed and solely defined by their implementation instead of models of the system to be verified. Some technologies mitigate parts of this problem, e.g., robotic middleware such as the Robotic Operating System (ROS) or concrete solutions such as automata-based specification of robot behavior. However, they all lack the required modeling depth to describe the structure, behavior, and communication of the system. We introduce an improved version of our previous model-driven approach based on Petri nets, integrating these three aspects of ROS-based systems. Using a formal modeling language enables verification of the described system and the generation of complete system parts in the form of ROS nodes. This reduces testing effort because the specification of component workflows and interfaces remains formally proven, while only changed implementations have to be revalidated. We extended our previous approach with novel model transformations, which considerably improved our approach's performance and memory requirements. We evaluate our approach in a case study involving multiple industrial robotic arms and show that the structure of and communication between ROS nodes can be described and verified. [ABSTRACT FROM AUTHOR]

Summary: The frequent geographical changes of mobile nodes in Internet of Things (IoT) systems affect communication, activities, and behaviors. In such scenarios, it is crucial to establish a system model capable of evaluating quality of service (QoS) measures. However, the existing formal modeling techniques pose complexities in modeling mobility. To deal with these challenges, this study aims to propose a model that simplifies the process of modeling mobility within IoT systems. This paper presents a method for modeling mobility within IoT systems by leveraging a widely recognized extension of stochastic Petri nets known as stochastic reward nets (SRNs). The proposed method enhances the SRN model by incorporating the location concept, resulting in a novel extension called mobile SRN (MSRN). In this work, a case study utilizes the MSRN to evaluate the suggested features, examining various scenarios and investigating the impact of factors such as environmental conditions, sensor sampling rate, and the permissible distance of the node from the sink. [ABSTRACT FROM AUTHOR]

DC converter stations have a high voltage level, a long transmission distance, and complex internal equipment, and contain power electronic devices, which seriously endanger the stable operation of the system itself and the active distribution network at the receiving end when faults occur. Accurate fault analysis and diagnosis are critical to the safe and stable operation of power systems. Traditional fault diagnosis methods often rely on a single source of information, leading to issues such as insufficient information utilization and incomplete diagnostic scope when applied to DC transmission systems. To address these problems, a fault diagnosis method for converter stations based on preliminary identification of the fault range and the fusion of evidence information of the switch signal and electrical quantity is proposed. First, the preprocessing of converter station sequential event recording (SER) events and a statistical analysis of event characteristics are completed to initially determine the range of the fault.Then, a fuzzy Petri net model and a BP neural network model are constructed on the basis of the fault data from a real-time digital simulation system (RTDS), and the corresponding evidence information of the switch signal and electrical quantity are obtained via iterative inference and deep learning methods. Finally, on the basis of D-S evidence theory, a comprehensive diagnosis result is obtained by fusing the switch and electric evidence information. Taking the fault data of a DC converter station as an example, the proposed method is analyzed and compared with the traditional method, which is based on single information. The results show that the proposed method can reliably and accurately identify fault points in the protected area of the converter station. [ABSTRACT FROM AUTHOR]

The presence of ethanol in the water solution during irradiation by ionizing radiation decreases the number of OH and H radicals. Since the living cell is mainly composed of water, this causes less damage to the DNA molecule irradiated by low-LET ionizing radiation where an indirect effect prevails. Ethanol thus acts as a radioprotective substance, scavenging radicals H and OH. This fact can be used in various practical applications in which living cells are irradiated by ionizing radiation to protect them. We used hybrid Petri nets to simulate all dynamic processes, including chemical reactions and the simultaneous diffusion of radical clusters. The mathematical simulating model enables us to simulate the damage to the DNA molecule by the radical cluster arising at various distances from this molecule. [ABSTRACT FROM AUTHOR]

