Статті в журналах: "Stochatic Time Petri Net"

1

Coman, Daniela, and Adela Ionescu. "Simulation and Performance Analysis of a FMS/CIM Using Stochastic Timed Petri Nets." Advanced Materials Research 837 (November 2013): 322–27. http://dx.doi.org/10.4028/www.scientific.net/amr.837.322.

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This paper focuses on the modelling, simulation and the performance analysis of a flexible manufacturing system using stochastic timed Petri nets so as to evaluate various performance parameters such as utilization rate of machines, deadlock detection, cycle time, and throughput rate of system in order to obtain the optimum productivity. The simulation of the manufacturing system using Petri nets provides the possibility to view the manufacturing process in time. Petri net model is implemented in Petri Net Toolbox under MATLAB environment. It is achieved the graphic construction of the net. Then, transporting it into a specific mathematical formalism it is made, so that the fulfiled structure to be fully retrieved and used to bring out the internal dynamics of the model. It is validated in this way the net topology, the evolution of (their dynamics), as well as the structural and behavioral properties (corresponding to checking if resources usage is stable and the model have no deadlocks). Some global performance indicators are determined in order to evaluate the performance of the proposed manufacturing system.

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2

Coman, Daniela, Nicu Bizdoaca, Anca Petrisor, Adela Ionescu, and Mihaela Florescu. "Modeling and Analysis of Soccer Robot Tasks Using Generalized Stochastic Petri Nets." Solid State Phenomena 166-167 (September 2010): 133–38. http://dx.doi.org/10.4028/www.scientific.net/ssp.166-167.133.

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Robot soccer competition provides an excellent opportunity for robotics research. In particular, the soccer robots must perform real-time visual recognition, navigate in a dynamic field, avoid the obstacle, collaborate with teammates, and kick the ball in the correct direction. All these tasks demand robots that are autonomous (sensing, thinking, and acting as independent creatures), efficient (functioning under time and resource constraints), cooperative (collaborating with each other robot to accomplish tasks that are beyond individual’s capabilities), and intelligent (reasoning and planing actions and perhaps learning from experience). This paper proposes a method of defining and analysing the attacking robot tasks using Petri nets. Attacking soccer robot behaviors are modeled using the generalized stochastic Petri nets. Using Petri nets allows qualitative and quantitative analysis of the task execution. Petri net model is implemented in Petri Net Toolbox under MATLAB environment. Therefore, it is validated the net topology, the evolution of (their dynamics), the structural and behavioral properties (corresponding to checking if resources usage is stable and the model have no deadlocks), as well as the stochastic performance.

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3

Proß, Sabrina, and Bernhard Bachmann. "An Advanced Environment for Hybrid Modeling of Biological Systems Based on Modelica." Journal of Integrative Bioinformatics 8, no. 1 (March 1, 2011): 1–34. http://dx.doi.org/10.1515/jib-2011-152.

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Summary Biological systems are often very complex so that an appropriate formalism is needed for modeling their behavior. Hybrid Petri Nets, consisting of time-discrete Petri Net elements as well as continuous ones, have proven to be ideal for this task. Therefore, a new Petri Net library was implemented based on the object-oriented modeling language Modelica which allows the modeling of discrete, stochastic and continuous Petri Net elements by differential, algebraic and discrete equations. An appropriate Modelica-tool performs the hybrid simulation with discrete events and the solution of continuous differential equations. A special sub-library contains so-called wrappers for specific reactions to simplify the modeling process.The Modelica-models can be connected to Simulink-models for parameter optimization, sensitivity analysis and stochastic simulation in Matlab.The present paper illustrates the implementation of the Petri Net component models, their usage within the modeling process and the coupling between the Modelica-tool Dymola and Matlab/Simulink. The application is demonstrated by modeling the metabolism of Chinese Hamster Ovary Cells.

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4

LU, Zhong. "System Maintainability Modeling Method Based on Colored Stochastic Time Petri Net." Journal of Mechanical Engineering 47, no. 10 (2011): 185. http://dx.doi.org/10.3901/jme.2011.10.185.

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5

Shailesh, Tanuja, Ashalatha Nayak, and Devi Prasad. "An UML Based Performance Evaluation of Real-Time Systems Using Timed Petri Net." Computers 9, no. 4 (November 27, 2020): 94. http://dx.doi.org/10.3390/computers9040094.

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Performance is a critical non-functional parameter for real-time systems and performance analysis is an important task making it more challenging for complex real-time systems. Mostly performance analysis is performed after the system development but an early stage analysis and validation of performance using system models can improve the system quality. In this paper, we present an early stage automated performance evaluation methodology to analyse system performance using the UML sequence diagram model annotated with modeling and analysis of real-time and embedded systems (MARTE) profile. MARTE offers a performance domain sub-profile that is used for representing real-time system properties essential for performance evaluation. In this paper, a transformation technique and transformation rules are proposed to map the UML sequence diagram model into a Generalized Stochastic Timed Petri net model. All the transformation rules are implemented using a metamodel based approach and Atlas Transformation Language (ATL). A case study from the manufacturing domain a Kanban system is used for validating the proposed technique.

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6

Li, Xiao Zhong, and Yi Jie Ding. "Knowledge Flow Modeling and Analysis in Supply Chain Based on Stochastic Petri Net." Advanced Materials Research 459 (January 2012): 381–85. http://dx.doi.org/10.4028/www.scientific.net/amr.459.381.

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Knowledge is an important resource providing competitive strategies for the firms. Managing knowledge through supply chain will bring more benefits to the businesses. Various factors during the process of knowledge flowing can cause different time delay. In order to analyze the problem of time delay of knowledge flow in supply chain, the knowledge flow model in supply chain based on stochastic Petri net is proposed and corresponding isomorphic Markov chain is given. The time performance and the efficiency of knowledge flow Petri net model are discussed. The proposed method can help the firm with the knowledge flow management and reorganization

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7

Aguiar, M. W. C., and R. H. Weston. "CIM-OSA and Stochastic Time Petri Nets for Behavioural Modelling and Model Handling in CIM Systems Design and Building." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 207, no. 3 (August 1993): 147–58. http://dx.doi.org/10.1243/pime_proc_1993_207_075_02.

