Petri Net Formalism Research Articles

Correctness Notions for Petri Nets with Identifiers

A model of an information system describes its processes and how resources are involved in these processes to manipulate data objects. This paper presents an extension to the Petri nets formalism suitable for describing information systems in which states refer to object instances of predefined types and resources are identified as instances of special object types. Several correctness criteria for resource- and object-aware information systems models are proposed, supplemented with discussions on their decidability for interesting classes of systems. These new correctness criteria can be seen as generalizations of the classical soundness property of workflow models concerned with process control flow correctness.

Colored Petri Nets for Modeling and Simulation of a Green Supply Chain System

Green supply chain is an emerging approach in supply chain management to reduce environmental impact of the process concerning the flow of goods and materials. As a discrete-event system, supply chain can be modeled using Petri Nets. Colored Petri Nets (CPNs) extend the classical Petri net formalism with data, time and hierarchy. These extensions makes it possible to deal with the green aspects of the supply chain.This paper deals with the Colored Petri Net approach to model and simulate a green supply chain system. The forward supply chain network starts from the raw material suppliers, to the manufacturers, wholesalers, retailers and to the final customers. The reverse supply chain network is made of collecting points, recycling plants, disassembly plants, and secondary material market. A government environment agency plays the role of regulation of the recycling process. A colored Petri net model of the green supply chain is developed and simulated with CPN Tools, a dedicated software for CPN models. The simulation results as well as the state-space analysis results validate the correctness of the model.

A novel fault detection and diagnostic Petri net methodology for dynamic systems

Faults can have significant, negative impacts on the operation and performance of simple and complex dynamic systems. Based on the integration of Bayesian network diagnostic features with Petri net formalism, the existing Bayesian-supported Petri net tool has demonstrated the flexibility of using the Petri net approach for diagnosing failure scenario of a dynamic system. However, studies on using the proposed hybrid Petri net approach for condition monitoring and early detection and diagnosis of single and multiple failures in a dynamic system with feedback control loops are yet to be investigated. Thus, this paper presents a methodology to address this research gap using the operation of a water tank level control system as a case study. The method combines the constructed Generalised Stochastic Petri Net (GSPN) model of the system operation with its corresponding fault diagnostic Petri net model, created using the proposed modified Bayesian Stochastic Petri Net (mBSPN) formalism. The GSPN model establishes the causal relationships between the system’s components and/or subsystems. It further identifies deviations in the sensor measurements of the observable process variables characterising the system operation. The information provided by the sensors in the system model are then inputted into the mBSPN model to diagnose the root cause of the observed deviations. The obtained results demonstrated the capability of using the proposed integrated Petri net methodology for system condition monitoring, early fault detection and diagnosis of single and multiple failures in a dynamic system with feedback control loops.

Impact of computer users on cyber defense strategies

AbstractCybersecurity research often focuses primarily or exclusively on the interactions between the attacker, trying to exploit the computer system, and the defender, trying to protect it. However, including the computer users is important because the users’ requirements are the reason the computer system exists.An extension of the Petri net formalism, Petri Nets with Players, Strategies, and Costs (PNPSC) was used to model cyberattacks described in the MITRE Common Attack Pattern Enumeration and Classification database. PNPSC models include the attacker, defender, and computer user as “players” attempting to achieve competing goals. Each player can observe the current marking of a subset of the PNPSC net's places and change the stochastic firing rates of a subset of the net's transitions in order to achieve their goals. A mapping between the markings of a player's observable places and the desired firing rates of player's controllable transitions is the player's strategy.A reinforcement learning algorithm was integrated with PNPSC models of three cyberattack patterns to learn strategies for the defender in simulations both with and without a representation of the computer user. A simulation experiment showed that the defender's reward was lower and the defender's learned strategy was different when the user was represented. A second simulation experiment and statistical analysis confirmed that the differences were not due simply to randomness. With the user represented, the system defender must balance security against usability. This research provides a more complete cyberattack model and shows that user models are important in future cybersecurity simulation.