This work addresses the analysis and characterization of deadlocks in discrete-event systems modeled by labeled Petri nets (LPNs) with undistinguishable and unobservable transitions. To provide a solution for the notorious problem, it is essential to present an effective characterization in such a way that deadlock control and synthesis are technically and methodologically possible. To this end, we introduce the notion of dangerous implicit vectors (DIVs), which implicitly threaten the system deadlock-freedom. The set of dead markings is divided into two subsets: dead basis markings (DBMs) and dangerous implicit markings (DIMs). An algorithm is designed to compute the sets of DIVs and DIMs at a given basis state of a system. Moreover, by virtue of linear algebraic equations, we formulate sufficient conditions for identifying the existence of blocking markings in an LPN. Finally, an algorithm is developed to construct an observed graph that is a compendious presentation of the reachability graph of a net system, with respect to the existence of dead reaches. At the end of this paper, experiment results that illustrate the correctness and effectiveness of the reported solution are presented. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of optimal sensor selection for ensuring diagnosability of discrete event systems. Given a nondiagnosable discrete event system modeled with labeled Petri nets, a new labeling function can be designed to enforce the system to be diagnosable. An ad‐hoc parallel composition of non‐deterministic finite automata (derived from the original labeled Petri net model) that are observed at multiple observation sites is employed. In order to optimize a given labeling function as well as a sensor selection, an integer linear programming problem is formulated to associate numerical sensor costs with transition relabelings. In a multi‐fault system, this method can determine the type of faults that occur and the fault sequences pertaining to this fault type if multiple faults occur. Examples are presented to demonstrate the proposed method. [ABSTRACT FROM AUTHOR]

Since the 1990s, Petri nets have been used in systems biology for quantitative modeling. Despite the increasing number of models developed during this period, doubts remain about their biological relevance. Although biological systems predominantly exhibit intracellular or cellular structures, the models rely largely on deterministic predictions, failing to capture the inherent randomness and uncertainties of such systems. The question arises whether these models accurately describe the dynamic behavior of biological systems. This paper introduces a methodology for selecting the appropriate modeling paradigms in systems biology. Initially, we construct a Petri net model and perform deterministic, stochastic, and fuzzy stochastic simulations. Then we perform various statistical tests to measure the discrepancies between the simulation results. Based on scale-density analysis, we determine the modeling approach that best approximates the biological system. Finally, we compare the results of the statistical tests and the scale-density analysis to identify the optimal modeling approach. We applied the proposed methodology to the synthesis of spinal motor neuron protein from the spinal motor neuron-2 gene. Analysis revealed significant discrepancies between the simulation results of different modeling paradigms. Due to the sparse nature of the underlying drug-disease network, we conclude that the fuzzy stochastic paradigm provides the most biologically relevant results. We predict drug combinations that could lead to an up to 149-fold increase in spinal motor neuron protein levels, indicating a promising treatment for the disease. This methodology has the potential for application to other gene-drug-disease networks and broader biological systems. [ABSTRACT FROM AUTHOR]

Petri nets are commonly applied in modeling biological systems. However, construction of a Petri net model for complex biological systems is often time consuming, and requires expertise in the research area, limiting their application. To address this challenge, we developed GINtoSPN, an R package that automates the conversion of multi-omics molecular interaction network extracted from the Global Integrative Network (GIN) into Petri nets in GraphML format. These GraphML files can be directly used for Signaling Petri Net (SPN) simulation. To demonstrate the utility of this tool, we built a Petri net model for neurofibromatosis type I. Simulation of NF1 gene knockout, compared to normal skin fibroblast cells, revealed persistent accumulation of Ras-GTPs as expected. Additionally, we identified several other genes substantially affected by the loss of NF1's function, exhibiting individual-specific variability. These results highlight the effectiveness of GINtoSPN in streamlining the modeling and simulation of complex biological systems. [ABSTRACT FROM AUTHOR]