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Means are considered that can structure design and building processes associated with integrated manufacturing systems. To meet the identified needs, the paper proposes the use of an environment for executing models which adopts and extends the concepts and guidelines identified by the CIM-OSA (computer integrated manufacturing-open sytems architecture) consortium. A key component of the environment concerns the execution of models of behaviour. The paper describes (with reference to on-going implementation work) how CIM-OSA behaviour models can be represented and handled by stochastic time Petri net model execution tools. The use of the design and building environment is illustrated with reference to a case study application involving the batch manufacture of a family of electronic products. Here, the necessary form of key CIM-OSA and Petri net models are described, as are results from the Petri net simulation studies. The paper also comments on the advantages and limitations of the CIM-OSA modelling approach and how certain of those limitations are circumvented by adopting the proposed environment for model execution.

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8

Shahzadi, Shabnam, Xianwen Fang, and David Anekeya Alilah. "Role of Stochastic Petri Net (SPN) in Process Discovery for Modelling and Analysis." Mathematical Problems in Engineering 2021 (June 30, 2021): 1–7. http://dx.doi.org/10.1155/2021/8699164.

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For exploitation and extraction of an event’s data that has vital information which is related to the process from the event log, process mining is used. There are three main basic types of process mining as explained in relation to input and output. These are process discovery, conformance checking, and enhancement. Process discovery is one of the most challenging process mining activities based on the event log. Business processes or system performance plays a vital role in modelling, analysis, and prediction. Recently, a memoryless model such as exponential distribution of the stochastic Petri net SPN has gained much attention in research and industry. This paper uses time perspective for modelling and analysis and uses stochastic Petri net to check the performance, evolution, stability, and reliability of the model. To assess the effect of time delay in firing the transition, stochastic reward net SRN model is used. The model can also be used in checking the reliability of the model, whereas the generalized stochastic Petri net GSPN is used for evaluation and checking the performance of the model. SPN is used to analyze the probability of state transition and the stability from one state to another. However, in process mining, logs are used by linking log sequence with the state and, by this, modelling can be done, and its relation with stability of the model can be established.

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9

Haas, Peter J., and Gerald S. Shedler. "Stochastic Petri Nets: Modeling Power and Limit Theorems." Probability in the Engineering and Informational Sciences 5, no. 4 (October 1991): 477–98. http://dx.doi.org/10.1017/s0269964800002242.

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Generalized semi-Markov processes and stochastic Petri nets provide building blocks for specification of discrete event system simulations on a finite or countable state space. The two formal systems differ, however, in the event scheduling (clock-setting) mechanism, the state transition mechanism, and the form of the state space. We have shown previously that stochastic Petri nets have at least the modeling power of generalized semi-Markov processes. In this paper we show that stochastic Petri nets and generalized semi-Markov processes, in fact, have the same modeling power. Combining this result with known results for generalized semi-Markov processes, we also obtain conditions for time-average convergence and convergence in distribution along with a central limit theorem for the marking process of a stochastic Petri net.

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10

Ammar, H. H., and S. M. R. Islam. "Time scale decomposition of a class of generalized stochastic Petri net models." IEEE Transactions on Software Engineering 15, no. 6 (June 1989): 809–20. http://dx.doi.org/10.1109/32.24734.

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11

Zhuang, Lu, Zhong Lu, and Ziwen Zhang. "Dynamic Reliability Model for Airborne Systems Based on Stochastic Petri Net." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 38, no. 4 (August 2020): 846–54. http://dx.doi.org/10.1051/jnwpu/20203840846.

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The reliability of the airborne systems have a significant influence on the safety of aircraft. The modern airborne systems have a high degree of automation and integration, which lead to obvious dynamic failure characteristics. Namely, system failure is not only dependent on the combination of units' failures but also related to their sequence. A dynamic reliability method for modeling airborne systems is proposed based on the stochastic Petri nets. Stochastic Petri nets are applied in reliability modeling for typical dynamic structures including warm standby, cold standby and load sharing, which are widely used in airborne systems. In this way, the dynamic (time-dependent) failure behaviors of the airborne system can be represented. In terms of the stochastic Petri net based reliability model, a reliability analysis method based on Monte Carlo simulation is proposed by generating system life samples for system reliability parameter calculation. Finally, an electrical power system is used as a case to illustrate the application and effectiveness of the present approaches. The results show that the difference by using the present method and the analytical method is below 2×10-7, which can be neglected in practice.

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12

Guo, Xuesong, and Naim Kapucu. "Examining Coordination in Disaster Response Using Simulation Methods." Journal of Homeland Security and Emergency Management 12, no. 4 (December 1, 2015): 891–914. http://dx.doi.org/10.1515/jhsem-2014-0092.

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Abstract Purpose of the research is to examine coordination in disaster response by computer simulation using Petri net. We addressed issues on coordination in disaster response by focusing on interorganizational processes. Defining the processes according to disaster exercise, we developed the model based on Stochastic Petri Net. Index items, including average delay time and busyness probability, were introduced to facilitate discussion. Simulation demonstrated utilization of process analysis in performance assessment of collaborative disaster response. Since fragmentation is critical factor hindering efficient response, its remedy or elimination should be focused for system optimization.

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13

Lu, Zhong, Zhiwen Zhang, Lu Zhuang, and Jia Zhou. "Reliability Model of the Fly-By-Wire System Based on Stochastic Petri Net." International Journal of Aerospace Engineering 2019 (November 12, 2019): 1–12. http://dx.doi.org/10.1155/2019/2124836.

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The fly-by-wire system plays an important role in modern civil aircraft. As a typical safety-critical system, its reliability will affect the safety of aircraft significantly. In the paper, stochastic Petri nets are applied in the reliability modeling and analysis for the fly-by-wire system to represent its dynamic (time-dependent) failure behaviors. Stochastic Petri net-based reliability models are established for all kinds of architectures including series, parallel, m-out-of-n, warm standby, cold standby, and load-sharing architectures, which are commonly used in the fly-by-wire system. A Monte Carlo simulation method is proposed for the stochastic Petri net-based reliability models to generate system lifetime samples, and the system reliability parameters can be calculated in terms of the lifetime samples. Finally, a fly-by-wire system is used as a case study to illustrate the application and effectiveness of our proposed approaches. The results show that the error of the reliability value in a flight duration obtained by our Monte Carlo simulation method is less than 1×10−4 compared with the analytical equation.

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14

Wu, Jinxia, and Chuang Liu. "A new pattern based Petri net to model sintering production process." Transactions of the Institute of Measurement and Control 40, no. 9 (December 11, 2017): 2771–78. http://dx.doi.org/10.1177/0142331217737834.

