Journal articles: 'Stochastic Time Petri Nets'

1

Molloy, M. K. "Discrete Time Stochastic Petri Nets." IEEE Transactions on Software Engineering SE-11, no. 4 (April 1985): 417–23. http://dx.doi.org/10.1109/tse.1985.232230.

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van der Aalst, W. M. P., K. M. van Hee, and H. A. Reijers. "Analysis of discrete-time stochastic petri nets." Statistica Neerlandica 54, no. 2 (July 2000): 237–55. http://dx.doi.org/10.1111/1467-9574.00139.

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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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Fűr, Attila. "Extended knowledge attributed Petri Nets." International Journal of Modeling, Simulation, and Scientific Computing 05, no. 02 (February 25, 2014): 1350028. http://dx.doi.org/10.1142/s1793962313500281.

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Choosing the best way for describing physical reality has always been standing in focus of research. Several methodologies have been developed based on classical mathematics, or statistics and also new disciplines — such as soft-computing techniques — appeared. Petri Nets as one of the most naturalistic modeling methodologies are well suited to describe complex process in general. However in some fields of modeling the describing power of basic Petri Nets proved not to be robust enough, therefore several extensions were made to the original concept. Colored tokens (Colored Petri Nets), stochastic delayed streaming of mobile entities (Stochastic Petri Nets), object oriented architecture (Object Oriented Petri Nets), numerical (Numerical Petri Nets) and linguistic attributes (Fuzzy Petri Nets) broaden the range of capabilities. In some fields of problem solving, usage of static and mobile knowledge bases is needed: e.g., flexible manufacturing systems, or intelligent traffic simulation. These problems to be investigated involved new conceptual developments of Petri Nets and led to the introduction of Knowledge Attributed Petri Nets. At the same time distributed control in simulation appeared, intelligent agents supported the connection of mobile knowledge bases and static inference engines in an effective way. The mentioned extensions brought general support in model synthesis, but some unsolved questions remained related to the implementation of intelligent mobile entities. This paper highlights a new level of AI controlled simulation introducing the Extended Knowledge Attributed Petri Nets that offer the capability of easy implementation of mobile inference engines and knowledge base, providing general mobile AI in Petri Nets.

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Juanole, G., Y. Atamna, N. Bergé, and J. M. Farines. "Modelling Time Critical Communication Networks with Stochastic Timed Petri Nets." IFAC Proceedings Volumes 25, no. 11 (June 1992): 143–48. http://dx.doi.org/10.1016/s1474-6670(17)50138-x.

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Lyon, Douglas. "Using Stochastic Petri Nets for Real-Time Nth-Order Stochastic Composition." Computer Music Journal 19, no. 4 (1995): 13. http://dx.doi.org/10.2307/3680988.

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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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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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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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Haas, Peter J., and Gerald S. Shedler. "Passage times in colored stochastic petri nets." Communications in Statistics. Stochastic Models 9, no. 1 (January 1993): 31–79. http://dx.doi.org/10.1080/15326349308807253.

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Amparore, Elvio G. "Stochastic modelling and evaluation using GreatSPN." ACM SIGMETRICS Performance Evaluation Review 49, no. 4 (June 2, 2022): 87–91. http://dx.doi.org/10.1145/3543146.3543165.

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GreatSPN is a tool that supports model-based (stochastic) analysis of Discrete Event Dynamic Systems (DEDS) modeled as Generalized Stochastic Petri Nets or one of its extensions like StochasticWell-formed Nets, Deterministic and Stochastic Petri Nets among the other. Performance evaluation of the timed and stochastic properties of the modeled systems was the initial reason for the tool development, and it is today a large and flexible framework that incorporates several analysis techniques, performance index types, variegated transition timing specifications, etc. In this paper we report the current status of the GreatSPN framework, with a focus on the modularity, the types of stochastic analysis, the specification and evaluation functionalities, and its role for the performance evaluation.

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Haas, Peter J., and Gerald S. Shedler. "Stochastic petri nets with timed and immediate transitions." Communications in Statistics. Stochastic Models 5, no. 4 (January 1989): 563–600. http://dx.doi.org/10.1080/15326348908807125.

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Wan, Zi Cheng, Huan Zhou, Yi Ping Deng, and Rong Li. "Hybrid Modeling Method Based on FSPN for Sensor Networks." Applied Mechanics and Materials 341-342 (July 2013): 1197–204. http://dx.doi.org/10.4028/www.scientific.net/amm.341-342.1197.