Searching for significant reactions and subprocesses in models of biological systems based on Petri nets

The primary aim of this research was to propose algorithms enabling the identification of significant reactions and subprocesses within models of biological systems constructed using classical Petri nets. These solutions allow to performance of two analysis methods: an importance analysis for identifying individual reactions critical to the functioning of the model and an occurrence analysis for finding essential subprocesses. To demonstrate the utility of these methods, analyses of an example model have been performed. In this case, it was a model related to the DNA damage response mechanism. It is worth noting that the proposed analyses can be applied to any biological phenomenon represented using the Petri net formalism. The presented analysis methods represent an extension of classical Petri net-based analyses. Their utility lies in their potential to enhance our comprehension of the biological phenomena under investigation. Furthermore, they can lead to the development of more effective medical therapies, as they can aid in the identification of potential molecular targets for drugs.

A new computational workflow to guide personalized drug therapy

Objective:Computational models are at the forefront of the pursuit of personalized medicine thanks to their descriptive and predictive abilities. In the presence of complex and heterogeneous data, patient stratification is a prerequisite for effective precision medicine, since disease development is often driven by individual variability and unpredictable environmental events. Herein, we present GreatNectorworkflow as a valuable tool for (i) the analysis and clustering of patient-derived longitudinal data, and (ii) the simulation of the resulting model of patient-specific disease dynamics. Methods:GreatNectoris designed by combining an analytic strategy composed of CONNECTOR, a data-driven framework for the inspection of longitudinal data, and an unsupervised methodology to stratify the subjects with GreatMod, a quantitative modeling framework based on the Petri Net formalism and its generalizations. Results:To illustrate GreatNectorcapabilities, we exploited longitudinal data of four immune cell populations collected from Multiple Sclerosis patients. Our main results report that the T-cell dynamics after alemtuzumab treatment separate non-responders versus responders patients, and the patients in the non-responders group are characterized by an increase of the Th17 concentration around 36 months. Conclusion:GreatNectoranalysis was able to stratify individual patients into three model meta-patients whose dynamics suggested insight into patient-tailored interventions.

From Compositional Petri Net Modeling to Macro and Micro Simulation by Means of Stochastic Simulation and Agent-Based Models

Computational modeling has become a widespread approach for studying real-world phenomena by using different modeling perspectives, in particular, the microscopic point of view concentrates on the behavior of the single components and their interactions from which the global system evolution emerges, while the macroscopic point of view represents the system’s overall behavior abstracting as much as possible from that of the single components. The preferred point of view depends on the effort required to develop the model, on the detail level of the available information about the system to be modeled, and on the type of measures that are of interest to the modeler; each point of view may lead to a different modeling language and simulation paradigm. An approach adequate for the microscopic point of view is Agent-Based Modeling and Simulation, which has gained popularity in the last few decades but lacks a formal definition common to the different tools supporting it. This may lead to modeling mistakes and wrong interpretation of the results, especially when comparing models of the same system developed according to different points of view. The aim of the work described in this paper is to provide a common compositional modeling language from which both a macro and a micro simulation model can be automatically derived: these models are coherent by construction and may be studied through different simulation approaches and tools. A framework is thus proposed in which a model can be composed using a Petri Net formalism and then studied through both an Agent-Based Simulation and a classical Stochastic Simulation Algorithm, depending on the study goal.

Data-aware conformance checking with SMT

Conformance checking is a key process mining task to confront the normative behavior imposed by a process model with the actual behavior recorded in a log. While this problem has been extensively studied for pure control-flow processes, data-aware conformance checking has received comparatively little attention. In this paper, we tackle the conformance checking problem for the challenging scenario of processes that combine data and control-flow dimensions. Concretely, we adopt the formalism of data Petri nets (DPNs) and show how solid, well-established automated reasoning techniques from the area of Satisfiability Modulo Theories (SMT) can be effectively harnessed to compute conformance metrics and optimal data-aware alignments. To this end, we introduce the CoCoMoT (Computing Conformance Modulo Theories) framework, with a fourfold contribution. First, we show how SMT allows to leverage SAT-based encodings for the pure control-flow setting to the data-aware case. Second, we introduce a novel preprocessing technique based on a notion of property-preserving clustering, to speed up the computation of conformance checking outputs. Third, we show how our approach extends seamlessly to the more comprehensive conformance checking artifacts of multi- and anti-alignments. Fourth, we describe a proof-of-concept implementation based on state-of-the-art SMT solvers, and report on experiments. Finally, we discuss how CoCoMoT directly lends itself to further process mining tasks like log analysis by clustering and model repair, and the use of SMT facilitates the support of even richer multi-perspective models, where, for example, more expressive DPN guards languages are considered or generic datatypes (other than integers or reals) are employed.