As the current agricultural industry is facing several challenges such as climate changes and lack of qualified farmers, it is extremely necessary to ensure sustainable agriculture and food supply by smart farming (SF). The SF can assist farmers and the associated stakeholders in making correct decisions on improving the yield and quality of agricultural products. In this study, an SF system based on low‐cost Raspberry Pi and Internet of Things (IoT) technologies has been successfully implemented. Through the data items detected by sensors to deeply manage the planting process, the IoT‐enabled communication protocol under ISO standards of Message Queuing Telemetry Transport (MQTT) was used. The bar charts of real‐time environmental parameters are presented on ThingsBoard to achieve the goal of data visualization. Meanwhile, a web server is built for the customized requirements, and the historical datasets are stored in the SQLite database system. Furthermore, a Petri net (PN) model was employed to detect all possible abnormal processes and to verify the feasibility and soundness of an IoT‐enabled system by using a software tool, WoPeD. Finally, the experimental results show that the plants cultivated by the proposed IoT‐enabled system are superior to those cultivated by the existing systems in many perspectives, including the monitoring distance, power consumption, precision, deadlock detection, and running time. [ABSTRACT FROM AUTHOR]

In the era of Industry 4.0, companies must quickly adapt to market and technological changes to remain competitive. While monolithic software systems are still common, Process- Driven Applications (PDA) offer flexible, sustainable, and integrable solutions, relying on Business Process Model and Notation (BPMN) for process modeling. However, BPMN lacks formal semantics, leading to potential errors during process execution. This paper introduces a verification model that integrates Colored Petri Nets (CPN) into the PDA development lifecycle to improve process verification. By converting BPMN models into CPN, the method allows for early detection of errors such as deadlocks and inconsistencies. A real-world, loan application, case study demonstrates that the BPMN + CPN approach reduces errors by 80%, significantly enhancing the reliability and robustness of PDA systems. [ABSTRACT FROM AUTHOR]

The most existing interconnection schemes among the wired/wireless networks cannot be directly employed to the interconnection among 5 G and wired industrial networks. This paper aims to investigate how to achieve the effective interconnection and modeling between 5 G and controller area network (CAN). Firstly, a data priority classification scheduling algorithm is proposed to solve the scheduling problem of protocol conversion between 5 G and CAN. Secondly, considering random and instantaneous transition characteristics of 5 G and CAN networks, a reliable interconnection model is established by using the generalized stochastic Petri net (GSPN) method. Thirdly, QoS key indicators and the corresponding measurement method are proposed by considering different types of data. Finally, simulation and real experiments are conducted to confirm the feasibility and effectiveness of the established model. [ABSTRACT FROM AUTHOR]

This paper presents an approach for the verification of access control in smart contracts written in the Digital Asset Modeling Language (DAML). The approach utilizes Colored Petri Nets (CPNs) and their analysis tool CPN Tools. It is a model-driven-based approach that employs a new meta-model for capturing access control requirements in DAML contracts. The approach is supported by a suite of tools that fully automates all of the steps: parsing DAML code, generating DAML model instances, transforming the DAML models into CPN models, and model checking the generated CPN models. The approach is tested using several DAML scripts involving access control extracted from different domains of blockchain applications. [ABSTRACT FROM AUTHOR]

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Abstract This paper addresses the problem of optimal sensor selection for ensuring diagnosability of discrete event systems. Given a nondiagnosable discrete event system modeled with labeled Petri nets, a new labeling function can be designed to enforce the system to be diagnosable. An ad‐hoc parallel composition of non‐deterministic finite automata (derived from the original labeled Petri net model) that are observed at multiple observation sites is employed. In order to optimize a given labeling function as well as a sensor selection, an integer linear programming problem is formulated to associate numerical sensor costs with transition relabelings. In a multi‐fault system, this method can determine the type of faults that occur and the fault sequences pertaining to this fault type if multiple faults occur. Examples are presented to demonstrate the proposed method.