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Sensor networks play a central role in the Internet of things, which attracts lots of attentions recently. Mathematical models are of much help to explore intricate scheduling on the sensor node or interactions between different sensor nodes. Although many existing approaches have shown that the sensor network behaves like a hybrid system, where discrete character and continuous character exist together, few of them have attempted to consider two characters together. In this paper, we propose a novel quantitative modeling framework based on Fluid Stochastic Petri nets (FSPNs), and provide comprehensive theoretical analysis to a typical sensor network example. Our modeling framework, which combines advantages of both Stochastic Petri Nets (SPNs) and Hybrid Functional Petri Nets (HFPNs), reflects the hybrid nature of sensor networks, and at the same time eases the problem of state space explosion. The modeling mechanism proposed in this paper constructs sensor network models that are comprised of both stochastic processes and fluid flow approximation technique. From the evaluation, it's shown that the new method performs well.

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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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Hélouët, Loïc, and Karim Kecir. "Realizability of schedules by stochastic time Petri nets with blocking semantics." Science of Computer Programming 157 (June 2018): 71–102. http://dx.doi.org/10.1016/j.scico.2017.12.004.

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Orlov, Sergey P., and Sergey V. Susarev. "Simulation models based on Petri nets for the analysis of maintenance and repair processes of complex technical systems." Vestnik of Samara State Technical University. Technical Sciences Series 30, no. 4 (February 1, 2023): 49–75. http://dx.doi.org/10.14498/tech.2022.4.4.

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The presented review analyzes the approaches and methods of using simulation models in the maintenance and repair organization of the complex technical objects and systems. The development of the concept of "Industry 4.0" and the Internet of things involves the transition from periodic and preventive maintenance to predictive maintenance based on the study of processes during the object operation. It is shown that system models based on Petri nets are convenient for describing and analyzing technological processes and equipment maintenance. The effectiveness of timed stochastic colored Petri nets for virtual tests in the design of maintenance and repair procedures in complex systems is revealed. The use of hierarchical Petri nets allows building complex models that describe interrelated processes. A general model based on a hierarchical network is proposed to study the processes of deterioration and degradation of the technical object aggregates and elements and to form a predictive maintenance strategy. The model includes a Gantt chart of production tasks, a set of active and reserve units, maintenance and repair modules. The examples of simulation models on Petri nets for various technical systems are considered. Solutions for flexible production systems, railway bridges, offshore wind turbines, an aircraft fleet, a group of robotic vehicles, and a complex of computer equipment of an enterprise are given. The models of various maintenance strategies are considered and the generality of the models based on hierarchical Petri nets is shown. The article formulates methodological principles for constructing hierarchical networks to simulate the operation and maintenance of technical systems. The article analyzes known software tools for the implementation of timed stochastic colored Petri nets. The summary concludes that the use of simulation models on Petri nets is promising for organizing maintenance and repair of complex technical objects and systems.

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Hong, Zhi Guo, Yong Bin Wang, and Min Yong Shi. "GSPN-Based Analysis of Storage Infrastructures for Rendering System." Advanced Materials Research 219-220 (March 2011): 1359–62. http://dx.doi.org/10.4028/www.scientific.net/amr.219-220.1359.

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By taking transmission delay into account, the optimization of distributed rendering environment (DRE) was concerned in this paper. Considering distributed animation rendering environment as the object of study, two Generalized Stochastic Petri Nets (GSPN) models for “completely distributed storage” infrastructure (CDSI) and “hybrid distributed storage” one (HDSI) were constructed respectively. Moreover, by choosing average time delay as the performance index, analysis was conducted by applying the equivalent formulas for solving Stochastic Petri Nets (SPN) models of serial and parallel types to these two GSPN models. Based on comparison of such models’ numerical simulation results, conclusion on these two infrastructures’ advantages and disadvantages is deprived thereby. It offers important quantitative foundations for choosing appropriate storage schemes and scheduling algorithms.

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Buchholz, Peter, and Miklós Telek. "Stochastic Petri nets with matrix exponentially distributed firing times." Performance Evaluation 67, no. 12 (December 2010): 1373–85. http://dx.doi.org/10.1016/j.peva.2010.08.023.

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Zhao, Guo Sheng, Jian Wang, Lin Li, and Nan Zhang. "Study on Four-Level Emergency Rejuvenation for Survivable System." Applied Mechanics and Materials 373-375 (August 2013): 1830–33. http://dx.doi.org/10.4028/www.scientific.net/amm.373-375.1830.