Computational modeling of signal transduction networks without kinetic parameters: Petri net approaches.

More and more computational techniques have been applied to model biological systems, especially signaling pathways in medical systems. Due to the large number of experimental data driven by high-throughput technologies, new computational concepts have been developed. Nevertheless, often the necessary kinetic data cannot be determined in sufficient number and quality because of experimental complexity or ethical reasons. At the same time, the number of qualitative data drastically increased, for example, gene expression data, protein-protein interaction data, and imaging data. Especially for large-scale models, the application of kinetic modeling techniques can fail. On the other hand, many large-scale models have been constructed applying qualitative and semiquantitative techniques, for example, logical models or Petri net models. These techniques make it possible to explore system's dynamics without knowing kinetic parameters. Here, we summarize the work of the last 10 years for modeling signal transduction pathways in medical applications applying Petri net formalism. We focus on analysis techniques based on system's invariants without any kinetic parameters and show predictions of all signaling pathways of the system. We start with an intuitive introduction into Petri nets and system's invariants. We illustrate the main concepts using the tumor necrosis factor receptor 1 (TNFR1)-induced nuclear factor κ-light-chain-enhancer of activated B cells (NF-κB) pathway as a case study. Summarizing recent models, we discuss the advantages and challenges of Petri net applications to medical signaling systems. In addition, we provide exemplarily interesting Petri net applications to model signaling in medical systems of the last years that use the well-known stochastic and kinetic concepts developed about 50 years ago.

Holistic View on the Structure of Immune Response: Petri Net Model

The simulation of immune response is a challenging task because quantitative data are scarce. Quantitative theoretical models either focus on specific cell-cell interactions or have to make assumptions about parameters. The broad variation of, e.g., the dimensions and abundance between lymph nodes as well as between individual patients hampers conclusive quantitative modeling. No theoretical model has been established representing a consensus on the set of major cellular processes involved in the immune response. In this paper, we apply the Petri net formalism to construct a semi-quantitative mathematical model of the lymph nodes. The model covers the major cellular processes of immune response and fulfills the formal requirements of Petri net models. The intention is to develop a model taking into account the viewpoints of experienced pathologists and computer scientists in the field of systems biology. In order to verify formal requirements, we discuss invariant properties and apply the asynchronous firing rule of a place/transition net. Twenty-five transition invariants cover the model, and each is assigned to a functional mode of the immune response. In simulations, the Petri net model describes the dynamic modes of the immune response, its adaption to antigens, and its loss of memory.

Modeling and Simulation of Shared Electric Automated and Connected Mobility Systems with Autonomous Repositioning: Performance Evaluation and Deployment

The boom seen in artificial intelligence in recent years has led to a revolution in the automotive industry. Numerous automakers around the world, such as Tesla, Toyota, Honda, and BMW, have achieved giant strides in the development of e-autonomous vehicles. Consequently, shared electric automated vehicle mobility (SEAVM) systems, which are a crucial part of future innovative transportation solutions, have attracted significant attention from the research community, particularly from a design perspective. However, the flexibility of shared automated mobility systems may lead to a self-operating technology issue (unequal distribution of vehicles), since users in these systems can pick up and drop off electric vehicles wherever they like. With this in mind, this paper addressed the issues of autonomous repositioning and the assignment of shared autonomous electric vehicle systems to balance a system’s network and fulfill its demand. Modeling, analysis and assessment of the system’s performance were carried out using stochastic Petri nets formalism, which included determining the average time areas were empty/congested and the number of unserved consumers, and estimating the redistribution service launch moment. Furthermore, many simulation scenarios were analyzed, including repositioning and without repositioning scenarios, in order to evaluate the efficiency of the model and to show the potential of using Petri nets as a probabilistic formalism approach for the modeling of e-automated mobility systems.