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In this paper, a new Petri net model based on pattern recognition method is presented for describing a certain stochastic hybrid systems. The application of this method concerns sintering production process. The main idea consists in describing the variation of patterns over time through the so-called ‘pattern class variable’ rather than state variable or output variable. A new petri net control model is constructed based on pattern class variable. The marks are defined as posterior probability of the cluster. By redefining the marks and transition on the basis of ordinary Petri nets, it can represent any combination of discrete-event and continuous element and has probability property. The simulation results are provided based on real plant data to illustrate the effectiveness of the proposed approach. This method might provide the satisfied results for the practical applications without having the exact mathematical models.

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15

Hong, Zhi Guo, Yong Bin Wang, and Min Yong Shi. "SPN-Based Performance Evaluation for ON-OFF Voice Traffic System." Advanced Materials Research 225-226 (April 2011): 1020–23. http://dx.doi.org/10.4028/www.scientific.net/amr.225-226.1020.

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By taking voice traffic system as study object, mathematical modeling methodology was used to investigate different parameters’ variations on system’s performance. Firstly, on the basis of analyzing the characteristics of voice traffic, this paper constructed a Stochastic Petri Net (SPN) model for ON-OFF voice traffic system. Furthermore, average time delay of the system was analyzed and model-based simulation was conducted with Stochastic Petri Net Package (SPNP) 6.0. For different parameters of ON to OFF rate and user’s voice connections, variation trends of number of user’s connections and ON to OFF rate are derived thereby. The methodology of modeling and simulation in this paper can be further used to analyze the performance of multimedia hybrid traffic system.

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16

Muñoz, Doyra Mariela, Antonio Correcher, Emilio García, and Francisco Morant. "Identification of Stochastic Timed Discrete Event Systems with st-IPN." Mathematical Problems in Engineering 2014 (2014): 1–21. http://dx.doi.org/10.1155/2014/835312.

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This paper presents a method for the identification of stochastic timed discrete event systems, based on the analysis of the behavior of the input and output signals, arranged in a timeline. To achieve this goal stochastic timed interpreted Petri nets are defined. These nets link timed discrete event systems modelling with stochastic time modelling. The procedure starts with the observation of the input/output signals; these signals are converted into events, so that the sequence of events is the observed language. This language arrives to an identifier that builds a stochastic timed interpreted Petri net which generates the same language. The identified model is a deterministic generator of the observed language. The identification method also includes an algorithm that determines when the identification process is over.

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17

Nabeel, Muhammad, Zeeshan Anwar, and Ali Ahsan. "Performance analysis of software maintenance process using stochastic Petri nets." Global Journal of Computer Sciences: Theory and Research 8, no. 1 (April 11, 2018): 01–13. http://dx.doi.org/10.18844/gjcs.v8i1.3285.

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Software maintenance is a time taking activity in the real world. Execution time of software maintenance process may get increased due to interdepartmental communication, thus, increasing the cost and decreasing the performance of the process. We suggested performance evaluation of software maintenance process through the transformation of activity diagram into generalised stochastic Petri nets (GSPN). For this study, execution time and cost of maintenance process are defined as performance measures, and the role-based approach is used to understand the flow of software maintenance activities in a software organisation. Activity diagram is constructed to be transformed into GSPN. We used PIPE2 to analyse the GSPN. PIPE2 calculates average number of tokens on a place in the GSPN, throughput of timed transition and state space analysis. State space involves calculation of the reachability of the GSPN net that shows whether a GSPN holds the property of safeness, boundness and is deadlock free. Keywords: Generalised stochastic Petri nets (GSPN), GSPN analysis, performance evaluation, performance modelling, software maintenance process, stochastic Petri nets.

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18

Lee, Gang-Soo, та Tadao Murata. "A β-distributed stochastic petri net model for software project time/cost management". Journal of Systems and Software 26, № 2 (серпень 1994): 149–65. http://dx.doi.org/10.1016/0164-1212(94)90085-x.

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19

Wu, Zenan, Liqin Tian, Yi Zhang, Yan Wang, and Yuquan Du. "Network Attack and Defense Modeling and System Security Analysis: A Novel Approach Using Stochastic Evolutionary Game Petri Net." Security and Communication Networks 2021 (November 13, 2021): 1–10. http://dx.doi.org/10.1155/2021/4005877.

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At present, most network security analysis theory assumes that the players are completely rational. However, this is not consistent with the actual situation. In this paper, based on the effectiveness constraints on both sides with network attack and defense, with the help of stochastic Petri net and evolutionary game theory, the Petri net model of network attack and defense stochastic evolutionary game is reconstructed, the specific definition of the model is given, and the modeling method is given through the network connection relationship and attack and defense strategy set. Using this model, a quantitative analysis of network attack events is carried out to solve a series of indicators related to system security, namely, attack success rate, average attack time, and average system repair time. Finally, the proposed model and analysis method are applied to a classic network attack and defense process for experimental analysis, and the results verify the rationality and accuracy of the model and analysis method.

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20

He, Hua, Shanchen Pang, and Zenghua Zhao. "Dynamic Scalable Stochastic Petri Net: A Novel Model for Designing and Analysis of Resource Scheduling in Cloud Computing." Scientific Programming 2016 (2016): 1–13. http://dx.doi.org/10.1155/2016/9259248.

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Performance evaluation of cloud computing systems studies the relationships among system configuration, system load, and performance indicators. However, such evaluation is not feasible by dint of measurement methods or simulation methods, due to the properties of cloud computing, such as large scale, diversity, and dynamics. To overcome those challenges, we present a novel Dynamic Scalable Stochastic Petri Net (DSSPN) to model and analyze the performance of cloud computing systems. DSSPN can not only clearly depict system dynamic behaviors in an intuitive and efficient way but also easily discover performance deficiencies and bottlenecks of systems. In this study, we further elaborate some properties of DSSPN. In addition, we improve fair scheduling taking into consideration job diversity and resource heterogeneity. To validate the improved algorithm and the applicability of DSSPN, we conduct extensive experiments through Stochastic Petri Net Package (SPNP). The performance results show that the improved algorithm is better than fair scheduling in some key performance indicators, such as average throughput, response time, and average completion time.

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21

Chen, Yong, Zhixian Zhan, and Kaiyu Niu. "Vulnerability Analysis of LTE-R Train-to-Ground Communication Time Synchronization." Applied Sciences 12, no. 11 (May 30, 2022): 5572. http://dx.doi.org/10.3390/app12115572.

