Petri Net Model Research Articles

Optimal Paradigms for Quantitative Modeling in Systems Biology Demonstrated for Spinal Motor Neuron Synthesis

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.

Automatic construction of Petri net models for computational simulations of molecular interaction network

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.

Airspace Safety Assessment and Risk Estimation based on the Fuzzy Petri Net Model with Multi-Risk Factor Analysis

In this paper an airspace safety assessment and risk estimation method based on the fuzzy Petri net (FPN) model is presented by analyzing 44 related multi-risk factors. In the proposed method, two kinds of real air accident data from 2010 until the present are used to statistically deduce the causes of the corresponding air accidents, namely accidents between manned aircraft, as well as the accidents between manned and unmanned aircraft. All of the data needed are drawn from the authoritative aviation safety network (ASN). These 44 related multi-risk factors are derived from four main aspects that include man, machine, medium, and management. From this, a multi-level evaluation index system for airspace safety is built. Furthermore, the determination of the risk index is based on the official reports which could make the proposed method more objective and accurate. Correspondingly, the airspace safety assessment and risk estimation model based on FPN can be generated by defining multi-risk factors and calculating the weight coefficients. To overcome the deficiency of many network nodes, a risk threshold is introduced to simplify the risk estimation model. The Zhuhai terminal area is taken as an example to assess and estimate its safety. The effectiveness and accuracy of the proposed method are also verified. Results indicate that management is a key factor in airspace safety, with a lack of training being a significant cause of a 126.59% rise in air risk.

Configuration of liveness-enforcing initial marking with the minimum resources for resource allocation systems

The enforcement of liveness is crucial for Petri nets models of resource allocation systems (RASs). It is interesting yet very challenging to establish an initial marking for Petri net plants so that the net is live. Such an initial marking is referred to as liveness-enforcing initial marking (LIM). Despite existing literature presenting various LIMs, no studies have addressed the issue of minimizing the number of resources in an LIM. This work focuses on designing an LIM with the minimum resources (LIM-MR) for a class of Petri nets called systems of sequential systems with shared resources (S4PRs) by assigning a token capacity to each resource place, such that the sum of all involved resources is minimized. This work first establishes a kind of necessary and sufficient liveness condition for S4PR, which is then encoded into a series of variables and constraints in a mixed-integer programming (MIP) formulation. Although LIM-MR may not be unique, solving the proposed MIP formulation can obtain at least one LIM-MR for S4PR under consideration. The experimental results show the solvability of this approach for S4PRs.

Petri net modeling and analysis of an IoT‐enabled system for real‐time monitoring of eggplants

AbstractAs 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.

Transactional dynamics in hyperledger fabric: A stochastic modeling and performance evaluation of permissioned blockchains

Blockchain, often integrated with distributed systems and security enhancements, has significant potential in various industries. However, environmental concerns and the efficiency of consortia-controlled permissioned networks remain critical issues. We use a Stochastic Petri Net model to analyze transaction flows in Hyperledger Fabric networks, achieving a 95% confidence interval for response times. This model enables administrators to assess the impact of system changes on resource utilization. Sensitivity analysis reveals major factors influencing response times and throughput. Our case studies demonstrate that block size can alter throughput and response times by up to 200%, underscoring the need for performance optimization with resource efficiency.

Risk analysis of urea manufacturing plant using fuzzy logic approach

The potential hazard element of chemical process industries has become severe with technological developments over the past few years. Fertilizer industries like the urea industry deal with highly toxic components in nature, causing severe consequences. This paper implements the fuzzy lambda-tau (λ-τ) approach with the Petri net (PN) model on a urea manufacturing plant. The PN model helps to reduce the complexity of the problem, whereas fuzzy logic helps to deal with the uncertainty and vagueness of data. The urea plant has been divided into three major units, that is, the reacting unit (RU), purifying unit (PU), and concentrating unit (CU). The different reliability parameters, such as failure rate, repair time, reliability, and mean time between failures (MTBF), are determined for all these units with different spread rates (±15%, ±25%, and ±35%). A significant change of around 75% and 9% was observed for overall repair time and MTBF, respectively, for a ±35% spread rate. The reliability parameters are found as a function of the square of the spread rate. These studies suggest that the PU of the urea plant is the most vulnerable one and thus requires timely maintenance to avoid any accidents in the future. Furthermore, a detailed qualitative study is done utilizing failure mode and effect analysis (FMEA) to outline the numerous failure causes in order to enhance the system's availability and maintainability. The limitations of conventional FMEA are addressed in this study by obtaining fuzzy RPN values after application of the fuzzy FMEA technique. On comparison of the RPN and FRPN values, the FRPN values are found to be more reliable while prioritizing the failure causes in process industries.