ON/OFF control for reaching a steady state attractive region in batches Petri nets

This paper addresses an event-driven control problem of controlled generalized batches Petri nets without discrete nodes, i.e., a class of hybrid Petri net formalisms. The goal of the controller is to reach a given steady state from an initial marking qualified as blocking, by controlling the flow of transitions. To this end, we firstly characterize an attractive region of the steady state as an optimal solution of a linear programming problem (LPP). Next, based on the ON/OFF state of transitions, which depends on the enabling conditions and the firing quantities, an ON/OFF event-driven control strategy is proposed for reaching, from a blocking initial marking quantity, the nearest marking quantity in the attractive region. The admissible controlled firing flow vector is computed according to a LPP which maximizes the firing flow of ON-transitions to its maximal firing flow while it imposes a null firing flow to OFF-transitions. The proposed strategy is event-driven and the control actions are updated only when specific events occur. The basic idea of this new control strategy is to fire each transition as fast as possible at any event step until the minimal firing quantity vector is reached.

A Petri Net Architecture for Real-Time Human Activity Recognition in Work Systems

Real-time human-centered assistance in industrial processes depends on the individual history of the work person's activities in the work system and requires adequate methods for tracking the person's actions. Most research in human activity recognition is based on recognizing actions from video data using computer vision methods. Digital equipment, standardized machine data interfaces, and smart wearable devices extend the possibilities to describe the current state of the work system. Petri nets have already been applied to human activity recognition, however, without the requirement of detecting actions in real-time. This paper proposes a Petri net architecture that enables hierarchical description-based human activity recognition in industrial work processes. We present an extension, a Partitioned Colored Petri Net, based on the colored Petri net formalism that infers activities from state transitions of the work system in real-time. In a case study, we demonstrate the Petri net's application for an error-based learning system that visualizes error consequences in augmented reality using experimentable digital twins.

Digital Twin in the Provision of Power Wheelchairs Context: Support for Technical Phases and Conceptual Model

Worldwide, many wheelchair users find it difficult to use or acquire a wheelchair that is appropriate for them, either because they do not have the necessary financial support or because they do not have access to trained healthcare professionals (HCPs), but they are essential for the correct provision of assistive products and user training. Consequently, although wheelchairs are designed to promote the well-being of many users, in many cases, they end up being abandoned or do not provide any benefit, with the chance of causing harm and potentially putting people in danger. This article proposes the creation and use of a Digital Twin (DT) of a Power Wheelchair (PWC) to promote the health of wheelchair users, by facilitating and improving the delivery of remote services by HCPs, as well as to include monitoring services to support timely maintenance. Specifically, a DT is a virtual counterpart that is seamlessly linked to a physical asset, both relying on data and information exchange for mirroring each other. Currently, DT is emerging and being applied to different areas as a promising approach to gather insightful data, which are shared between the physical and virtual worlds and facilitate the means to design, monitor, analyze, optimize, predict, and control physical entities. This article gives an overview of the Digital Twin concept, namely its definition, types, and properties, and seeks to synthesize the technologies and tools frequently used to enable Digital Twins; we also explain how a DT can be used in the technical phases of the PWC provision process and propose a conceptual model highlighting the use of an MDD approach benefiting from a Petri net formalism, which is presented to systematize the development of a PWC DT.

Construction and Analysis of Petri Net Model for Distributed Cyber Physical Systems

A Distributed Cyber-Physical System (DCPS) composition poses challenges in determining its emergent behaviour. These challenges occur due to (1) the appearance of causal loops of information and energy flow through cyber and physical channels and (2) inherent non-determinism in the temporally ordered flow of events within independently evolving interacting processes of Constituent Systems (CSs). Hence, there is a need to construct a model of the envisaged schematic of DCPS composition for analysis and verification of its significant properties in the conceptual design stage of the system development life cycle.
 This paper presents a procedure to construct DCPS composition models in Petri net formalism using distributed abstractions. The model for each CS is obtained from elementary constructs using compositional operators. The interaction among CSs occurs through channels obtained by connecting send and receive constructs of two CSs participating in an interaction. The internal processing within a CS characterizing its primary function is abstracted in a generic passthrough construct. Representing these constructs with compositional operators results in the complete DCPS model in Petri net formalism. A toolchain with Reference net workshop (Renew) as an integrated Petri net editing and analysis platform is configured to support DCPS modelling, simulation and analysis. The Renew tool functionality has been enhanced with a plugin designed and developed by authors to facilitate the drawing of the distributed composition model.
 A low-level Petri net analysis (Lola) v2.0 plugin is employed to verify the Petri net and temporal properties of the modelled DCPS scenarios. The properties of the resultant model are verified using well-established algorithms to analyze Petri nets. Further, system properties specified using temporal logic can be verified using model-checking algorithms for Petri nets. A moderately complex scenario involving interactions among six CSs illustrates the presented approach.