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The time synchronization of LTE-R train-to-ground communication systems plays an important role in ensuring the safety of high-speed railways. In the LTE-R time synchronization process, existing problems, such as the time synchronization message broadcast address and LTE-R all-IP architecture, are vulnerable to attack. In order to analyze the impact of these problems, we propose a new vulnerability analysis method of LTE-R time synchronization based on stochastic Petri nets. Firstly, we construct a stochastic Petri net model of an LTE-R time synchronization process under attack. Secondly, steady-state probability expressions are obtained using the model isomorphism Markov chain. Finally, bychanging the firing rate of several key vulnerable nodes, the relationship curve between the firing rate and the steady-state probability of the clock node is obtained. Simulations show that the vulnerability of LTE-R time synchronization is most affected by the attack on eNodeB of the LTE-R base station. The results can provide a certain theoretical basis for the evolution of high-speed railway GSM-R communication systems to LTE-R.

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22

Orlov, Sergey P., Sergey V. Susarev, and Roman A. Uchaikin. "Application of Hierarchical Colored Petri Nets for Technological Facilities’ Maintenance Process Evaluation." Applied Sciences 11, no. 11 (May 31, 2021): 5100. http://dx.doi.org/10.3390/app11115100.

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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.

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KAVI, KRISHNA M., FREDERICK T. SHELDON, and SHERMAN REED. "SPECIFICATION AND ANALYSIS OF REAL-TIME SYSTEMS USING CSP AND PETRI NETS." International Journal of Software Engineering and Knowledge Engineering 06, no. 02 (June 1996): 229–48. http://dx.doi.org/10.1142/s0218194096000119.

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Formal methods such as CSP (Communicating Sequential Processes) are widely used for reasoning about concurrency, communication, safety, and liveness issues. Some of these models have been extended to permit reasoning about real-time constraints. Yet, the research in formal specification and verification of complex systems has often ignored the specification of stochastic properties of the system under study. We are developing methods and tools to permit stochastic analyses of CSP-based specifications. Our basic objective is to evaluate candidate design specifications by converting formal systems descriptions into the information needed for analysis. In doing so, we translate a CSP-based specification into a Petri net which is analyzed to predict system behavior in terms of reliability and performability as a function of observable parameters (e.g., topology, fault-tolerance, deadlines, communications, and failure categories). This process can give insight into further refinements of the original specification (i.e., identify potential failure processes and recovery actions). Relating the parameters needed for performability analysis to user level specifications is essential for realizing systems that meet user needs in terms of cost, functionality, and other nonfunctional requirements. An example translation is given (in addition, some general examples of CSP → Petri net translations can be viewed in Appendix A). Based on this translation, we report both the discrete and continuous time Markovian analysis which provides reliability predictions for the candidate specification. The term “CSP-based” is used here to distinguish between the notation of Hoare’s original CSP and our textual representations which are similar to occum. Our CSP-based grammar does not restrict consideration of the properties of CSP (traces, refusal sets, livelock, etc.), but we are not considering those properties. We are only interested that the structural properties are preserved. We define performability as a measure of the system’s ability in meeting deadlines, in the presence of failures and variance in task execution times.

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24

Li, Huiyong, Xiaofeng Wu, and Yanhong Wang. "Dynamic Performance Analysis of STEP System in Internet of Vehicles Based on Queuing Theory." Computational Intelligence and Neuroscience 2022 (April 10, 2022): 1–13. http://dx.doi.org/10.1155/2022/8322029.

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The Internet of vehicles (IoV) is an important research area of the intelligent transportation systems using Internet of things theory. The complex event processing technology is a basic issue for processing the data stream in IoV. In recent years, many researchers process the temporal and spatial data flow by complex event processing technology. Spatial Temporal Event Processing (STEP) is a complex event query language focusing on the temporal and spatial data flow in Internet of vehicles. There are four processing models of the event stream processing system based on the complex event query language: finite automata model, matching tree model, directed acyclic graph model, and Petri net model. In addition, the worst-case response time of the event stream processing system is an important indicator of evaluating the performance of the system. Firstly, this paper proposed a core algorithm of the temporal and spatial event stream processing program based on STEP by Petri net model. Secondly, we proposed a novel method to estimate the worst-case response time of the event stream processing system, which is based on stochastic Petri net and queuing theory. Finally, through the simulation experiment based on queuing theory, this paper proves that the data stream processing system based on STEP has good dynamic performance in processing the spatiotemporal data stream in Internet of vehicles.

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25

Gaied, Mouhaned, Anis M’halla, Dimitri Lefebvre, and Kamel Ben Othmen. "Robust control for railway transport networks based on stochastic P-timed Petri net models." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 233, no. 7 (January 25, 2019): 830–46. http://dx.doi.org/10.1177/0959651818823583.

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This article is devoted to the modeling, performance evaluation and robust control of the railway transport network in Sahel Tunisia. The regular increase in the number of passengers makes the management of transportation systems more and more complex. Railway transport requires specific needs. Indeed, many decision and optimization problems occur from the planning phase to the implementation phase. Railway transport networks can be considered as discrete event systems with time constraints. The time factor is a critical parameter, since it includes schedules to be respected in order to avoid overlaps, delays and collisions between trains. The uncertainties affect the service and the availability of transportation resources and, consequently, the transport scheduling plan. Petri nets have been recognized as powerful modeling and analysis tools for discrete event systems with time constraints. Consequently, they are suitable for railway transport systems. In this article, stochastic P-time Petri nets are used for the railway transport networks in Sahel Tunisia. A global model is first detailed. Then, this model is used to analyze the network traffic and evaluate the performance of the system. Robustness again disturbances is introduced and a control strategy is developed to reduce the consequences of the disturbances in order to maintain the expected schedule.

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26

Zhou, Huan, Chuang Lin, Yi Ping Deng, and Zi Cheng Wan. "Determine Execution Time and Selection Probabilities in Process Mining via Petri Nets." Advanced Materials Research 760-762 (September 2013): 1951–58. http://dx.doi.org/10.4028/www.scientific.net/amr.760-762.1951.

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In process mining research, process discovery techniques can produce or rebuild models with the information from logs. There are already algorithms supporting control-flow perspective mining which focus on the order of events and provide understanding workflow paths. But few of them take time perspective and path selection probabilities into consideration, which are important in performance evaluating, delay prediction, decision making, as well as process redesigning and optimizing. This paper provides a novel algorithm which determines the information of time perspective and selection probabilities from a log and integrates them with the control-flow perspective. By applying this algorithm, a stochastic Petri net is provided which is useful in performance analyzing and process optimizing.