In automated manufacturing systems (AMSs), because of unpredictable failures, resources can lose functions such that the deadlock control methods, in existence, are invalidated. In this paper, a robust deadlock control approach is proposed for AMSs with multiple unreliable resources. The considered AMSs modelled by Petri nets (PNs) allow to acquire different types of resources at each processing stage. In order to visualise the fact that resource failures occur in AMSs, recovery subnets are designed for the modelling AMSs to depict the failures and recoveries of resources. Based on a siphon detection method performed by a set of integer linear programming formulations, a control specification is proposed. Control places (monitors) with their control variables are designed for the detected unmarked siphons at a marking to guarantee that they are always marked even if some unreliable resources break down. Iteratively, all unmarked siphons are detected and controlled. Therefore, a robust deadlock supervisor is synthesised to ensure the controlled system's liveness no matter there exist resource failures or not. The theoretical analyses and proof are given to verify the correctness of the proposed method. Finally, the comparative studies are presented to expound the proposed method's effectiveness and efficiency. [ABSTRACT FROM AUTHOR]

NFV (Network Function Virtualization) is an innovative paradigm that seeks to improve the flexibility and efficiency of network services. NFV focuses on virtualizing network functions, allowing them to be executed on generic hardware, which decouples software and hardware and allows for more agile and scalable implementations. Through NFV, the concept of SFC (Service Function Chain) emerges, which consists of a sequence of VNFs (Virtual Network Functions), such as gateways, firewalls, and routers, arranged in an orderly manner. A critical challenge faced by SFC is its sensitivity to latency: delay increases as the chain of VNFs lengthens, which can compromise the quality of service. Minimizing this latency is crucial to ensure the efficiency of SFC systems. However, testing different SFC architectures in real environments is costly. As a solution, this study proposes using Stochastic Petri Nets (SPNs) for a performance evaluation of SFC architectures. The developed SPN model allows for analyzing different configurations of VNFs in sequential, parallel, and hybrid architectures. Four case studies were carried out exploring the behavior of the proposed model under different analyses and scenarios. The results obtained were validated through simulations in GNS3 (Graphical Network Simulator-3). The data demonstrate that changes in the SFC architecture can result in significant performance improvements and latency reduction. [ABSTRACT FROM AUTHOR]

The study of real discrete event systems requires the use of models to cope with complexity and large scale. The only way to understand and analyse their behaviour prior to implementation is, in practice, through distributed simulation. Although it is a widely studied discipline, the difficulty of developing efficient distributed simulation code remains a challenge. The use of model driven engineering approaches allows a smooth way from informal specifications to executable code showing traces of the system behaviour. Formal models allow to conduct the phases of this engineering process, and in this work, the formalism is Petri nets. In the simulation literature, Petri nets have been shown to be particularly suitable for modelling and simulation of discrete event systems. This article reviews the role of Petri nets as the core formalism to support a model‐driven engineering approach for the execution of large scale models using distributed simulation. It deals with different aspects related to the Petri net‐based languages used at different stages of the modelling and simulation process, from conceptual modelling of complex systems to the generation of code for executing simulations of Petri net‐based models. After the review, the article proposes an efficient representation of Petri net‐based models. It is analysed from the perspective of the essential properties required for distributed simulation, and was found to provide efficient execution, scalability and dynamic configuration. The article highlights the importance of considering modelling constraints in order to guarantee good properties such as liveness and structural boundedness of Petri net components for the execution of large‐scale Petri net models. The Petri net‐based methodology is illustrated from the perspective of the impact of the formalism to help developing well‐formed models and efficient code for distributed simulation. [ABSTRACT FROM AUTHOR]

Process mining is a field of computer science that deals with the discovery and analysis of process models based on automatically generated event logs. Currently, many companies are using this technology to optimize and improve their business processes. However, a discovered process model may be too detailed, sophisticated, and difficult for experts to understand. In this paper, we consider a problem of discovering the hierarchical business process model from a low-level event log, i. e., the problem of the automatic synthesis of more readable and understandable process models based on the data stored in the event logs of information systems. The discovery of better-structured and more readable process models is extensively studied in the framework of process mining research from different perspectives. In this paper, we present an algorithm for discovering hierarchical process models represented as two-level workflow Petri nets. The algorithm is based on predefined event partitioning so that this partitioning defines a sub-process corresponding to a high-level transition at the top level of a two-level net. In contrast to existing solutions, our algorithm does not impose restrictions on the process control flow and allows for concurrency and iterations.