Monitor-based synthesis in enforcing disjunctive generalised mutual exclusion constraints

This paper focuses on enforcing disjunctive generalised mutual exclusion constraints, referred to as OR-GMEC, on Petri net models. In this case, the legal marking set is non-convex, while the admissible marking set can either be convex or non-convex. The study presents a necessary condition for the existence of a monitor-based solution for a non-convex admissible marking set. Subsequently, the disjunctive constraints are developed to derive an optimal supervisory controller, and an algorithm is proposed for solution computation. The design procedure includes off-line computation mechanisms, yielding an optimal (maximally permissive) supervisor with only a few monitors. The key advantage of the suggested approach is that, unlike the current techniques, the number of monitors in the supervisor’s structure does not rise as the number of constraints increases.

Research of methods of modeling of mass service enterprise

Objective. The purpose of the study is to use artificial intelligence tools to optimize and model the automated organization of work at a mass service enterprise. Method. The research is based on the use of a Petri net as a modeling tool, as well as mathematical hardware that makes it possible to implement simulation models of subsystems and conduct additional research on GPSS artificial intelligence models. Result. To process the results of the modeling process, the Petri net modeling method was used and a network activity model graph was developed. The modeling process used with the Petri Net application allows such functions to be described more clearly. The principles of modeling systems based on the GPSS language and Petri nets are considered. Conclusion. It is advisable to use the language devices GPSS and SP, which provide information support for the activities of a mass service enterprise, modeling the structural organization and information flows.

Method of determining timing parameters of real time systems

Real-time systems are widely used and actively implemented in advanced developments across many industries, from medicine to aerospace. Research and modelling of real-time systems are crucial tasks at the design stage, as they help in the determination of whether the system being modelled meets the specified timing characteristics and, accordingly, assess the system's ability to satisfy timing requirements. After all, the success of a real-time system depends not only on their logical correctness but also on the time it takes for the system to generate a result. Considering the various types of tasks, such as synchronous and asynchronous, parallel and sequential, determining their timing characteristics at the design stage is quite a complex problem. It is also essential to consider the sequence of tasks and their arrival times since there are cases where one task depends on the result of another task, and thus, the arrival time of a new task to the scheduler's queue depends on the completion time of the previous task. Previous studies have investigated methods for evaluating the timing characteristics of tasks in real-time systems by analyzing data obtained from modeling the distribution of processor time among tasks according to selected scheduler algorithms using Petri net models in both single-processor and multi-processor systems. These methods ensured the acquisition of task timing characteristics when choosing a specific type of processor and scheduler, which is necessary for the initial technical design of a real-time system. However, the methods have not considered the dynamic nature of task yielding, which is an essential component of modern real-time systems. This paper proposes a method for determining the timing characteristics of real-time systems at the design stage. The proposed method helps to identify the arrival time of tasks, taking into account various types of tasks and their dependencies. The identified timing characteristics can subsequently be used for modelling the system's operation and determining the optimal task scheduling algorithm.

Automated generation of digital models for manufacturing systems: The event-centric process mining approach

Digital and simulation models support the design and management of complex systems. However, system modelling is a time-demanding and knowledge-intensive activity. Moreover, modern manufacturing systems are subjected to frequent changes in production plans and subsequent reconfigurations. Therefore, the quick regeneration of the digital models is necessary to align digital twins and cyber-physical systems. This paper proposes a novel event-centric process mining paradigm, a process discovery algorithm, and a set of Key Performance Indicators for the fast and automated generation of digital models and their benchmarking. The discovery algorithm is based on the Event Relationship Graph of the conceptual model of the physical line. The algorithm is tested in four realistic systems of increasing complexity to verify the accuracy in modelling multi-product systems with re-entrant flows and random reworks in the presence of the assembly, disassembly, and split processes beyond the processing operations, and multi-operation workstations. The Event Relationship Graphs of the four systems are presented through the equivalent Petri nets models. The proposed approach is suitable for systems where the sensor positions are known and meaningful, like manufacturing systems, and it is effective for the quick automated generation of digital models for the activities of production planning and control as it requires a few seconds of computation time and a few hours of system observation.

