The Quantitative Assessment of Domino Effects Based on Stochastic Petri Nets

2008 ◽  
Vol 44-46 ◽  
pp. 537-544
Author(s):  
Shi Yi Bao ◽  
Jian Xin Zhu ◽  
Li J. Wang ◽  
Ning Jiang ◽  
Zeng Liang Gao
Keyword(s):  
Petri Nets ◽  
State Space ◽  
Petri Net ◽  
Quantitative Assessment ◽  
Stochastic Petri Nets ◽  
Industrial Park ◽  
Domino Effect ◽  
State Space Explosion ◽  
Stochastic Petri Net ◽  
Chemical Industrial Park

The quantitative analysis of “domino” effects is one of the main aspects of hazard assessment in chemical industrial park. This paper demonstrates the application of heterogeneous stochastic Petri net modeling techniques to the quantitative assessment of the probabilities of domino effects of major accidents in chemical industrial park. First, five events are included in the domino effect models of major accidents: pool fire, explosion, boiling liquid expanding vapour explosion (BLEVE) giving rise to a fragment, jet fire and delayed explosion of a vapour cloud. Then, the domino effect models are converted into Generalized Stochastic Petri net (GSPN) in which the probability of the domino effect is calculated automatically. The Stochastic Petri nets’ models, which are state-space based ones, increase the modeling flexibility but create the state-space explosion problems. Finally, in order to alleviate the state-space explosion problems of GSPN models, this paper employs Stochastic Wellformed Net (SWN), a particular class of High-Level (colored) SPN. To conduct a case study on a chemical industrial park, the probability of domino effects of major accidents is calculated by using the GSPN model and SWN model in this paper.

Vulnerability, Uncertainty and Probability (VUP) Quantification of a Network of Interacting Satellites Using Stochastic Petri Nets (SPN)

2013 ◽  
Author(s):  
Atefeh Einafshar ◽  
Farrokh Sassani
Keyword(s):  
Markov Chain ◽  
Quantitative Analysis ◽  
Petri Nets ◽  
State Space ◽  
Petri Net ◽  
Stochastic Petri Nets ◽  
Discrete State ◽  
New Approach ◽  
Stochastic Petri Net ◽  
Discrete State Space

A new approach to Vulnerability, Uncertainty and Probability (VUP) quantification procedure using Stochastic Petri Nets within a network of interacting satellites is presented. A Stochastic Petri Net based model is developed to quantify VUP in a network of interacting satellites. Three indicators are proposed to determine the VUP definitions in interacting network of satellites. The proposed VUP quantification scheme addresses a methodology which employs a Stochastic Petri Net for quantitative analysis of the behavior of the network. With the random variables associated with the Petri Net transitions, the dynamic behavior of the cooperating satellites in a SPN model can be mapped onto a time-continuous Markov chain with discrete state space. After generating a Markov Stochastic Petri Net model, the probability of a given condition in the network at a specified time can be computed and quantified as well as the vulnerability and uncertainty of the system using the identified indicators.

Study of Performance Equivalent Simplification Analysis and Application of Stochastic Petri Nets

2013 ◽  
Vol 756-759 ◽  
pp. 2975-2978
Author(s):  
Da Bin Qi ◽  
Qiu Ju Li
Keyword(s):  
Petri Nets ◽  
State Space ◽  
Model Performance ◽  
Stochastic Petri Nets ◽  
Workflow Model ◽  
State Spaces ◽  
The Real ◽  
State Space Explosion ◽  
Model Based

State spaces of Stochastic Petri Nets (SPN) are exponent explosion based on subordinate models quantities, it is feasible to solve state space explosion. This article introduces basic theories of SPN performance equivalence simplification, integrates the real workflow of sanction management, constructs workflow model based on SPN comparatively, further more, simplifies the model by equivalence simplification theories, reduces models complexity, solves the model performance quantity analysis effective.

scholarly journals Dynamic Reliability Model for Airborne Systems Based on Stochastic Petri Net

2020 ◽  
Vol 38 (4) ◽  
pp. 846-854
Author(s):  
Lu Zhuang ◽  
Zhong Lu ◽  
Ziwen Zhang
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Electrical Power ◽  
Stochastic Petri Nets ◽  
Reliability Model ◽  
Electrical Power System ◽  
Reliability Modeling ◽  
Dynamic Reliability ◽  
Stochastic Petri Net ◽  
Reliability Method