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A method of four-level emergency rejuvenation for survivable system was proposed. Firstly, failure models of survivable system were formally described based on stochastic Petri nets, in which a number of measurable index parameters for rejuvenation were also given out. And then a four-level recursive emergency rejuvenation strategy was presented based on system-level, service-level, process-level and thread-level, the computing process of rejuvenation priority is also defined and the chain of rejuvenation is obtained. Eventually, the implementation process of four-level autonomous emergency rejuvenation strategy was described using stochastic Petri nets. Compared with the traditional cyclical recovery strategy, the proposed method reduced the time and costs of emergency recovery, and enhanced the recoverable elasticity of survivable system.

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Muñoz, Doyra Mariela, Antonio Correcher, Emilio García, and Francisco Morant. "Stochastic DES Fault Diagnosis with Coloured Interpreted Petri Nets." Mathematical Problems in Engineering 2015 (2015): 1–13. http://dx.doi.org/10.1155/2015/303107.

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This proposal presents an online method to detect and isolate faults in stochastic discrete event systems without previous model. A coloured timed interpreted Petri Net generates the normal behavior language after an identification stage. The next step is fault detection that is carried out by comparing the observed event sequences with the expected event sequences. Once a new fault is detected, a learning algorithm changes the structure of the diagnoser, so it is able to learn new fault languages. Moreover, the diagnoser includes timed events to represent and diagnose stochastic languages. Finally, this paper proposes a detectability condition for stochastic DES and the sufficient and necessary conditions are proved.

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Xu, Wen Jie, and Jin Yao. "Molding and Optimization of Workflow Based on Stochastic Timed Petri Nets in Customized Supply Chain Management." Advanced Materials Research 201-203 (February 2011): 1082–85. http://dx.doi.org/10.4028/www.scientific.net/amr.201-203.1082.

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Customized Supply Chain Management (CSCM) has been made much account of attention in Flexible Manufacturing Systems (FSM). Products are customized by customer’s special needs at stochastic time. Then Manufacturing Oriented to Customization (MOC) would inevitably be faced by those enterprises that had to meet the changeable and complex needs of customers. However, there were large quantities of difficulties would appear in MOC supply chains, such as information overload, technology and resource constraints. All of these problems made it hard to quickly and effectively respond to customers’ needs. Therefore, we need to find a new way to deal effectively with the problems about how to respond quickly to supply chains oriented to customization. Petri Nets have been extensively used for modeling and simulating of the dynamics of flexible manufacturing systems. However, Petri Nets have not been very popular for molding of workflow in CSCM environmental. In this paper Stochastic Timed Petri Nets (STPN) were used to solve the above problems. The enterprises’ workflow was analyzed, and then the STPN model was constructed according to the characteristics of its internal supply chain. In order to minimize total tardiness time of workflow, the structure of STPN was optimized in a proper way. The results suggest that the STPN approach is also valid to minimize due date of each transition in CSCM and responses to customized needs more quickly than before.

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Horvath, A., and M. Telek. "Time domain analysis of non-Markovian stochastic Petri nets with PRI transitions." IEEE Transactions on Software Engineering 28, no. 10 (October 2002): 933–43. http://dx.doi.org/10.1109/tse.2002.1041050.

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Hüls, Jannik, Carina Pilch, Patricia Schinke, Henner Niehaus, Joanna Delicaris, and Anne Remke. "State-space Construction of Hybrid Petri Nets with Multiple Stochastic Firings." ACM Transactions on Modeling and Computer Simulation 31, no. 3 (July 31, 2021): 1–37. http://dx.doi.org/10.1145/3449353.

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Hybrid Petri nets have been extended to include general transitions that fire after a randomly distributed amount of time. With a single general one-shot transition the state space and evolution over time can be represented either as a Parametric Location Tree or as a Stochastic Time Diagram . Recent work has shown that both representations can be combined and then allow multiple stochastic firings. This work presents an algorithm for building the Parametric Location Tree with multiple general transition firings and shows how its transient probability distribution can be computed using multi-dimensional integration. We discuss the (dis-)advantages of an interval arithmetic and a geometric approach to compute the areas of integration. Furthermore, we provide details on how to perform a Monte Carlo integration either directly on these intervals or convex polytopes, or after transformation to standard simplices. A case study on a battery-backup system shows the feasibility of the approach and discusses the performance of the different integration approaches.

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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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M’hala, Anis. "A Monitoring Approach Based on Fuzzy Stochastic P-Timed Petri Nets of a Railway Transport Network." Journal of Advanced Transportation 2021 (April 27, 2021): 1–18. http://dx.doi.org/10.1155/2021/5595065.