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27

Li, Jia, Yunni Xia, and Xin Luo. "Reliability Prediction of Ontology-Based Service Compositions Using Petri Net and Time Series Models." Scientific World Journal 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/760202.

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OWL-S, one of the most important Semantic Web service ontologies proposed to date, provides a core ontological framework and guidelines for describing the properties and capabilities of their web services in an unambiguous, computer interpretable form. Predicting the reliability of composite service processes specified in OWL-S allows service users to decide whether the process meets the quantitative quality requirement. In this study, we consider the runtime quality of services to be fluctuating and introduce a dynamic framework to predict the runtime reliability of services specified in OWL-S, employing the Non-Markovian stochastic Petri net (NMSPN) and the time series model. The framework includes the following steps: obtaining the historical response times series of individual service components; fitting these series with a autoregressive-moving-average-model (ARMA for short) and predicting the future firing rates of service components; mapping the OWL-S process into a NMSPN model; employing the predicted firing rates as the model input of NMSPN and calculating the normal completion probability as the reliability estimate. In the case study, a comparison between the static model and our approach based on experimental data is presented and it is shown that our approach achieves higher prediction accuracy.

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Lu, Zhong, Jie Liu, Li Dong, and Xihui Liang. "Maintenance Process Simulation Based Maintainability Evaluation by Using Stochastic Colored Petri Net." Applied Sciences 9, no. 16 (August 9, 2019): 3262. http://dx.doi.org/10.3390/app9163262.

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Maintainability is a critical design characteristic of products. Maintainability evaluation plays an important role in maintainability design. Existing maintainability evaluation approaches neglect logistic effects on system maintainability. In this paper, tuples of stochastic colored petri nets (SCPN) are used to express the constituents of a maintenance process; and the maintenance process model is developed based on the SCPN. Approaches for calculating the required maintenance resources are proposed according to the state equation of the SCPN, and a method for calculating maintenance time is proposed by using an SCPN based discrete-event simulation. Finally, the line maintenance of a wheel steering system is used as a case study to illustrate the application and effectiveness of our proposed approaches. The work discussed herein provides a maintainability evaluation methodology based on the maintenance task demonstration that is conducted on the digital mockup of products. The approaches can be applied in the design stage when there are no physical mockups, and the maintainability design can be carried on concurrently with the development of products.

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Wang, Dong Dong, Lu Xi Liu, and Ping Sun. "Hydraulic System Reliability Analysis of Slurry Transportation Based on Stochastic Failure Petri Net." Applied Mechanics and Materials 644-650 (September 2014): 832–35. http://dx.doi.org/10.4028/www.scientific.net/amm.644-650.832.

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As the development of the slurry pipeline transportation system complexity and intelligent,it is more difficult to establish the reliability of the system.This pape take advantage of the descriptions of dynamic systems of stochastic failure petri net,applying in the field of slurry pipeline transport system reliability analysis.At same time,with the combination of Markov theory, it established the model of the hydraulic system reliability analysis.The feasibility and availability of the method is proved through an example of hydraulic system of slurry pipeline transportation.

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30

Jiang, Zhi Gao, Ming Dong, Peng Tian, and Dong Yang. "Modeling and Simulation of Re-Entrant Semiconductor Wafer Fabrication Lines with PM Using GSPN." Advanced Materials Research 97-101 (March 2010): 2469–72. http://dx.doi.org/10.4028/www.scientific.net/amr.97-101.2469.

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Semiconductor wafer fabrication factories are characterized by re-entrant flows, dynamic and uncertain environments, strict production control requirements and so on. Re-entrant flow means a product routing that consists of multiple visits to a workstation during the manufacturing processes. In this paper, a modeling approach based on generalized stochastic Petri nets is presented. Specifically, a Petri net model representing a re-entrant flow line with three centers and six machines is modeled. Work release policies (WRP) and queuing disciplines (QD) are also added to the model, which take into account the machine preventive maintenance (PM) requirement. Finally, a simulation study is used to analyze the model, which provides support for scheduling decision in shorter time.

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Zhitong, Huang, Zhu Xi, and Wang Jiacun. "A New method for time delay analysis of stochastic petri net models — hybrid state space method." IFAC Proceedings Volumes 24, no. 14 (June 1991): 80–85. http://dx.doi.org/10.1016/s1474-6670(17)69328-5.

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Jiacun, Wang. "A new method for the aggregation of complex stochastic petri net models based upon time delay." IFAC Proceedings Volumes 24, no. 14 (June 1991): 148–54. http://dx.doi.org/10.1016/s1474-6670(17)69341-8.

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33

Nukavarapu, N., and S. Durbha. "HEALTHCARE CRITICAL INFRASTRUCTURE STOCHASTIC INTERDEPENDENCIES SIMULATION MODEL FOR SMART CITIES: FLOOD DISASTER SCENARIO." ISPRS Annals of Photogrammetry, Remote Sensing and Spatial Information Sciences V-4-2020 (August 3, 2020): 123–29. http://dx.doi.org/10.5194/isprs-annals-v-4-2020-123-2020.

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Abstract. Healthcare Critical Infrastructure (HCI) is not an independent network; the operation of a healthcare facility depends on many other Critical Infrastructure (CI) networks such as electric supply CI, water supply CI, etc., forming an interdependent CI network. During a flooding disaster event, as the flood levels rise, the interdependent HCI network becomes vulnerable. A failure in one of the CI results in failure of the dependent CI. During a disaster event such as flooding, the failures propagate and cause cascading failures like a domino effect. The paper proposes an IoT based flood sensor network integrated with a stochastic Petri net interdependent healthcare critical infrastructure network simulation model. An IoT (Internet of Things) based flood water level sensor network can deliver real-time information on the flood conditions at the various interdependent CI facilities in the interdependent network, using the Sensor Observation Services (SOS). The Stochastic Petri Net (SCPN) based interdependent Healthcare Critical Infrastructure (HCI) simulation model, is used to model and simulate the stochastic interdependencies between the interdependent HCI networks. The real-time flood sensor network is integrated with the SCPN based interdependent HCI simulation model. The end to end system is developed in a spatiotemporal environment. This kind of an integrated simulation model will help the end-user to understand system dynamics in real-time, visualize and predict the propagation of cascading failure scenarios in an Interdependent HCI network in a spatiotemporal environment, during a flooding scenario. Real-time information simulation would help disaster response personnel to respond to the question, ‘what if something else happens?

