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A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Computing and Artificial Intelligence".

Deadline for manuscript submissions: closed (31 May 2022) | Viewed by 21144

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Special Issue Editors

Dr. Luis Gomes

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Guest Editor

Department of Electrical and Computer Engineering, NOVA School of Science and Technology, NOVA University Lisbon, Caparica, Portugal
Interests: petri nets; embedded systems; hardware/software co-design; reconfigurable computing platforms; FPGA; model-based development; design automation; cyberphysical systems; globally asynchronous locally synchronous (GALS) systems
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. João Paulo Barros

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Guest Editor

Department of Engineering, Polytechnic Institute of Beja, 7800-309 Beja, Portugal
Interests: Petri nets; graphical specification languages; languages and tools for object-oriented and model-driven software development; mobile computing; computer science education; curriculum development
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Models play a fundamental role in science and engineering, as abstraction and reduction allow the intended rigor and preciseness. Their readability also allows and facilitates their use as the basis for communication between users and engineers.

Petri nets are very suitable to support this interaction as they can graphically specify sequence, concurrency, conflicts, and synchronizations. Petri nets provide a mathematically rigorous language for the construction of models with precise semantics, which can then be simulated and verified with modern computing tools.

This has made Petri nets a well-known formalism widely used in different application areas. In order to tune the models to specific application areas, several extensions of Petri nets have been defined, originating from different classes of Petri nets (e.g., synchronized, colored, timed, object-oriented, continuous).

The main aim of this Special Issue is to seek high-quality submissions addressing original research on Petri net modeling, as well as on topics relevant to distributed and concurrent systems.

The topics of interest include but are not limited to:

System design and model-driven development using nets;
Structuring and composability in Petri nets modeling;
Verification and model checking using nets;
Tools for modeling and verification;
Tools for rapid prototyping using nets;
Code generation from Petri nets models;
Relationships between Petri nets and other approaches;
Applications in different areas, such as healthcare systems, industrial automation, home and building automation, smart grids, manufacturing systems, real-time systems, chemistry processes, and social sciences;
Applications to cyberphysical systems, Internet of Things, embedded systems, controller network, automotive networks, and wireless sensor networks, among others.

Papers reporting new and unpublished advances on any aspect of these topics are welcomed.

Prof. Dr. Luis Gomes
Prof. Dr. João Paulo Barros
Guest Editors

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Keywords

Model-based development
Model-driven engineering
System simulation
Verification
Model checking
Computer tools
Behavioral models
Executable models

Published Papers (10 papers)

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Research

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19 pages, 410 KiB

Open AccessArticle

Path Planning of Multi-Type Robot Systems with Time Windows Based on Timed Colored Petri Nets

by Zhou He, Ruijie Zhang, Ning Ran and Chan Gu

Appl. Sci. 2022, 12(14), 6878; https://0-doi-org.brum.beds.ac.uk/10.3390/app12146878 - 07 Jul 2022

Cited by 8 | Viewed by 1334

Abstract

Mobile robots are extensively used to complete repetitive operations in industrial areas such as intelligent transportation, logistics, and manufacturing systems. This paper addresses the path planning problem of multi-type robot systems with time windows based on timed colored Petri nets. The tasks to be completed are divided into three different types: common, exclusive and collaborative. An analytical approach to plan a group of different types of mobile robots is developed to ensure that some specific robots will visit task regions within given time windows. First, a multi-type robot system and its environment are modeled by a timed colored Petri net. Then, some methods are developed to convert the task requirements that contain logic constraints and time windows into linear constraints. Based on integer linear programming techniques, a planning approach is proposed to minimize the total cost (i.e., total travel distance) of the system. Finally, simulation studies are investigated to show the effectiveness of the developed approach. Full article

(This article belongs to the Special Issue Recent Advances in Petri Nets Modeling)

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26 pages, 2079 KiB

Open AccessArticle

Coloured Petri Nets-Based Modeling and Validation of Insulin Infusion Pump Systems

by Tássio Fernandes Costa, Álvaro Sobrinho, Lenardo Chaves e Silva, Leandro Dias da Silva and Angelo Perkusich

Appl. Sci. 2022, 12(3), 1475; https://0-doi-org.brum.beds.ac.uk/10.3390/app12031475 - 29 Jan 2022

Cited by 4 | Viewed by 2131

Abstract

Safety and effectiveness are crucial quality attributes for insulin infusion pump systems. Therefore, regulatory agencies require the quality evaluation and approval of such systems before the market to decrease the risk of harm, motivating the usage of a formal Model-Based Approach (MBA) to improve quality. Nevertheless, using a formal MBA increases costs and development time because it requires expert knowledge and thorough analyses of behaviors. We aim to assist the quality evaluation of such systems in a cost-effective and time-efficient manner, providing re-usable project artifacts by applying our proposed approach (named MBA with CPN—