To solve the problems of chaotic information management and difficult traceability in the manufacturing process of transformer coils, a traceability and management method oriented towards the manufacturing process of transformer coils has been proposed. This method integrates industrial internet identification resolution and extension of Petri net modeling theory. A comprehensive identification and resolution framework for coil manufacturing processes has been constructed. In this manuscript, the authors proposed an industrial data-sharing space based on the producer-consumer model with unified coding identification. This enables information sharing for all resources, including personnel, machinery, materials, methods, environment, and measurements. A method for modeling extensible identification primitives of coil manufacturing process information was proposed, which formalizes the correlation and data structure of process information. A Petri net model for the comprehensive acquisition and integration of elemental information in coil manufacturing processes, as well as a mathematical model for quality traceability, were constructed, thereby forming a complete path for quality traceability information. Finally, based on the method proposed above, a software and hardware environment for identification and traceability for coil manufacturing was established. Taking a certain type of coil as an example, validation was carried out; the results indicate a significant enhancement in the production management and information traceability capabilities of the coil production workshop. This study provides reference and guidance for the process traceability management of power equipment manufacturing. [ABSTRACT FROM AUTHOR]

Designing modular products covers a wider range of tasks than traditional design. There are publications presenting selected issues related to the design of modular products, but generally, there are no comprehensive descriptions of this process. The authors of the article are convinced that the development and implementation of a proven algorithm for designing modular products will increase the effectiveness and efficiency of such work. Designs of modular products, and especially families of such products, can be long-term, therefore, in addition to using the experience gained from such projects, it is justified to use model tests. It was decided to use Petri nets to build a model of the design process. The places of this network are individual tasks carried out during design, and the transitions are the decisions of selected process participants enabling the initiation of subsequent tasks. Decisions are made based on criteria for assessing the effectiveness of individual tasks. The schedule of an actual project of a family of modular devices carried out in one of the renowned centres of the optoelectronics industry was used to formulate them. Analysis of known varieties of Petri nets showed that model construction is possible using coloured time nets. Conclusions were formulated regarding the proposed algorithm of the design process and methods of its evaluation. [ABSTRACT FROM AUTHOR]

In this study, we propose a model called LFSPN, which serves as an extension of stochastic Petri nets dedicated to the multi-agent systems paradigm. The main objective is to specify, verify, validate, and evaluate the flow of materials within an automated production chain. We illustrate the practicality of our model by engaging in a systematic process of modeling and simulation of a production chain involving material flow. To evaluate the performance, we employ a mobile learning agent, which has distinct characteristics, namely mobility and learning. So, the distinctive characteristics of the learning agent are manifested in two key behaviors: mobility and learning. Notably, the learning agent is equipped with a flexible learning algorithm that integrates stochastic elements based on transitions. We suggest using a MATLAB simulation to determine the firing time of each transition within a sequence, guided by three different probability laws (exponential, normal, and log-normal). This sequence is designed to optimize the production process objective while facilitating learning cycles through agent rewards, specified by a production and consumption of tokens in our evolving model. We validate the effectiveness of our model by performing a comparative analysis with similar existing works. The advantages of our LFSPN model are twofold. Firstly, it offers a representation with two levels of abstraction: a graph representing the classic components of an SPN, and an additional layer encompassing the learning and migration aspects inherent to a mobile learning agent. Secondly, our model stands out for its flexibility and simulation simplicity. [ABSTRACT FROM AUTHOR]