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WU, JIALIANG, and EBERHARD VOIT. "HYBRID MODELING IN BIOCHEMICAL SYSTEMS THEORY BY MEANS OF FUNCTIONAL PETRI NETS." Journal of Bioinformatics and Computational Biology 07, no. 01 (February 2009): 107–34. http://dx.doi.org/10.1142/s0219720009004047.

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Many biological systems are genuinely hybrids consisting of interacting discrete and continuous components and processes that often operate at different time scales. It is therefore desirable to create modeling frameworks capable of combining differently structured processes and permitting their analysis over multiple time horizons. During the past 40 years, Biochemical Systems Theory (BST) has been a very successful approach to elucidating metabolic, gene regulatory, and signaling systems. However, its foundation in ordinary differential equations has precluded BST from directly addressing problems containing switches, delays, and stochastic effects. In this study, we extend BST to hybrid modeling within the framework of Hybrid Functional Petri Nets (HFPN). First, we show how the canonical GMA and S-system models in BST can be directly implemented in a standard Petri Net framework. In a second step we demonstrate how to account for different types of time delays as well as for discrete, stochastic, and switching effects. Using representative test cases, we validate the hybrid modeling approach through comparative analyses and simulations with other approaches and highlight the feasibility, quality, and efficiency of the hybrid method.

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Wang, Junfeng, Zicheng Fei, Qing Chang, and Shiqi Li. "Energy Saving Operation of Manufacturing System Based on Dynamic Adaptive Fuzzy Reasoning Petri Net." Energies 12, no. 11 (June 11, 2019): 2216. http://dx.doi.org/10.3390/en12112216.

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The energy efficient operation of a manufacturing system is important for sustainable development of industry. Apart from the device and process level, energy saving methods at the system level has attracted increasing attention with the rapid growth of the industrial Internet of things technology, which makes it possible to sense and collect real-time data from the production line and provide more opportunities for online control for energy saving purposes. In this paper, a dynamic adaptive fuzzy reasoning Petri net is proposed to decide the machine energy saving state considering the production information of a discrete stochastic manufacturing system. Fuzzy knowledge for energy saving operations of a machine is represented in weighted fuzzy production rules with certain values. The rules describe uncertain, imprecise, and ambiguous knowledge of machine state decisions. This makes an energy saving sleep decision in advance when a machine has the inclination of starvation or blockage, which is based on the real-time production rates and level of connected buffers. A dynamic adaptive fuzzy reasoning Petri net is formally defined to implement the reasoning process of the machine state decision. A manufacturing system case is used to demonstrate the application of our method and the results indicate its effectiveness for energy saving operation purposes.

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36

Qabaja, Hamzeh, Mujahid I. Ashqer, Marwan Bikdash, and Huthaifa I. Ashqar. "A Meso-Scale Petri Net Model to Simulate a Massive Evacuation along the Highway System." Future Transportation 3, no. 1 (March 2, 2023): 311–28. http://dx.doi.org/10.3390/futuretransp3010019.

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Natural disasters may require that the residents of the affected area be evacuated immediately using a potentially damaged infrastructure. In this paper, we developed a mesoscopic simulation modeling approach for modeling traffic flow over a large geographic area and involving many people and vehicles. This study proposed a novel model, namely, Colored Deterministic and Stochastic Petri Net (CDSPN), which can mesoscopically provide an individual vehicular traffic dynamic. Each vehicle has a unique identifier, speed, distance to go, assigned target, and a specific route. It also proposed a method to automatically construct a Petri net model that represents the evacuation of Guilford County (GC), North Carolina, from standard Geographic Information Systems (GIS) shapefiles. We showed that this model could successfully simulate the dynamics of hundreds of thousands of vehicles moving on the highway system towards pre-specified safe targets such as medical facilities, exit points, or designated shelters. The vehicles are assumed to obey traffic laws, and the model reflects the complexities of the actual highway systems. The developed software can be used to analyze in reasonable detail the evacuation process, such as identifying bottlenecks and estimating efficiency and the time needed. An explicit list of 18 assumptions is stated and discussed. The Petri net for GC evacuation is reasonably massive, consisting of 35,476 places and 43,540 transitions with 531,595 colored tokens, where each token represents a vehicle in GC. We simulate the evacuation, develop statistics, and evaluate patterns of evaluation. We found that the evacuation took about 8.7 h.

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37

Li, Xiao, Yongkui Shi, Zaiyong Wang, and Wenquan Zhang. "Modified Stochastic Petri Net-Based Modeling and Optimization of Emergency Rescue Processes during Coal Mine Accidents." Geofluids 2021 (August 13, 2021): 1–13. http://dx.doi.org/10.1155/2021/4141236.

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The coal mine accidents seriously affect the safety and efficiency of mining for coal mining enterprises. The reliable emergency rescue (ER) processes are explored to minimize the loss of accidents. This paper introduces the stochastic Petri net (SPN) and Markov chain (MC) models based on the system structure flow to analyze the ER processes of coal mine accidents. In addition, a triangle fuzzy strategy is presented to optimize the SPN model. The “9·28” major water inrush accident in Shanxi Fenxi Zhengsheng Coal Company of China is adopted to evaluate the time performance and accident data of the ER process. The MC model-based steady-state probabilities of the system under various states are used to calculate the average delay time of this system. The triangular fuzzy strategy is used to analyze the change value of the total time in the ER system at the unit transition speed when the firing rate of each transition is changed, which finds the most time-consuming key activities in the ER process. The results show that SPN and MC can reflect the dynamic behaviors of ER process, which provides a reference for the rescue operations of other coal mine accidents. The triangular fuzzy strategy can quickly find out the key activities affecting the ER time, which greatly decreases the calculations generated by analyzing the total time of the system changed at the unit transition speed.

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38

Fedorova, Aleksandra, Viktar Beliautsou, and Armin Zimmermann. "Colored Petri Net Modelling and Evaluation of Drone Inspection Methods for Distribution Networks." Sensors 22, no. 9 (April 29, 2022): 3418. http://dx.doi.org/10.3390/s22093418.

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The UAV industry is developing rapidly and drones are increasingly used for monitoring industrial facilities. When designing such systems, operating companies have to find a system configuration of multiple drones that is near-optimal in terms of cost while achieving the required monitoring quality. Stochastic influences such as failures and maintenance have to be taken into account. Model-based systems engineering supplies tools and methods to solve such problems. This paper presents a method to model and evaluate such UAV systems with coloured Petri nets. It supports a modular view on typical setup elements and different types of UAVs and is based on UAV application standards. The model can be easily adapted to the most popular flight tasks and allows for estimating the monitoring frequency and determining the most appropriate grouping and configuration of UAVs, monitoring schemes, air time and maintenance periods. An important advantage is the ability to consider drone maintenance processes. Thus, the methodology will be useful in the conceptual design phase of UAVs, in monitoring planning, and in the selection of UAVs for specific monitoring tasks.