M B A / C P N

). We defined a Coloured Petri nets MBA and a case study on a commercial insulin infusion pump system to verify and validate a reference model (as a component of

M B A / C P N

), describing quality assessment scenarios. We also conducted an empirical evaluation to verify the productivity and reusability of modelers when using the reference model. Such a model is relevant to reason about behaviors and quality evaluation of such concurrent and complex systems. During the empirical evaluation, using the reference model, 66.7% of the 12 interviewed modelers stated no effort, while 8.3% stated low effort, 16.7% medium effort, and 8.3% considerable effort. Based on the modelers’ knowledge, we implemented a web-based application to assist them in re-using our proposed approach, enabling simulation-based training. Although a reduced number of modelers experimented with our approach, such an evaluation provided insights to improve the

M B A / C P N

. Given the empirical evaluation and the case study results,

M B A / C P N

showed to be relevant to assess the quality of insulin infusion pump systems. Full article

(This article belongs to the Special Issue Recent Advances in Petri Nets Modeling)

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23 pages, 5968 KiB

Open AccessFeature PaperArticle

Petri Net Toolbox for Multi-Robot Planning under Uncertainty

by Carlos Azevedo, António Matos, Pedro U. Lima and Jose Avendaño

Appl. Sci. 2021, 11(24), 12087; https://0-doi-org.brum.beds.ac.uk/10.3390/app112412087 - 18 Dec 2021

Cited by 2 | Viewed by 2573

Abstract

Currently, there is a lack of developer-friendly software tools to formally address multi-robot coordination problems and obtain robust, efficient, and predictable strategies. This paper introduces a software toolbox that encapsulates, in one single package, modeling, planning, and execution algorithms. It implements a state-of-the-art approach to representing multi-robot systems: generalized Petri nets with rewards (GSPNRs). GSPNRs enable capturing multiple robots, decision states, action execution states and respective outcomes, action duration uncertainty, and team-level objectives. We introduce a novel algorithm that simplifies the model design process as it generates a GSPNR from a topological map. We also introduce a novel execution algorithm that coordinates the multi-robot system according to a given policy. This is achieved without compromising the model compactness introduced by representing robots as indistinguishable tokens. We characterize the computational performance of the toolbox with a series of stress tests. These tests reveal a lightweight implementation that requires low CPU and memory usage. We showcase the toolbox functionalities by solving a multi-robot inspection application, where we extend GSPNRs to enable the representation of heterogeneous systems and system resources such as battery levels and counters. Full article

(This article belongs to the Special Issue Recent Advances in Petri Nets Modeling)

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19 pages, 1089 KiB

Open AccessArticle

Petri Net Modeling for Ising Model Formulation in Quantum Annealing

by Morikazu Nakamura, Kohei Kaneshima and Takeo Yoshida

Appl. Sci. 2021, 11(16), 7574; https://0-doi-org.brum.beds.ac.uk/10.3390/app11167574 - 18 Aug 2021

Cited by 2 | Viewed by 1904

Abstract

Quantum annealing is an emerging new platform for combinatorial optimization, requiring an Ising model formulation for optimization problems. The formulation can be an essential obstacle to the permeation of this innovation into broad areas of everyday life. Our research is aimed at the proposal of a Petri net modeling approach for an Ising model formulation. Although the proposed method requires users to model their optimization problems with Petri nets, this process can be carried out in a relatively straightforward manner if we know the target problem and the simple Petri net modeling rules. With our method, the constraints and objective functions in the target optimization problems are represented as fundamental characteristics of Petri net models, extracted systematically from Petri net models, and then converted into binary quadratic nets, equivalent to Ising models. The proposed method can drastically reduce the difficulty of the Ising model formulation. Full article

(This article belongs to the Special Issue Recent Advances in Petri Nets Modeling)

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18 pages, 2098 KiB

Open AccessArticle

Petri Net-Based Semi-Compiled Code Generation for Programmable Logic Controllers

by Igor Azkarate, Mikel Ayani, Juan Carlos Mugarza and Luka Eciolaza

Appl. Sci. 2021, 11(15), 7161; https://0-doi-org.brum.beds.ac.uk/10.3390/app11157161 - 03 Aug 2021