DNS Cache Poisoning/Honeypot Analysis Based on Data Exfiltration Using Stochastic Petri Nets Method to Enhance Cyber Security Hygiene

According to some experts, organizations make investments of huge sum of dollars concerning firewalls, encryption, and other tightly closed access devices, yet it is all naught, considering that none regarding these solutions tackle the weakest link within the safety chain. That speech perfectly captures the present day stress experienced by skilled network protection specialists. Researchers’ threat detection techniques can pick up a lot of false positive alarms throughout the detection process; false positive alarms are accountable for company’s unneeded system lock down. A stochastic model is necessary to represent a communication system since the nature of the traffic between them is unpredictable. SPN was utilized in this study to build statistical model for networks with security chains. By permitting the formalization of both real-time and non-Markovian behavior, the new stochastic Petri net formalism improves model fidelity. This allowed us to see special structures within the stochastic processes produced by SPN models. We have applied this principle by proposing an effective simulation method that supports deadlock detection and easy-to-compute point estimates and confidence intervals. The method is novel because it can automatically detect hidden regenerative structures that do not conform to different simple conditions, and can be easily determined by analytical methods.

Mathematical modeling of the molecular switch of TNFR1-mediated signaling pathways applying Petri net formalism and in silico knockout analysis.

The paper describes a mathematical model of the molecular switches of cell survival, apoptosis, and necroptosis in cellular signaling pathways initiated by tumor necrosis factor 1. Based on experimental findings in the literature, we constructed a Petri net model based on detailed molecular reactions of the molecular players, protein complexes, post-translational modifications, and cross talk. The model comprises 118 biochemical entities, 130 reactions, and 299 edges. We verified the model by evaluating invariant properties of the system at steady state and by in silico knockout analysis. Applying Petri net analysis techniques, we found 279 pathways, which describe signal flows from receptor activation to cellular response, representing the combinatorial diversity of functional pathways.120 pathways steered the cell to survival, whereas 58 and 35 pathways led to apoptosis and necroptosis, respectively. For 65 pathways, the triggered response was not deterministic and led to multiple possible outcomes. We investigated the in silico knockout behavior and identified important checkpoints of the TNFR1 signaling pathway in terms of ubiquitination within complex I and the gene expression dependent on NF-κB, which controls the caspase activity in complex II and apoptosis induction. Despite not knowing enough kinetic data of sufficient quality, we estimated system’s dynamics using a discrete, semi-quantitative Petri net model.

Cinco-Based Approach for Agent Petri Net Models

In this paper, a simplified simulation approach of the Agent Petri Nets (APN) model is proposed to facilitate and accelerate the development and evaluation of system models. The main idea is to apply the new trends of model-driven approach to the design of specific tools and provide facilities to evaluate quickly the developed system. The CINCO tooling suite is used to full generation of a specific graphical modelling tool for the APN model. The simulation code is simply added to the generated code. This tool allows users to build models based on Agent Petri Nets formalism and at the same time to execute these models. Combined APN with the CINCO tool greatly simplifies the development of modelling applications and allows users to get an early experience with a prototype system. To highlight the ability of the proposed tool, a real-life example of a traffic light adaptive system is considered and discussed here.

A modular framework for optimal scheduling of industrial processes

Abstract This paper proposes an extended Petri net formalism as a suitable language for composing optimal scheduling problems of industrial production processes with real and binary decision variables. The proposed approach is modular and scalable, as the overall process dynamics and constraints can be collected by parsing of all atomic elements of the net graph. To conclude, we demonstrate the use of this framework for modeling the moulding sand preparation process of a real foundry plant.

Steady state analysis of M/G/1 retrial queue with vacation and server timeout using a Petri net formalism

Steady state analysis of M/G/1 retrial queue with vacation and server timeout using a Petri net formalism