Evaluation of time-based virtual machine migration as moving target defense against host-based attacks

Moving Target Defense (MTD) consists of applying dynamic reconfiguration in the defensive side of the attack-defense cybersecurity game. Virtual Machine (VM) migration could be used as MTD against specific host-based attacks in the cloud computing environment by remapping the distribution of VMs in the existing physical hosts. This way, when the attacker’s VM is moved to a different machine, the attack has to be restarted. However, one significant gap here is how to select a proper VM migration-based MTD schedule to reach the desired levels of system protection. This paper develops a Stochastic Petri Net (SPN) model to address this issue. The model leverages empirical knowledge about the dynamics of the attack defense in a VM migration-enabled setup. First, we present the results of an experimental campaign to acquire knowledge about the system’s behavior. The experiments provide insights for the model design. Then, based on the model, we propose a tool named PyMTDEvaluator, which provides a graphical interface that serves as a wrapper for the simulation environment of the model. Finally, we exercise the tool using Multi-Criteria Decision-Making methods to aid the MTD policy selection. Hopefully, our results and methods will be helpful for system managers and cybersecurity professionals.

Consistency Analysis of Collaborative Process Data Change Based on a Rule-Driven Method

In business process management, business process change analysis is the key link to ensure the flexibility and adaptability of the system. The existing methods mostly focus on the change analysis of a single business process from the perspective of control flow, ignoring the influence of data changes on collaborative processes with information interaction. In order to compensate for this deficiency, this paper proposes a rule-driven consistency analysis method for data changes in collaborative processes. Firstly, it analyzes the influence of data changes on other elements (such as activities, data, roles, and guards) in collaborative processes, and gives the definition of data influence. Secondly, the optimal alignment technology is used to explore how data changes interfere with the expected behavior of deviation activities, and decision rules are integrated into the Petri net model to accurately evaluate and screen out the effective expected behavior that conforms to business logic and established rules. Finally, the initial optimal alignment is repaired according to the screened effective expected behavior, and the consistency of business processes is recalculated. The experimental results show that the introduced rule constraint mechanism can effectively avoid the misjudgment of abnormal behavior. Compared with the traditional method, the average accuracy, recall rate, and F1-score of effective expected behavior are improved by 4%, 4.7%, and 4.3%, respectively. In addition, the repaired optimal alignment significantly enhances the system’s ability to respond quickly and self-adjust to data changes, providing a strong support for the intelligent and automated transformation of business process management.

Periodic Scheduling Optimization for Dual-Arm Cluster Tools with Arm Task and Residency Time Constraints via Petri Net Model

In order to improve quality assurance in wafer manufacturing, there are strict process requirements. Besides the well-known residency time constraints (RTCs), a dual-arm cluster tool also requires each robot arm to execute a specific set of tasks. We call such a tool an arm task-constrained dual-arm cluster tool (ATC-DACT). To do this, one of the arms is identified as the dirty one and the other as the clean one. The dirty one can deal with raw wafers, while the clean one can deal with processed wafers. This requirement raises a new problem for scheduling a cluster tool. This paper discusses the scheduling problem of ATC-DACTs with RTCs. Due to the arm task constraints, the proven, effective swap strategy is no longer applicable to ATC-DACTs, making the scheduling problem difficult. To address this problem, we explicitly describe the robot waiting as an event and build a Petri net (PN) model. Then, we propose a hybrid task sequence (HTS) as an operation strategy by combining the swap and backward strategies. Based on the HTS, the necessary and sufficient conditions for schedulability are established; also, a linear programming model is developed. We then develop an algorithm using these results to optimally schedule the system. Industrial case studies demonstrate the application of this method.