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.

scholarly journals Unfolding through processes to compute the complete prefix of Petri nets

2017 ◽  
Vol Volume 27 - 2017 - Special... ◽  
Author(s):  
Médésu Sogbohossou ◽  
Antoine Vianou
Keyword(s):  
Petri Nets ◽  
State Space ◽  
Partial Order ◽  
Petri Net ◽  
The State ◽  
Classical Approach ◽  
New Approach ◽  
State Space Explosion ◽  
Single Process ◽  
Partial Order Semantics

The partial-order technique of the unfolding implicitly represents state-space of a Petri net (PN), by in particular preserving the concurrency relations between the events. That makes it possible to contain state-space explosion problem in case of strong concurrency. A complete prefix of unfolding is used to cover all the state-space of a bounded PN: its computation according to the classical approach is based on the concept of adequate order, taking directly into account only safe PN. In this paper, a new approach independent of the concept of adequate order and faithful to the partial-order semantics, consists in creating the events of the unfolding in the context of a single process at the same time. The results of the tests are conclusive for safe and nonsafe PN. Some solutions are presented to improve compactness of the prefix obtained. La technique d'ordre partiel du dépliage représente implicitement l'espace d'état d'un réseau de Petri (RdP), en conservant notamment les relations de concurrence entre les événements. Cela permet de contenir le phénomène de l'explosion combinatoire en cas de forte concurrence. Un préfixe complet de dépliage sert à couvrir tout l'espace d'état d'un RdP borné: son calcul suivant l'approche classique se base sur le concept d'ordre adéquat, ne prenant directement en compte que les RdP saufs. Dans cet article, une nouvelle approche indépendante du concept d'ordre adéquat et fidèle à la sémantique d'ordre partiel, consiste à créer les événements du dépliage dans le contexte d'un unique processus à la fois. Les résultats des tests sont concluants pour les RdP saufs et non saufs. Des solutions sont présentées pour améliorer la compacité du préfixe obtenu.

ALGORITHM FOR CONSTRUCTING A REACHABILITY TREE FOR STOCHASTIC PETRI NETS

2021 ◽  
pp. 34-40
Author(s):  
Д.С. Звягин
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Final Stage ◽  
Distribution Systems ◽  
Stochastic Petri Nets ◽  
Matrix Equations ◽  
Correct Process ◽  
Reachability Sets ◽  
Process Failures ◽  
Reachability Tree

Описываются основные определения дерева достижимости сетей Петри. Также рассматриваются различные примеры стохастических сетей Петри, в которых после выставления начальных маркировок в первых позициях определяются значения во всех остальных позициях. Показаны примеры определения маркировок при помощи высчитывания вектора диагональной свертки. Для каждого примера стохастической сети Петри проводится анализ данной сети. Данный анализ необходим для различных распределительных систем и процессов, особенно на заключительном этапе. Основными методами анализа являются дерево достижимости и матричные уравнения. Рассматривается один из таких методов анализа сетей Петри. С использованием дерева достижимости можно проанализировать, выявить и исправить сбои в процессах, которые могут произойти при наличии тупиковых состояний и при неправильной последовательности срабатывания переходов. Исходя из рассмотренных примеров предлагается обобщенный алгоритм построения дерева достижимости для стохастических сетей Петри. Предложенный алгоритм построения дерева достижимости стохастических сетей Петри можно применять для всех сетей как с конечным, так и с бесконечным множеством достижимости. Данный алгоритм будет являться полезным инструментом при анализе стохастических сетей Петри The article describes the basic definitions of the reachability tree of Petri nets. It also considers various examples of stochastic Petri nets, in which, after setting the initial markings in the first positions, the values in all other positions are determined. The work shows examples of determining markings by calculating the vector of the diagonal convolution. Each example of a stochastic Petri net is analyzed. This analysis is necessary for various distribution systems and processes, especially in the final stage. The main analysis methods are reachability tree and matrix equations. I consider one of such methods for analyzing Petri nets. Using the reachability tree, you can analyze, identify, and correct process failures that can occur when there are deadlocks and when transitions are fired incorrectly. Based on the examples considered, I propose a generalized algorithm for constructing a reachability tree for stochastic Petri nets. The proposed algorithm for constructing the reachability tree of stochastic Petri nets can be applied to all nets with both finite and infinite reachability sets. This algorithm will be a useful tool for analyzing stochastic Petri nets