Oil refining is a branch of industry that delivers energy to move our vehicles. The transportation of people and goods by airplanes, ships, trains, trucks, buses, and cars is unthinkable for modern mankind without the use of refined petroleum automotive fuels. Thus, the optimal functioning of this industrial branch is vital to contemporary human society. The modeling of processes that take place during refined oil products' manufacturing, which are parallel in their essence, by generalized nets enables their activity optimization and better management. The generalized nets, which are in principle extensions of Petri nets, are applied in this research as a toolkit to model all processes from crude oil selection and delivery to a high complex refinery (Nelson index of 10.6) to the production of a great diversity of fuels, propylene, and polypropylene. The proposed article is a continuation and extension of the articles, published in Mathematics Journal in 2021 and 2023. It is the first (theoretical part) of our comprehensive study of modeling petroleum products' production processes in a refinery, and the second part will discuss the results of the software implementation of the model. [ABSTRACT FROM AUTHOR]

Self-driving cars are one of the main areas of research today, but it has to be acknowledged that the information from the sensors (the perceptron) is a huge amount of data, which is now unmanageable even when projected onto a single traffic junction. In the case of self-driving, the nodes have to be sequenced and organized according to the planned route. A self-driving car in Hungary would have to be able to interpret more than 70,000 traffic junctions to be able to drive all over the country. Besides the huge amount of data, another problem is the issue of validation and verification. For self-driving cars, this implies a level of complexity using traditional methods that calls into question the economics of the already existing system. Fuzzy Petri nets provide an alternative solution to both problems. They allow us to obtain a model that accurately describes the reliability of a node through its dynamics, which is essential in perception since the more reliable a node is, the smaller the deep learning mesh required. In this paper, we outline the analysis of a traffic node's safety using Petri nets and fuzzy analysis to gain information on the reliability of the node, which is essential for the modeling of self-driving cars, due to the deep learning model of perception. The reliability of the dynamics of the node is determined by using the modified fuzzy Petri net procedure. The need for a fuzzy extension of the Petri net was developed by knowledge of real traffic databases. [ABSTRACT FROM AUTHOR]

In order to express the energy flow, motion flow, and control flow in wireless rechargeable sensor networks accurately and intuitively, and to maximize the charging benefit of MVs (mobile vehicles), a type of MTS-HACO (Mobile Transition Sequence Hybrid Ant Colony Optimization) is proposed. Firstly, node places are grouped according to the firing time of node's energy consumption transition to ensure that in each time slot, MV places only enable charging transitions for the node places with lower remaining lifetimes. Then, the FSOMCT (Firing Sequence Optimization of Mobile Charging Transition) problem is formulated under the constraints of MV places capacity, travelling arc weight, charging arc weight, and so on. The elite strategy and the Max–Min Ant Colony system are further introduced to improve the ant colony algorithm, while the improved FWA (fireworks algorithm) optimizes the path constructed by each ant. Finally, the optimal mobile charging transition firing sequence and charging times are obtained, ensuring that MVs have sufficient energy to return to the base station. Simulation results indicate that, compared with the periodic algorithm and the PE-FWA algorithm, the proposed method can improve charging benefit by approximately 48.7% and 26.3%, respectively. [ABSTRACT FROM AUTHOR]

In recent years, manufacturers have increasingly applied automation techniques to enhance efficiency and remain competitive. Material handling is an essential activity in any production process. Its effectiveness has a significant impact on production costs. Automated guided vehicle (AGV) systems have become a strategic tool for factories and automated warehouses. They can reduce production costs and improve delivery times in a competitive business scenario. One of the main problems encountered in managing AGVs is the dispatching decision. The present paper proposes a vehicle dispatching system based on a multi-attribute cascaded fuzzy system with a state-space-based Petri net model to predict the future states of the factory. This work aims to reduce the production system's makespan and/or tardiness values. Additionally, the paper presents one simulated factory scenario to evaluate the proposed fuzzy system against five other dispatching methods. The statistical validation results of the simulations show a 97% confidence level in the hypotheses of this work. [ABSTRACT FROM AUTHOR]

