Petri net

About: Petri net is a research topic. Over the lifetime, 25039 publications have been published within this topic receiving 406994 citations.

Necessary and sufficient conditions for deadlock-free operation in flexible manufacturing systems using a colored Petri net model

Abstract: Concurrent competition for finite resources by multiple parts in flexible manufacturing systems (FMS) results in deadlock. This is an important issue to be addressed in the operation of the system. A Petri net model, called colored resource-oriented Petri net (CROPN), is developed in this paper. The concurrent resource contention and the important characteristics of the production processes necessary for deadlock control are well modeled by this model. Based on the developed model, necessary and sufficient conditions and an efficient control law are presented for deadlock-free operation in FMS. This control law is a policy of dynamic resource allocation. It determines when a resource can be allocated to which job to avoid deadlock. This control law allows as many active parts as possible to be in the system, while deadlock is totally avoided. This control law is easy to implement and can be embedded into the real-time scheduler. A simple example is used to illustrate the application of the approach.

Application of Petri net based analysis techniques to signal transduction pathways

Abstract: Signal transduction pathways are usually modelled using classical quantitative methods, which are based on ordinary differential equations (ODEs). However, some difficulties are inherent in this approach. On the one hand, the kinetic parameters involved are often unknown and have to be estimated. With increasing size and complexity of signal transduction pathways, the estimation of missing kinetic data is not possible. On the other hand, ODEs based models do not support any explicit insights into possible (signal-) flows within the network. Moreover, a huge amount of qualitative data is available due to high-throughput techniques. In order to get information on the systems behaviour, qualitative analysis techniques have been developed. Applications of the known qualitative analysis methods concern mainly metabolic networks. Petri net theory provides a variety of established analysis techniques, which are also applicable to signal transduction models. In this context special properties have to be considered and new dedicated techniques have to be designed. We apply Petri net theory to model and analyse signal transduction pathways first qualitatively before continuing with quantitative analyses. This paper demonstrates how to build systematically a discrete model, which reflects provably the qualitative biological behaviour without any knowledge of kinetic parameters. The mating pheromone response pathway in Saccharomyces cerevisiae serves as case study. We propose an approach for model validation of signal transduction pathways based on the network structure only. For this purpose, we introduce the new notion of feasible t-invariants, which represent minimal self-contained subnets being active under a given input situation. Each of these subnets stands for a signal flow in the system. We define maximal common transition sets (MCT-sets), which can be used for t-invariant examination and net decomposition into smallest biologically meaningful functional units. The paper demonstrates how Petri net analysis techniques can promote a deeper understanding of signal transduction pathways. The new concepts of feasible t-invariants and MCT-sets have been proven to be useful for model validation and the interpretation of the biological system behaviour. Whereas MCT-sets provide a decomposition of the net into disjunctive subnets, feasible t-invariants describe subnets, which generally overlap. This work contributes to qualitative modelling and to the analysis of large biological networks by their fully automatic decomposition into biologically meaningful modules.

A Petri net approach to the study of persistence in chemical reaction networks

Abstract: Persistence is the property, for differential equations in R(n), that solutions starting in the positive orthant do not approach the boundary of the orthant. For chemical reactions and population models, this translates into the non-extinction property: provided that every species is present at the start of the reaction, no species will tend to be eliminated in the course of the reaction. This paper provides checkable conditions for persistence of chemical species in reaction networks, using concepts and tools from Petri net theory, and verifies these conditions on various systems which arise in the modeling of cell signaling pathways.

Stochastic Petri Nets

Abstract: Will reading habit influence your life? Many say yes. Reading stochastic petri nets is a good habit; you can develop this habit to be such interesting way. Yeah, reading habit will not only make you have any favourite activity. It will be one of guidance of your life. When reading has become a habit, you will not make it as disturbing activities or as boring activity. You can gain many benefits and importances of reading.

Process mining based on regions of languages

Abstract: In this paper we give an overview, how to apply region based methodsfor the synthesis of Petri nets from languages to process mining The research domain of process mining aims at constructing a process modelfrom an event log, such that the process model can reproduce the log, and doesnot allow for much more behaviour than shown in the log We here considerPetri nets to represent process models Event logs can be interpreted as finite languagesRegion based synthesis methods can be used to construct a Petri net froma language generating the minimal net behaviour including the given languageTherefore, it seems natural to apply such methods in the process mining domainThere are several different region based methods in literature yielding differentPetri nets We adapt these methods to the process mining domain and comparethem concerning efficiency and usefulness of the resulting Petri net