Wudalianchi volcanism and mantle dynamics in Northeast China: New insight from Pn and Sn tomography

We determine new tomographic models of Pn anisotropic velocity and Sn isotropic velocity in and around the Wudalianchi volcanic area by inverting high-quality Pn and Sn arrival times manually picked from waveforms recorded at the newly deployed high-dense WAVESArray portable seismic stations. Our high-resolution Pn and Sn velocity models reveal strong lateral heterogeneities in the uppermost mantle under the study region. The average Pn and Sn velocities in the uppermost mantle are 8.2 and 4.5 km/s, respectively. Both Pn and Sn velocity models exhibit obvious low-velocity (low-V) anomalies under the Wudalianchi and Keluo volcanoes, whereas under the Songliao basin distinct high-velocity (high-V) zones are revealed. In particular, our Pn model reveals two separate low-V anomalies under the Nuominhe and Halaha volcanic groups, suggesting that they have different deep origins. A large-scale L-shaped low-V zone exists under the Keluo, Wudalianchi, Erkeshan, and Xunke volcanoes, characterized by Pn-wave fast propagation directions (FPDs) parallel with the low-V zone, suggesting that these volcanoes may have the same deep origin. Furthermore, southeast-opened U-shaped Pn FPDs exist around the Wudalianchi volcano, whereas NE-SW FPDs appear under the Great Xing'an range, which are generally consistent with SKS splitting measurements. This feature may reflect lithosphere-asthenosphere coupling beneath the Wudalianchi volcano associated with horizontal flows in the big mantle wedge and compressional tectonics under the Great Xing'an range. These results shed new lights on the Wudalianchi volcanism and mantle dynamics beneath Northeast China.

Model of Sustainable Household Mobility in Multi-Modal Transportation Networks

Nowadays, urban and suburban areas face increasing environmental pressures, and encouraging sustainable transportation behaviors at the household level has become crucial. This paper presents a model of a decision support system (DSS) for promoting sustainable household mobility choices in multi-modal transport networks. The system was modeled using an enhanced Petri Net approach, allowing for the dynamic representation of complex transport networks and multi-modal journey options. The model incorporated various sustainability factors. These were combined into a single environmental impact score, which was considered alongside travel time and cost in the route optimization process. Simulation results demonstrated the DSS’s capability to guide users toward more sustainable mobility choices. The model also showed potential as a tool for policymakers to assess the impact of various sustainable transportation initiatives and infrastructure investments. This paper discussed the versatile applications of the system. It also addressed the limitations of Petri Net models in transportation systems and suggested future research directions.

On Multirobot Path Planning Based on Petri Net Models and LTL Specifications

On Multirobot Path Planning Based on Petri Net Models and LTL Specifications

DDS-P: Stochastic models based performance of IoT disaster detection systems across multiple geographic areas

Effective management of catastrophic events in high-risk zones necessitates a holistic technological approach to protect ecosystems, biodiversity, and native populations. Limitations in sensor range and connectivity hamper real-time data gathering in secluded areas, while financial and technical hurdles hinder the creation of cost-effective, automated systems. This study presents stochastic models, the LoRaW protocol, and cloud technology to enhance sensor deployment simulations. Wireless Sensor Networks and LoRa technology are crucial for extensive monitoring and communication infrastructures. Stochastic Petri Net models optimize system components by assessing crucial performance indicators, such as average response time and system utilization, thus improving disaster response and supporting research hypotheses.

An asset management modelling framework for wind turbine blades considering monitoring system reliability

By incorporating information about asset condition from a monitoring system, engineers can utilize asset management models to manage maintenance activities on wind turbine blades throughout their lifespan. This can lower operating and maintenance costs and increase the life of the blades. The asset management model relies on the monitoring system as a source of information, however, commonly the reliability of the monitoring system is not considered. This paper presents a wind turbine blade asset management Petri net (PN) model that covers the blade asset management process, including degradation, inspection, condition monitoring (CM), and maintenance processes. The paper proposes two contributions. Firstly, while taking into account detailed industry guidelines, the developed model can forecast the future blade condition for a given asset management strategy. Secondly, it investigates the impact of the reliability of the monitoring system on the asset management modelling results. With the aid of the developed model, the number of repair actions and probability distributions of blade condition discovery time are obtained. In addition, the PN gives an indication of how misreporting (underestimation and overestimation) occurs and the extent of the misreporting. The simulation results illustrate the degree of uncertainty introduced into the monitoring results by the reliability of the monitoring system and, consequently, the extent to which this factor influences the maintenance strategies. The proposed model can be used to support asset management decisions when monitoring system performance degrades.

A New Stochastic Petri Net Modeling Approach for the Evolution of Online Public Opinion on Emergencies: Based on Four Real-Life Cases

A New Stochastic Petri Net Modeling Approach for the Evolution of Online Public Opinion on Emergencies: Based on Four Real-Life Cases