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39

Miwa, Yoshimasa, Chen Li, Qi-Wei Ge, Hiroshi Matsuno, and Satoru Miyano. "On Determining Firing Delay Time of Transitions for Petri Net Based Signaling Pathways by Introducing Stochastic Decision Rules." In Silico Biology 10, no. 1,2 (2010): 49–66. http://dx.doi.org/10.3233/isb-2010-0417.

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40

Shojafar, Mohammad, Zahra Pooranian, Mohammad Reza Meybodi, and Mukesh Singhal. "ALATO: An efficient intelligent algorithm for time optimization in an economic grid based on adaptive stochastic Petri net." Journal of Intelligent Manufacturing 26, no. 4 (August 27, 2013): 641–58. http://dx.doi.org/10.1007/s10845-013-0824-0.

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41

LAI, RICHARD, and TONY TSANG. "ANALYSING THE PERFORMANCE OF A RESOURCE RESERVATION PROTOCOL SPECIFICATION USING A GSPN METHOD." International Journal of Software Engineering and Knowledge Engineering 20, no. 04 (June 2010): 549–73. http://dx.doi.org/10.1142/s0218194010004815.

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Performance analysis derived from a formal specification of a multimedia protocol provides important information on the performance characteristics of a multimedia system before implementation; this information includes time-dependent functional behaviours, and statistical traffic characteristics. We have developed an extended Estelle, called Time-Estelle, suitable for specifying time-dependent performance characteristic of a multimedia system, and a method based on GSPN (Generalized Stochastic Petri Net) for analysing the performance of a protocol specified in Time-Estelle. This paper describes an application of this method to analyse the performance of an industrial multimedia protocol, the Resource ReSerVation Protocol (RSVP) specified in Time-Estelle; it also presents the performance analysis results which are expressed in terms of blocking probability, packet dropping probability, channel utilisation and packet delay, with variations in time intervals.

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Elusakin, Tobi, Mahmood Shafiee, Tosin Adedipe, and Fateme Dinmohammadi. "A Stochastic Petri Net Model for O&M Planning of Floating Offshore Wind Turbines." Energies 14, no. 4 (February 20, 2021): 1134. http://dx.doi.org/10.3390/en14041134.

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With increasing deployment of offshore wind farms further from shore and in deeper waters, the efficient and effective planning of operation and maintenance (O&M) activities has received considerable attention from wind energy developers and operators in recent years. The O&M planning of offshore wind farms is a complicated task, as it depends on many factors such as asset degradation rates, availability of resources required to perform maintenance tasks (e.g., transport vessels, service crew, spare parts, and special tools) as well as the uncertainties associated with weather and climate variability. A brief review of the literature shows that a lot of research has been conducted on optimizing the O&M schedules for fixed-bottom offshore wind turbines; however, the literature for O&M planning of floating wind farms is too limited. This paper presents a stochastic Petri network (SPN) model for O&M planning of floating offshore wind turbines (FOWTs) and their support structure components, including floating platform, moorings and anchoring system. The proposed model incorporates all interrelationships between different factors influencing O&M planning of FOWTs, including deterioration and renewal process of components within the system. Relevant data such as failure rate, mean-time-to-failure (MTTF), degradation rate, etc. are collected from the literature as well as wind energy industry databases, and then the model is tested on an NREL 5 MW reference wind turbine system mounted on an OC3-Hywind spar buoy floating platform. The results indicate that our proposed model can significantly contribute to the reduction of O&M costs in the floating offshore wind sector.

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Vahidipour, S. Mehdi, Mohammad Reza Meybodi, and Mehdi Esnaashari. "Finding the Shortest Path in Stochastic Graphs Using Learning Automata and Adaptive Stochastic Petri Nets." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 25, no. 03 (May 22, 2017): 427–55. http://dx.doi.org/10.1142/s0218488517500180.

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Shortest path problem in stochastic graphs has been recently studied in the literature and a number of algorithms has been provided to find it using varieties of learning automata models. However, all these algorithms suffer from two common drawbacks: low speed and lack of a clear termination condition. In this paper, we propose a novel learning automata-based algorithm for this problem which can speed up the process of finding the shortest path using parallelism. For this parallelism, several traverses are initiated, in parallel, from the source node towards the destination node in the graph. During each traverse, required times for traversing from the source node up to any visited node are estimated. The time estimation at each visited node is then given to the learning automaton residing in that node. Using different time estimations provided by different traverses, this learning automaton gradually learns which neighbor of the node is on the shortest path. To set a condition for the termination of the proposed algorithm, we analyze the algorithm using a recently introduced model, Adaptive Stochastic Petri Net (ASPN-LA). The results of this analysis enable us to establish a necessary condition for the termination of the algorithm. To evaluate the performance of the proposed algorithm in comparison to the existing algorithms, we apply it to find the shortest path in six different stochastic graphs. The results of this evaluation indicate that the time required for the proposed algorithm to find the shortest path in all graphs is substantially shorter than that required by similar existing algorithms.

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44

Liu, Xia, Wen Hua Ye, Bi Sheng Wei, and Sheng Leng. "Research on Multi-Level Modeling Method for Aircraft Assembly Line." Advanced Materials Research 490-495 (March 2012): 538–42. http://dx.doi.org/10.4028/www.scientific.net/amr.490-495.538.

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The process time of aircraft assembly line is easily influenced by the efficiency of workers, the supply circumstance of components and the assembly quality. While the aircraft assembly line is hardly to reconfigure after it is in use, in order to optimize the assembly line before its application, a new object-oriented modeling method based on hierarchy and stochastic petri net has been put forward in this paper. The behavior and the structural characteristics of the model have been analyzed according to the solution of linear invariant. Finally, the model of aircraft wing assembly line has been established as an example, which proves the feasibility of the modeling method.

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Zheng, Junjun, Hiroyuki Okamura, and Tadashi Dohi. "Availability Analysis of Software Systems with Rejuvenation and Checkpointing." Mathematics 9, no. 8 (April 13, 2021): 846. http://dx.doi.org/10.3390/math9080846.