Cited by 3 | Viewed by 2778

Abstract

Industrial discrete event dynamic systems (DEDSs) are commonly modeled by means of Petri nets (PNs). PNs have the capability to model behaviors such as concurrency, synchronization, and resource sharing, compared to a step transition function chart or GRAphe Fonctionnel de Commande Etape Transition (GRAFCET) which is a particular case of a PN. However, there is not an effective systematic way to implement a PN in a programmable logic controller (PLC), and so the implementation of such a controller outside a PLC in some external software that will communicate with the PLC is very common. There have been some attempts to implement PNs within a PLC, but they are dependent on how the logic of places and transitions is programmed for each application. This work proposes a novel application-independent and platform-independent PN implementation methodology. This methodology is a systematic way to implement a PN controller within industrial PLCs. A great portion of the code will be validated automatically prior to PLC implementation. Net structure and marking evolution will be checked on the basis of PN model structural analysis, and only net interpretation will be manually coded and error-prone. Thus, this methodology represents a systematic and semi-compiled PN implementation method. A use case supported by a digital twin (DT) is shown where the automated solution required by a manufacturing system is carried out and executed in two different devices for portability testing, and the scan cycle periods are compared for both approaches. Full article

(This article belongs to the Special Issue Recent Advances in Petri Nets Modeling)

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29 pages, 4294 KiB

Open AccessArticle

Temporal Analysis of Influence of Resource Failures on Cyber-Physical Systems Based on Discrete Timed Petri Nets

by Fu-Shiung Hsieh

Appl. Sci. 2021, 11(14), 6469; https://0-doi-org.brum.beds.ac.uk/10.3390/app11146469 - 13 Jul 2021

Cited by 9 | Viewed by 1380

Abstract

Advancement of IoT and ICT provide infrastructure to manage, monitor and control Cyber-Physical Systems (CPS) through timely provision of real-time information from the shop floor. Although real-time information in CPS such as resource failures can be detected based on IoT and ICT, improper response to resource failures may cripple CPS and degrade performance. Effective operations of CPS relies on an effective scheme to evaluate the impact of resource failures, support decision making needed and take proper actions to respond to resource failures. This motivates us to develop a methodology to assess the impact of resource failures on operations of CPS and provide the decision support as needed. The goal of this study is to propose solution algorithms to analyze robustness of CPS with respect to resource failures in terms of the impact on temporal properties. Given CPS modeled by a class of discrete timed Petri nets (DTPNs), we develop theory to analyze robustness of CPS by transforming the models to residual spatial-temporal network (RSTN) models in which capacity loss due to resources is reflected. We formulate an optimization problem to determine the influence of resource failures on CPS based on RSTNs and analyze the feasibility to meet the order deadline. To study the feasibility to solve a real problem, we analyze the computational complexity of the proposed algorithms. We illustrate the proposed method by application scenarios. We conduct experiments to study efficiency and verify computational feasibility of the proposed method to solve a real problem. Full article

(This article belongs to the Special Issue Recent Advances in Petri Nets Modeling)

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16 pages, 3088 KiB

Open AccessArticle

Modeling a New AQM Model for Internet Chaotic Behavior Using Petri Nets

by José M. Amigó, Guillem Duran, Ángel Giménez, José Valero and Oscar Martinez Bonastre

Appl. Sci. 2021, 11(13), 5877; https://0-doi-org.brum.beds.ac.uk/10.3390/app11135877 - 24 Jun 2021

Cited by 6 | Viewed by 1930

Abstract

Formal modeling is considered one of the fundamental phases in the design of network algorithms, including Active Queue Management (AQM) schemes. This article focuses on modeling with Petri nets (PNs) a new scheme of AQM. This innovative AQM is based on a discrete dynamical model of random early detection (RED) for controlling bifurcations and chaos in Internet congestion control. It incorporates new parameters

(α, β)

that make possible better stability control over oscillations of an average queue length (AQL) at the router. The PN is validated through the matrix equation approach, reachability tree, and invariant analysis. The correctness is validated through the key properties of reachability, boundedness, reversibility, deadlock, and liveness. Full article

(This article belongs to the Special Issue Recent Advances in Petri Nets Modeling)

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26 pages, 6203 KiB

Open AccessArticle

Application of Hierarchical Colored Petri Nets for Technological Facilities’ Maintenance Process Evaluation

by Sergey P. Orlov, Sergey V. Susarev and Roman A. Uchaikin

Appl. Sci. 2021, 11(11), 5100; https://0-doi-org.brum.beds.ac.uk/10.3390/app11115100 - 31 May 2021