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This paper proposes a monitoring approach based on stochastic fuzzy Petri nets (SFPNs) for railway transport networks. In railway transport, the time factor is a critical parameter as it includes constraints to avoid overlaps, delays, and collisions between trains. The temporal uncertainties and constraints that may arise on the railway network may degrade the planned schedules and consequently affect the availability of the transportation system. This leads to many problems in the decision and optimization of the railway transport systems. In this context, we propose a new fuzzy stochastic Petri nets for monitoring (SFPNM). The main goal of the proposed supervision approach is to allow an early detection of traffic disturbance to avoid catastrophic scenarios and preserve stability and security of the studied railway networks. Finally, to demonstrate the effectiveness and accuracy of the approach, an application to the case study of the Tunisian railway network is outlined.

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SAITO, Kazuaki, Atsushi OHTA, and Tomiji HISAMURA. "An Application of Stochastic Time Petri Nets to Scheduling Problems with Uncertain Processing Times." Transactions of the Society of Instrument and Control Engineers 25, no. 4 (1989): 476–81. http://dx.doi.org/10.9746/sicetr1965.25.476.

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Lefebvre, Dimitri, Edouard Leclercq, and Eric Sanlaville. "Tolerance intervals for stochastic processes with timed continuous Petri nets." IFAC-PapersOnLine 48, no. 3 (2015): 1018–23. http://dx.doi.org/10.1016/j.ifacol.2015.06.217.

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Chen, Po-Zung, Steven C. Bruell, and Giafranco Balbo. "Formulating and solving optimization problems using stochastic timed Petri nets." Microelectronics Reliability 31, no. 4 (January 1991): 769–92. http://dx.doi.org/10.1016/0026-2714(91)90013-w.

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Stetsenko, I. V. "State equations of stochastic timed petri nets with informational relations." Cybernetics and Systems Analysis 48, no. 5 (September 2012): 784–97. http://dx.doi.org/10.1007/s10559-012-9457-0.

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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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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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Narahari, Y., and N. Viswanadham. "Performance modelling of a fault-tolerant real-time multiprocessor using stochastic Petri nets." Sadhana 11, no. 1-2 (October 1987): 187–208. http://dx.doi.org/10.1007/bf02811318.

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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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Bucci, G., L. Sassoli, and E. Vicario. "Correctness verification and performance analysis of real-time systems using stochastic preemptive time Petri nets." IEEE Transactions on Software Engineering 31, no. 11 (November 2005): 913–27. http://dx.doi.org/10.1109/tse.2005.122.

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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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HENZINGER, THOMAS, BARBARA JOBSTMANN, and VERENA WOLF. "FORMALISMS FOR SPECIFYING MARKOVIAN POPULATION MODELS." International Journal of Foundations of Computer Science 22, no. 04 (June 2011): 823–41. http://dx.doi.org/10.1142/s0129054111008441.

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In this survey, we compare several languages for specifying Markovian population models such as queuing networks and chemical reaction networks. All these languages — matrix descriptions, stochastic Petri nets, stoichiometric equations, stochastic process algebras, and guarded command models — describe continuous-time Markov chains, but they differ according to important properties, such as compositionality, expressiveness and succinctness, executability, and ease of use. Moreover, they provide different support for checking the well-formedness of a model and for analyzing a model.

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Sochnev, Aleksei. "METHODS FOR PRESENTING PETRI NETS MODELING RESULTS OF PRODUCTION SYSTEMS." Applied Mathematics and Control Sciences, no. 2 (June 30, 2020): 29–40. http://dx.doi.org/10.15593/2499-9873/2020.2.02.