A New Formalism for Diagnosis and Safe Development of Information Systems

2016 ◽  
pp. 206-228
Author(s):  
Calin Ciufudean
Keyword(s):  
Information Systems ◽  
Foraging Behavior ◽  
Petri Net ◽  
Discrete Event ◽  
Stochastic Petri Nets ◽  
Failure Diagnosis ◽  
Ant Colonies ◽  
New Formalism ◽  
Stochastic Petri Net ◽  
Performance Analysis And Design

Failure diagnosis in large and complex information systems (LCIS) is a critical task due to respect the safe development of these systems. A discrete event system (DES) approach to the problem of failure diagnosis of LCIS is presented in this chapter. A classic solution to solve DES's diagnosis is a stochastic Petri nets. Unfortunately, the solution of a stochastic Petri net is severely restricted by the size of its underlying Markov chain. On the other hand, it has been shown that foraging behavior of ant colonies can give rise to the shortest path, which will reduce the state explosion of stochastic Petri net. Therefore, a new model of stochastic Petri net, based on foraging behavior of real ant colonies is introduced in this paper. This model can contribute to the diagnosis, the performance analysis and design of information systems.

Stochastic Petri Nets: Modeling Power and Limit Theorems

1991 ◽  
Vol 5 (4) ◽  
pp. 477-498 ◽  
Author(s):  
Peter J. Haas ◽  
Gerald S. Shedler
Keyword(s):  
Petri Nets ◽  
State Space ◽  
Markov Processes ◽  
Discrete Event ◽  
Building Blocks ◽  
The State ◽  
Stochastic Petri Nets ◽  
Transition Mechanism ◽  
Modeling Power ◽  
Semi Markov Processes

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.

scholarly journals An Incremental and Backward-Conflict Guided Method for Unfolding Petri Nets

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 392
Author(s):  
Dongming Xiang ◽  
Xiaoyan Tao ◽  
Yaping Liu
Keyword(s):  
State Space ◽  
Structural Properties ◽  
Petri Net ◽  
Concurrent Systems ◽  
Improved Method ◽  
Key Factors ◽  
State Space Explosion ◽  
Series Of Experiments ◽  
Recursive Relations

The unfolding technique of Petri net can characterize the real concurrency and alleviate the state space explosion problem. Thus, it is greatly suitable to analyze/check some potential errors in concurrent systems. During the unfolding process of a Petri net, the calculations of configurations, cuts, and cut-off events are the key factors for the unfolding efficiency. However, most of the unfolding methods do not specify a highly efficient calculations on them. In this paper, we reveal some recursive relations and structural properties of these factors. Subsequently, we propose an improved method for computing configurations and cuts. Meanwhile, backward conflicts are used to guide the calculations of cut-off events. Moreover, a case study and a series of experiments are done to illustrate the effectiveness and application scenarios of our methods.

scholarly journals The Combination of Petri Nets and Queueing Theory

2019 ◽  
Vol 9 (1S5) ◽  
pp. 293-294
Keyword(s):  
Petri Nets ◽  
Waiting Time ◽  
Petri Net ◽  
Queueing Theory ◽  
Time Delays ◽  
Queueing Network ◽  
Literature Survey ◽  
Future Research ◽  
Implementation Cost ◽  
Stochastic Petri Net

In this paper, We reviews that most of the articles under the topics petri net (PN), stochastic petri net (SPN), collared petri net (CPN), timed petri net (TPN) and queueing theory(queueing network) were created models and methods independently. After review we came to a conclusion, that the combination of petri net and queueing theory types is used to reduce the implementation cost on the applications. This literature survey shows the outline of recent works done using petri net(SPN,CPN,TPN) and queueing theory models in different applications. The main aim of the queueing theory is to reduce the waiting time, delays in travels, cost. So future research and extension to further the fruitful applications reducing delays using the combination of petri net (SPN,CPN,TPN) and queueing theory (queueing network) are discussed in this article.

Sign in / Sign up

Export Citation Format

Share Document