Forest fires cause damage to life, biodiversity, and properties, affecting natural ecosystems, healthy and only. During the practical application of fire prevention, numerous detection techniques have been thoroughly researched to prevent devastating fires. The techniques improve early fire detection and accelerate emergency response, reducing damage and optimizing system containment operations. Wildfire detection requires a robust infrastructure for equipment, maintenance, and ongoing monitoring. Effective cooperation between components and integration of technologies is key to a consistent and comprehensive response to fires. This article proposes a fire monitoring system using drones, cameras, and edge computing technologies. We use Stochastic Petri Nets (SPN) to model the structure and evaluate the system's performance. The model is parameterizable, allowing adjustments to the components' resource capabilities and service time. Twenty-four parameters can be defined, making it possible to evaluate a wide variety of different scenarios. The results obtained in different scenarios in this work have the potential for auxiliary administrators of monitoring systems to estimate more than six analyses and plan more optimized architectures as needed. [ABSTRACT FROM AUTHOR]

In a sequence of papers, the author examined several statistical affinity measures for selecting the coarse degrees of freedom (CDOFs) or coarse nodes (Cnodes) in algebraic multigrid (AMG) for systems of elliptic partial differential equations (PDEs). These measures were applied to a set of relaxed vectors that exposes the problematic error components. Once the CDOFs are determined using any one of these measures, the interpolation operator is constructed in a bootstrap AMG (BAMG) procedure. However, in a recent paper of Kahl and Rottmann, the statistical least angle regression (LARS) method was utilized in the coarsening procedure and shown to be promising in the CDOF selection. This method is generally used in the statistics community to select the most relevant variables in constructing a parsimonious model for a very complicated and high‐dimensional model or data set (i.e., variable selection for a "reduced" model). As pointed out by Kahl and Rottmann, the LARS procedure has the ability to detect group relations between variables, which can be more useful than binary relations that are derived from strength‐of‐connection, or affinity measures, between pairs of variables. Moreover, by using an updated Cholesky factorization approach in the regression computation, the LARS procedure can be performed efficiently even when the original set of variables is large; and due to the LARS formulation itself (i.e., its l1$$ {l}_1 $$‐norm constraint), sparse interpolation operators can be generated. In this article, we extend the LARS coarsening approach to systems of PDEs. Furthermore, we incorporate some modifications to the LARS approach based on the so‐called elastic net and relaxed lasso methods, which are well known and thoroughly analyzed in the statistics community for ameliorating several major issues with LARS as a variable selection procedure. We note that the original LARS coarsening approach may have addressed some of these issues in similar or other ways but due to the limited details provided there, it is difficult to determine the extent of their similarities. Incorporating these modifications (or effecting them in similar ways) leads to improved robustness in the LARS coarsening procedure, and numerical experiments indicate that the changes lead to faster convergence in the multigrid method. Moreover, the relaxed lasso modification permits an indirect BAMG (iBAMG) extension to the interpolation operator. This iBAMG extension applied in an intra‐ or inter‐variable interpolation setting (i.e., nodal‐based coarsening), as well as in variable‐based coarsening, which will not preserve the nodal structure of a finest‐level discretization on the lower levels of the multilevel hierarchy, will be examined. For the variable‐based coarsening, because of the parsimonious feature of LARS, the performance is reasonably good when applied to systems of PDEs albeit at a substantial additional cost over a nodal‐based procedure. [ABSTRACT FROM AUTHOR]

This article is a tribute to Thomas J. Fararo, a pioneer in the field of mathematical sociology. Fararo believed that mathematical sociology should focus on the theoretical unification of different theories and frameworks. The article provides biographical details about Fararo's life and his contributions to the field. It also includes papers from three scholars who discuss Fararo's impact on sociological theory through mathematical modeling and the prospects for achieving his vision of unification. The article emphasizes the importance of communication and collaboration across research groups for successful theoretical integration. [Extracted from the article]