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The article considers the issues of presenting the results of simulation experiments with models based on Petri nets for a researcher. The need for a qualitative review of the applied methods for visualizing Petri nets of both the processes themselves and the modeling results has been identified and justified. An analysis of publications on the subject of Petri nets allowed us to conclude that the visualization of such models and the results of their modeling is a known weak point. It is this factor that significantly limits the use of Petri nets as a tool for solving practical problems. The characteristic features of the calendar planning problem and the applied forms of presenting the results of its solution are analyzed. Based on the analysis of literary sources and empirical data, the feasibility of solving the planning problem on the basis of preliminary simulation modeling by Petri nets is substantiated. The method of automatic formation of Gantt diagrams is formalized. The mechanisms for identifying the state of system resources by transitions of the network model are determined. In developing the approach, the attributes and characteristics of its elements already existing in the simulation network model were used to the maximum. An example of using the proposed approach based on the model of a typical robotic technological complex is given. According to the results of the experiment, it was revealed that the software implementation of the described formal rules does not significantly affect the speed of model simulation for the presented robotic system. The proposed approach has the same versatility as the mathematical apparatus used timed Petri nets. This allows us to describe the results of modeling systems and processes of different types, for example, transport or information. An important advantage of the implemented mechanism for the connection of Petri nets and Gantt diagrams is the transfer of the dynamic nature of networks to the process analysis procedures based on diagrams. There is also the possibility of introducing stochastic characteristics of the processes both in the simulation model and in the generated Gantt diagram. The direction of further research on the topic of the article may be the application and corresponding refinement of the obtained formal rules for simulating a network with identification of resources for other classes of Petri nets often used in practice, for example, color Petri nets or E-nets.

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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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Zhen Liu. "Performance analysis of stochastic timed Petri nets using linear programming approach." IEEE Transactions on Software Engineering 24, no. 11 (1998): 1014–30. http://dx.doi.org/10.1109/32.730548.

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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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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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Carnevali, Laura, Marco Paolieri, and Enrico Vicario. "The ORIS tool." ACM SIGMETRICS Performance Evaluation Review 49, no. 4 (June 2, 2022): 81–86. http://dx.doi.org/10.1145/3543146.3543164.

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ORIS is a tool for quantitative modeling and evaluation of concurrent systems with non-Markovian durations. It provides a Graphical User Interface (GUI) for model specification as Stochastic Time Petri Nets (STPNs), validation by interactive simulation, and evaluation by several techniques, computing instantaneous and cumulative rewards. It also provides an open-source Java Application Programming Interface (API) to automate the workflow, and it can be used as a toolkit for derivation and evaluation of STPNs in model driven engineering. As distinguishing features, ORIS implements transient and steady-state analysis of STPNs with underlying Markov Regenerative Process (MRP), and transient analysis of STPNs with underlying Generalized Semi- Markov Process (GSMP). It also implements nondeterministic analysis of Time Petri Nets (TPNs), simulation of STPNs, and solution methods for Continuous-Time Markov Chains (CTMCs) and MRPs with at most one non-exponential timer in each state. The well-engineered software architecture of ORIS supports agile implementation of new STPN features, new modeling formalisms, and new analysis methods.

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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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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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Sun, Tao, Guo Sheng Zhao, Jian Wang, Yan Su, and Hai Long Liu. "A Method of Autonomous Recoverment for Survivable System." Advanced Materials Research 765-767 (September 2013): 1382–86. http://dx.doi.org/10.4028/www.scientific.net/amr.765-767.1382.

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A method of autonomous recoverment for survivable system was proposed. Firstly, failure models of survivable system were formally described based on stochastic Petri nets, in which a number of measurable index parameters for recoverment were also given out. And then a recursive autonomous recoverment strategy was presented,Compared with the traditional cyclical recovery strategy, recoverment strategies reduced the time and costs of emergency recovery.

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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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Bortolini, Marco, Maurizio Faccio, Mauro Gamberi, Riccardo Manzini, and Francesco Pilati. "Stochastic timed Petri nets to dynamically design and simulate industrial production processes." International Journal of Logistics Systems and Management 25, no. 1 (2016): 20. http://dx.doi.org/10.1504/ijlsm.2016.078490.

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Tamura, Hiroyuki, and Itsuo Hatono. "Modeling and scheduling of flexible manufacturing systems using timed/stochastic petri nets." IFAC Proceedings Volumes 24, no. 14 (June 1991): 96–101. http://dx.doi.org/10.1016/s1474-6670(17)69331-5.

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Chiola, G., G. Franceschinis, R. Gaeta, and M. Ribaudo. "GreatSPN 1.7: Graphical editor and analyzer for timed and stochastic Petri nets." Performance Evaluation 24, no. 1-2 (November 1995): 47–68. http://dx.doi.org/10.1016/0166-5316(95)00008-l.

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Lisboa, Adriano C., Flevio H. B. De Souza, Cesar M. Ribeiro, Carlos A. Maia, Rodney R. Saldanha, Felipe L. B. Castro, and Douglas A. G. Vieira. "On Modelling and Simulating Open Pit Mine Through Stochastic Timed Petri Nets." IEEE Access 7 (2019): 112821–35. http://dx.doi.org/10.1109/access.2019.2934718.

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Journal articles on the topic 'Stochastic Time Petri Nets'

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