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.

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.

scholarly journals Laws of Little in an open queueing network

2012 ◽  
Vol 17 (3) ◽  
pp. 327-342 ◽  
Author(s):  
Saulius Minkevičius ◽  
Stasys Steišūnas
Keyword(s):  
Waiting Time ◽  
Queueing Theory ◽  
Queue Length ◽  
Heavy Traffic ◽  
Queueing Network ◽  
Fluid Limit ◽  
Fluid Approximation ◽  
Large Numbers ◽  
Virtual Waiting Time ◽  
Open Queueing Network

The object of this research in the queueing theory is theorems about the functional strong laws of large numbers (FSLLN) under the conditions of heavy traffic in an open queueing network (OQN). The FSLLN is known as a fluid limit or fluid approximation. In this paper, FSLLN are proved for the values of important probabilistic characteristics of the OQN investigated as well as the virtual waiting time of a customer and the queue length of customers. As applications of the proved theorems laws of Little in OQN are presented.

Infinite Petri Nets as Models of Grids

2015 ◽  
pp. 187-204 ◽  
Author(s):  
Dmitry A. Zaitsev ◽  
Ivan D. Zaitsev ◽  
Tatiana R. Shmeleva
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Regular Structure ◽  
Parametric Representation ◽  
Future Research ◽  
Parametric Form ◽  
Infinite Systems ◽  
Analysis Technique ◽  
Parametric Description

An overview of works, early published by the authors, has been done that explains peculiarities of composition and analysis technique developed for investigation of infinite Petri nets with regular structure which were introduced for modeling networks, clusters, and computing grids. Parametric description of Petri nets, parametric representation of infinite systems for calculation place/transition invariants, and solving them in parametric form allowed the invariance proof for infinite Petri net models. Complex deadlocks were disclosed and a possibility of the network blocking via ill-intended traffic revealed. Prospective directions for future research of infinite Petri nets were formulated.

Business Process Modeling and Analysis Based on Queue Logical Petri Nets

2019 ◽  
Vol 29 (01) ◽  
pp. 115-137 ◽  
Author(s):  
Lei Liu ◽  
Wei Liu ◽  
Yuyue Du
Keyword(s):  
Petri Nets ◽  
Business Process ◽  
Waiting Time ◽  
Petri Net ◽  
Process Modeling ◽  
Modeling Tools ◽  
Modeling And Analysis ◽  
Average Waiting Time ◽  
Stay Time ◽  
Complete Process

In the present modeling tools, there is no proper model to describe the fairness of resource scheduling for sharing systems. In order to solve this problem well, we propose a new sharing system and Queue Logical Petri nets. In this paper, a complete process of entering and leaving a garage is modeled by a Queue Logical Petri nets. Based on random arrival and exponential arrival, the average waiting time of vehicles, the average stay time in the queue and the average number of waiting vehicles in the queue are analyzed. According to reachable sequence of Queue Logical Petri net, the Invariant, the utilization of garage and the number of waiting vehicles are analyzed. And the validity of the sharing system with queue is proved by compared with other methods in the experiment.

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.

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.

A literature overview of knowledge sharing between Petri nets and ontologies

2016 ◽  
Vol 31 (3) ◽  
pp. 239-260 ◽  
Author(s):  
Haitao Cheng ◽  
Zongmin Ma
Keyword(s):  
Artificial Intelligence ◽  
Knowledge Representation ◽  
Knowledge Sharing ◽  
Petri Nets ◽  
Petri Net ◽  
Knowledge Engineering ◽  
Future Research ◽  
Knowledge Domain ◽  
Literature Overview ◽  
Popular Knowledge

AbstractKnowledge representation is a subarea of artificial intelligence concerned with using formal symbols to represent a set of facts within a knowledge domain. Two popular knowledge representation languages, namely Petri net and ontology, are promising knowledge sharing and reusing methods in knowledge engineering. The combination of Petri net and ontology can facilitate achieving complementary advantages. Currently, many efforts have been done on knowledge sharing between Petri nets and ontologies. To investigate these issues and more importantly serve as identifying the direction of knowledge sharing between Petri nets and ontologies, in this paper we give a comprehensive literature overview of knowledge sharing between Petri net models and ontology models to satisfy the obvious need. In detail, we discuss the knowledge sharing from two aspects: the different knowledge representation approaches of ontology to represent and reason Petri net and issues of constructing Petri net from ontology. In addition, other important issues on applications and directions for future research are discussed in detail.

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