In manufacturing, concepts like the Internet of Things or Cyber-physical Systems accelerate the development from traditional production facilities towards smart factories. Thereby, emerging digital technologies increasingly connect information networks with production processes, forming complex smart factory networks (SFNs). Due to their reliance on information flows and the high degree of cross-linking, SFNs are, in particular, vulnerable to IT availability risks caused by attacks and errors. Against this backdrop, we present a modelling approach for analyzing the effects of IT threats on production processes. Based on Petri Nets, we provide modular SFN components for modelling SFN architectures and for simulating stochastic attack and error propagation. With this, we support the analysis and comparison of different SFN architectures regarding spreading effects, availability of information and production components, and associated effects on productivity. Our approach enables and serves as a foundation for decision support on SFN layouts from a risk perspective and the derivation of IT security mitigation measures in both research and practice. We evaluate our artefact by implementing and applying a software prototype in artificial and real-life settings. [ABSTRACT FROM AUTHOR]

Event structures have emerged as a foundational model for concurrent computation, explaining computational processes by outlining the events and the relationships that dictate their execution. They play a pivotal role in the study of key aspects of concurrent computation models, such as causality and independence, and have found applications across a broad range of languages and models, spanning realms like persistence, probabilities, and quantum computing. Recently, event structures have been extended to address reversibility, where computational processes can undo previous computations. In this context, reversible event structures provide abstract representations of processes capable of both forward and backward steps in a computation. Since their introduction, event structures have played a crucial role in bridging operational models, traditionally exemplified by Petri nets and process calculi, with denotational ones, i.e., algebraic domains. In this context, we revisit the standard connection between Petri nets and event structures under the lenses of reversibility. Specifically, we introduce a subset of contextual Petri nets, dubbed reversible causal nets, that precisely correspond to reversible prime event structures. The distinctive feature of reversible causal nets lies in deriving causality from inhibitor arcs, departing from the conventional dependence on the overlap between the postset and preset of transitions. In this way, we are able to operationally explain the full model of reversible prime event structures. [ABSTRACT FROM AUTHOR]

Reversible CCS (RCCS) is a well-established, formal model for reversible communicating systems, which has been built on top of the classical Calculus of Communicating Systems (CCS). In its original formulation, each CCS process is equipped with a memory that records its performed actions, which is then used to reverse computations. More recently, abstract models for RCCS have been proposed in the literature, essentialy, by directly associating RCCS processes with (reversible versions of) event structures. In this paper we propose a different abstract model: starting from one of the well-known encoding of CCS into Petri nets we apply a recently proposed approach to incorporate causallyconsistent reversibility to Petri nets, obtaining as result the (reversible) net counterpart of every RCCS term. [ABSTRACT FROM AUTHOR]

The airport apron is a high-risk area for aircraft collisions due to its heavy operational load and high aircraft density. Currently, existing quantitative models for apron collision risk provide limited consideration and classification of risk areas. In response, this paper proposes a Petri net-based method for assessing aircraft collision risk. The method predicts the probability of aircraft reaching different areas at different times based on operational data, enabling the calculation of collision risks within the Petri net framework. This approach highlights areas with potential collision risks and provides a classification evaluation. Subsequently, aircraft path re-planning is carried out to reduce collision risks. The model simplifies the complex operations of the apron system, making the calculation process clearer. The results show that, during the mid-phase of aircraft taxiing, there is a significant deviation between the actual and ideal positions of aircraft. Areas with high taxiway occupancy are more prone to collision risks. On peak days, due to relatively high flight volumes, the frequency of collision risks is 14% higher than on regular days, with an average risk increase of 23.3%, and the risks are more concentrated. Therefore, reducing collision risks through path planning becomes more challenging. It is recommended to focus attention on areas with high taxiway occupancy during peak periods and carefully plan routes to ensure apron safety. [ABSTRACT FROM AUTHOR]