Cited by 9 | Viewed by 2122

Abstract

The high reliability of modern engineering systems is achieved by performing predictive maintenance. Mathematical models based on stochastic timed colored Petri nets are an effective tool for developing complex production processes for Industry 4.0. This article discusses the maintainability evaluation used in hierarchical Petri net models. The hierarchical simulation model was built using timed colored Petri nets, and was constructed with four levels of repair and maintenance modules. New module structures are proposed for simulating the schedule of production tasks and interaction with technological units. The emphasis is on the processes of predicting maintenance and repair, moving units to service, replacing units, and forming a reserve. The design of the simulation modules allows the setting of probabilistic parameters for the distributions of equipment failures, requests for unit maintenance, repair time, and recovery time after repair. The article proposes to use the hierarchical Petri model in conjunction with solving the problem of minimizing the cost of service. The iterative procedure consists of obtaining an approximate unit distribution by tasks, subsequent simulation of the technological process, and adjusting the optimization problem constraints. For example, the hierarchical Petri net is considered to assess the maintainability of autonomous agricultural vehicles. The results of the simulation experiments are presented. A simulation of the agrotechnical production process was performed, during which vehicles were maneuvered, taken out for repair or maintenance, and returned to the reserve fund. The interdependencies of preventive maintenance periods, service operations, failure rates, and predictive maintenance requests were obtained in order to comply with the task scheduling. The proposed model is a generalization, but it is especially effective in studying mobile equipment servicing. Full article

(This article belongs to the Special Issue Recent Advances in Petri Nets Modeling)

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18 pages, 393 KiB

Open AccessArticle

An Asymptotic Cyclicity Analysis of Live Autonomous Timed Event Graphs

by Ja-Hee Kim

Appl. Sci. 2021, 11(11), 4769; https://0-doi-org.brum.beds.ac.uk/10.3390/app11114769 - 22 May 2021

Viewed by 1326

Abstract

Designing a discrete event system converging to steady temporal patterns is an essential issue of a system with time window constraints. Until now, to analyze asymptotic stability, we have modeled a timed event graph’s dynamic behavior, transformed it into the matrix form of (max,+) algebra, and then constructed a precedence graph. This article’s aim is to provide a theoretical basis for analyzing the stability and cyclicity of timed event graphs without using (max,+) algebra. In this article, we propose converting one timed event graph to another with a dynamic behavior equivalent to that of the original without going through the conversion process. This paper also guarantees that the derived final timed event graph has the properties of a precedence graph. It then investigates the relationship between the properties of the derived precedence graph and that of the original timed event graph. Finally, we propose a method to analyze asymptotic cyclicity and stability for a given timed event graph by itself. The analysis this article provides makes it easy to analyze and improve asymptotic time patterns of tasks in a given discrete event system modeled with a live autonomous timed event graph such as repetitive production scheduling. Full article

(This article belongs to the Special Issue Recent Advances in Petri Nets Modeling)

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Review

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30 pages, 1912 KiB

Open AccessReview

Fluid Net Models: From Behavioral Properties to Structural Objects

by Manuel Navarro-Gutiérrez, Antonio Ramírez-Treviño and Manuel Silva

Appl. Sci. 2022, 12(12), 6123; https://0-doi-org.brum.beds.ac.uk/10.3390/app12126123 - 16 Jun 2022

Viewed by 1194

Abstract

Increasing the production in manufacturing systems is one of the main demands in modern systems. The naive approach that this goal can be achieved when more or faster resources are used is not always valid. In fact, the complex interactions among system’s elements may lead to paradoxical behaviors; for example, using faster machines could reduce the equilibrium throughput (number of part fabricated per unit time in steady state) of the system, or even worse, block all system activities, reducing it to zero. This work leverages the concepts about fluidization and analysis techniques used in Timed Continuous Petri nets (TCPN) presented in earlier works to study the behavior of the equilibrium throughput when more/faster machines are used. Herein, we illustrate how discontinuities induced bifurcations of the equilibrium throughput are due to the existence of paths that can increase/decrease the marking of certain subnets. In particular, if paths gaining/losing tokens are fired without a particular balance, then the equilibrium throughput exhibits discontinuities since the equilibrium marking loses hyperbolicity. Moreover, these discontinuities imply other undesired throughput behaviors; for example, the existence of non-monotonicities of the equilibrium throughput (when more/faster resources are used in the system, its equilibrium throughput is reduced). The discontinuities together with a homothecy property are used to explain non-monotonicities in the equilibrium throughput. A relevant aspect is that these undesired system behaviors appear when the net has structural objects named problematic configurations that are associated with certain subnets in which there are no P-semiflows. Although the number of these configurations increase exponentially in the size of the net, some reduction rules are introduced to remove configurations, while the problematic ones are kept (or can be recovered) in the reduced net. This saves computation time in the analysis and, more importantly, provides useful insights about the root of undesired behaviors. This work focus on systems that can be modeled with fluid (or continuous) mono T-semiflow Timed Continuous Petri nets. Even if under certain constraints, they are capable of capturing many characteristics of modern systems, such as interleaving of cooperation and competition. Full article

(This article belongs to the Special Issue Recent Advances in Petri Nets Modeling)

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