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In software reliability engineering, software-rejuvenation and -checkpointing techniques are widely used for enhancing system reliability and strengthening data protection. In this paper, a stochastic framework composed of a composite stochastic Petri reward net and its resulting non-Markovian availability model is presented to capture the dynamic behavior of an operational software system in which time-based software rejuvenation and checkpointing are both aperiodically conducted. In particular, apart from the software-aging problem that may cause the system to fail, human-error factors (i.e., a system operator’s misoperations) during checkpointing are also considered. To solve the stationary solution of the non-Markovian availability model, which is derived on the basis of the reachability graph of stochastic Petri reward nets and is actually not one of the trivial stochastic models such as the semi-Markov process and the Markov regenerative process, the phase-expansion approach is considered. In numerical experiments, we illustrate steady-state system availability and find optimal software-rejuvenation policies that maximize steady-state system availability. The effects of human-error factors on both steady-state system availability and the optimal software-rejuvenation trigger timing are also evaluated. Numerical results showed that human errors during checkpointing both decreased system availability and brought a significant effect on the optimal rejuvenation-trigger timing, so that it should not be overlooked during system modeling.

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Ma, Shengcheng, Xin Chen, Zhuo Li, and Yingjie Yang. "A Retrieval Optimized Surveillance Video Storage System for Campus Application Scenarios." Journal of Electrical and Computer Engineering 2018 (2018): 1–10. http://dx.doi.org/10.1155/2018/3839104.

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This paper investigates and analyzes the characteristics of video data and puts forward a campus surveillance video storage system with the university campus as the specific application environment. Aiming at the challenge that the content-based video retrieval response time is too long, the key-frame index subsystem is designed. The key frame of the video can reflect the main content of the video. Extracted from the video, key frames are associated with the metadata information to establish the storage index. The key-frame index is used in lookup operations while querying. This method can greatly reduce the amount of video data reading and effectively improves the query’s efficiency. From the above, we model the storage system by a stochastic Petri net (SPN) and verify the promotion of query performance by quantitative analysis.

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Pang, Shanchen, Weiguang Zhang, Tongmao Ma, and Qian Gao. "Ant Colony Optimization Algorithm to Dynamic Energy Management in Cloud Data Center." Mathematical Problems in Engineering 2017 (2017): 1–10. http://dx.doi.org/10.1155/2017/4810514.

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With the wide deployment of cloud computing data centers, the problems of power consumption have become increasingly prominent. The dynamic energy management problem in pursuit of energy-efficiency in cloud data centers is investigated. Specifically, a dynamic energy management system model for cloud data centers is built, and this system is composed of DVS Management Module, Load Balancing Module, and Task Scheduling Module. According to Task Scheduling Module, the scheduling process is analyzed by Stochastic Petri Net, and a task-oriented resource allocation method (LET-ACO) is proposed, which optimizes the running time of the system and the energy consumption by scheduling tasks. Simulation studies confirm the effectiveness of the proposed system model. And the simulation results also show that, compared to ACO, Min-Min, and RR scheduling strategy, the proposed LET-ACO method can save up to 28%, 31%, and 40% energy consumption while meeting performance constraints.

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48

Shang, Hui, Christophe Bérenguer, and John Andrews. "Delayed maintenance modelling considering speed restriction for a railway section." Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability 231, no. 4 (June 22, 2017): 411–28. http://dx.doi.org/10.1177/1748006x17709200.

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The deterioration of track geometry depends on several factors of which the speed of the train is one. Imposing a speed restriction can slow down the track deterioration and allows a longer survival time before a serious condition is achieved. Preventive maintenance delays can be authorized during the survival time. However, speed restrictions also reduce the system throughput. On the other hand, a longer interval between preventive maintenance activities has a lower maintenance action cost and it also enables grouping the maintenance activities to save set-up costs as well as system downtime. If the repair delay is too long, it may cause unacceptable conditions on the track and lead to higher maintenance costs and accidents. Therefore, it is interesting to assess the effect of a speed restriction on the delayed maintenance strategies for a railway track section. We want to solve a maintenance optimization problem to find the optimal tuning of the maintenance delay time and imposition of a speed restriction. To this aim, a delayed maintenance model is developed, in which track deterioration depends on the train speed and the number of passing trains. The model is used to determine an optimal speed restriction strategy and a preventive repair delay for the optimization of the system benefit and unavailability. Coloured Petri Nets are adopted to model the maintenance and operation of the railway track section. The Coloured Petri Net model describes the gradual track deterioration as a stochastic process. Different speed restriction policies and maintenance delay strategies are modelled and activated by the observed component states. Monte Carlo simulations are carried out to estimate the maintenance cost, the system benefit and the system downtime under different policies. Numerical results show the maintenance decision variable trade-off.

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El Akchioui, Nabil. "Fluidification of Stochastic Petri Net by Non Linear Timed Continuous Petri Net." American Journal of Embedded Systems and Applications 5, no. 4 (2017): 29. http://dx.doi.org/10.11648/j.ajesa.20170504.11.

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Lian, Yuanfeng, Yueyao Geng, and Tian Tian. "Anomaly Detection Method for Multivariate Time Series Data of Oil and Gas Stations Based on Digital Twin and MTAD-GAN." Applied Sciences 13, no. 3 (February 1, 2023): 1891. http://dx.doi.org/10.3390/app13031891.

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Due to the complexity of the oil and gas station system, the operational data, with various temporal dependencies and inter-metric dependencies, has the characteristics of diverse patterns, variable working conditions and imbalance, which brings great challenges to multivariate time series anomaly detection. Moreover, the time-series reconstruction information of data from digital twin space can be used to identify and interpret anomalies. Therefore, this paper proposes a digital twin-driven MTAD-GAN (Multivariate Time Series Data Anomaly Detection with GAN) oil and gas station anomaly detection method. Firstly, the operational framework consisting of digital twin model, virtual-real synchronization algorithm, anomaly detection strategy and realistic station is constructed, and an efficient virtual-real mapping is achieved by embedding a stochastic Petri net (SPN) to describe the station-operating logic of behavior. Secondly, based on the potential correlation and complementarity among time series variables, we present a MTAD-GAN anomaly detection method to reconstruct the error of multivariate time series by combining mechanism of knowledge graph attention and temporal Hawkes attention to judge the abnormal samples by a given threshold. The experimental results show that the digital twin-driven anomaly detection method can achieve accurate identification of anomalous data with complex patterns, and the performance of MTAD-GAN anomaly detection is improved by about 2.6% compared with other methods based on machine learning and deep learning, which proves the effectiveness of the method.

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