Batch deterministic and stochastic Petri nets modeling, analysis and its application to supply chain (original) (raw)

A Graph Theoretic Approach: Petri net

Int. J. of Mathematical Sciences and Applications, 2011

This work attempts to understand some of the basic properties of Petri nets and their relationships to directed bipartite graphs. Different forms of directed graphs are widely used in computer science. Normally various names are given to these structures. E.g. directed acyclic graphs (DAGs), control flow graphs (CFGs), task graphs, generalized task graphs (GTGs), state transition diagrams (STDs), state machines, etc. Some structures might exhibit bi-similarity. The justification for this work is that Petri nets are based on graphs and have some similarities to them. Transforming Petri nets into graphs opens up a whole set of new interesting possible experimentations. Normally this is overlooked. Directed Graphs have a lot of theory and research associated with them. This work could be further developed and used for Petri net evaluation. The related works justifies the reasoning how and why Petri nets are obtained or supported using graphs. The transformation approach can be formal or informal. The main problem tackled is how graphs can be obtained from Petri nets. Possible solutions that use reduction methods to simplify the Petri net are presented. Different methods to extract graphs from the basic or fundamental Petri net classes are explained. Some examples are given and the findings are briefly discussed.

A Symbolic State-Transition Graph for a Class of Dynamic Petri Nets

2009

The design of dynamic, adaptable discrete-event systems calls for adequate modeling formalisms and tools in order to manage possible changes occurring during system's lifecycle. A com- mon approach is to pollute the design with details not concerning the current system behavior, rather its evolution. That hampers analysis, reuse and main- tenance in general. A Petri net-based reective model (based on classical Petri nets) was recently proposed to support dynamic discrete-event system's design, and was applied to dynamic workow's management. Behind there is the idea that keeping functional as- pects separated from evolutionary ones, and applying evolution to the (current) system only when neces- sary, results in a clean formal model for dynamic sys- tems. This model preserves the ability of verifying properties typical of classical Petri nets. As a rst step toward the implementation (in the short time) of a discrete-event simulator, Reective Petri nets are provided in thi...

From Petri Nets to Graph Transformation Systems

2010

Hans-Jörg Kreowski was among the first researchers to point out that Place/Transition Petri nets can be interpreted as instances of Graph Transformation Systems, a fact now considered folklore. We elaborate on this observation, discussing how several different models of Petri nets can be encoded faithfully into Graph Transformation Systems. The key idea we pursue is that the net encoding is uniquely determined, and distinct net models are mapped to alternative approaches to graph transformation.

Towards a Petri net Model for Graph Transformation Systems

2019

Graph transformation systems (GTS) have been successfully proposed as a general, theoretically sound model for concurrency. Petri nets (PN), on the other side, are a central and intuitive formalism for concurrent or distributed systems, well supported by a number of analysis techniques/tools. Some PN classes have been shown to be instances of GTS. In this paper, we change perspective presenting an operational semantics of GTS in terms of Symmetric Nets, a well-known class of Coloured Petri nets featuring a structured syntax that outlines model symmetries. Some practical exploitations of the proposed operational semantics are discussed. In particular, a recently developed structural calculus for SN is used to validate graph rewriting rules in a symbolic way.

On system’s model transformation by Petri nets

2004

Abstract: Petri nets are widely used in control systems specification, but, as with all graphical languages, some structuring mechanisms are necessary to fight model size explosion. To that end, this paper proposes to represent a set of model transformations, applicable to any type of Petri net model, through another Petri net model; this associated net is named a transformation net. Node fusions are then viewed as steps in the transformation net evolution.

Modelling systems by hybrid Petri nets. An application to supply chains

2008

Petri Nets (PNs) are a discrete event model firstly proposed by CA Petri in his Ph. D. thesis in the early 1960s (Petri, 1962). The main feature of a (discrete) PN is that its state is a vector of non-negative integers. This is a major advantage with respect to other formalisms such as automata, where the state space is a symbolic unstructured set, and has been exploited to develop many analysis techniques that do not require to enumerate the state space (structural analysis)(Silva et al., 1996).

A Review of Petri Net Modeling of Dynamical Systems

2012

Petri nets are graphical and mathematical modeling tools which are gaining popularity in recent years. It is a tool for the representation of complex logical systems, such as synchronization, sequentially, concurrency and conflict. The present introduction highlights some of the formalism of Petri nets with special emphasis on reachability and coverability analysis. We have also extended our topic by explaining place & transition invariance with examples.

Ladder Diagram Petri Nets: Discrete Event Systems

Petri Nets in Science and Engineering, 2018

Ladder diagram language (LD) is a common programming language in industry to develop control algorithms of discrete event systems (DESs). Besides, it is one of the five programming languages supported by the International Electrotechnical Commission through the IEC-61131-3 standard. On the other hand, Petri net (PN) theory is both a graphical and mathematical tool used to model discrete event systems, particularly in this study, control lines used in industrial algorithms. Control algorithms in LD are generally developed based on the experience of control system programmers. Therefore, it is still a relevant problem how to formalize the current and new control algorithms. In this chapter, are analyzed lines in LD used more frequently in control algorithms. Additionally, an element-to-element transformation methodology from a LD program to a PN model is proposed.