Формальное описание систем средствами Петри-объектных моделей

The article considers the new formal methods for system's description based on object-oriented methodology and stochastic timed Petri net. The state equation of stochastic timed Petri net with conflict and multi-transitions is received. The concept of Petri-object is proposed and construction technology of simulation model with Petri-objects using is developed.В статье рассматривается новый способ формального описания систем, основывающийся на объектно-ориентированной технологии и стохастической временной сети Петри. Получены уравнения состояний стохастической временной сети Петри с конфликтными и многоканальными переходами. Предложено понятие Петри-объекта и разработана технология конструирования имитационной модели системы с использованием Петри-объектов

Уравнения состояний стохастических временных сетей Петри с информационными связями

Розглянуто застосування мереж Петрі з часовими затримками для імітаційного моделювання систем. Отримано рівняння перетворень стану мережі Петрі та фундаментальні матричні рівняння стохастичної мережі Петрі з часовими затримками, багатоканальними та конфліктними переходами, інформаційними зв’язками.The use of timed Petri nets in systems simulation is analyzed. The equations of timed Petri net state transformations and fundamental matrix equations of stochastic timed Petri net with conflict and multi-transitions, with information ties are obtained

Web Application for Visual Modeling of Discrete Event Systems

This research work has resulted in the development of a web application that enables discrete event systems simulation to be created using a Petri-object approach. It provides the development of a model in two stages. In the first stage, the dynamics of the classes of objects are created using Petri net. In the second stage, the model is composed of objects with given dynamics. The simulation algorithm is based on stochastic Petri net with multichannel transitions and is implemented using Ruby. The web application enables the design of the model's dynamics by manipulation with graphics objects and saving it not only as a graphics object but also as a program method. This greatly improves the overall performance of the simulation model development

Cluster Grid based Response-time analysis module for the PIPE Tool.

Generalized Stochastic Petri Nets (GSPNs) are a widely used high-level formalism used for modelling discrete-event systems. The Platform Independent Petri net Editor (PIPE) is an open source software project that allows creation, analysis and simulation of Petri Nets. This tool paper presents a PIPE module for response-time analysis of a Petri net’s underlying Continuous Time Markov Chain (CTMC). Jobs are submitted via a web interface, from within PIPE or from a browser. The parallel computations are run using Grid Engine on a cluster hosted at Imperial College London. 1

Петрі-об’єктна модель системи управління транспортним рухом

The article considers the simulation of traffic control's system based on Petri-object modeling. The dynamics of Petri-objects of the system are described by stochastic timed Petri net with conflict and multichannel transitions that allows to recreating various types of traffic control.В статье рассматривается имитационное моделирование системы управления транспортным движением, основывающееся на Петри-объектной технологии. Динамика Петри-объектов системы описывается стохастической временной сетью Петри с конфликтными и многоканальными переходами, что позволяет воссоздать различные виды управления транспортным движением

Automated rare event simulation for stochastic petri nets

We introduce a method to automatically apply rare event simulation to stochastic Petri nets, which are often used in the stochastic model checking community to model highly reliable systems. Rare event simulation can be much faster than standard simulation by exploiting information about the typical behaviour of the system. Previously, such information came from heuristics, human insight, or analysis on the full state space. We present a formal algorithm that obtains the required information from the (high-level) stochastic Petri net description, without generating the full state space. Essentially, our algorithm reduces the state space of the model to a (much smaller) graph in which each node represents a set of states for which the most likely path to failure has the same form. An earlier version of this work has been presented to the model checking commmunity (at QEST 2013). We believe that the described methodology, which has since then been improved through a correctness proof and a more efficient initial state space partitioning, may also be of interest to the RESIM community

Compositional modelling using Petri nets with the analysis power of stochastic hybrid processes

A general stochastic hybrid process (GSHP) is a mathematical formalism that covers most of the requirements posed by the modelling of complex operations, such as time dependencies, multi-dimensional continuous as well as discrete processes, discontinuities, randomness and model uncertainties. In addition, it is possible to study GSHP by using stochastic analysis methodologies, thereby empowering it with powerful mathematical properties. This guarantees unambiguous simulation possibility of the model and allows speeding up this simulation while keeping the model properties intact. However, using GSHP to construct a model of a complex operation is not easy. To support the modelling and the subsequent verification both by mathematical and by multiple operational domain experts, a supporting graphical modelling formalism is desired. Petri nets have shown to be useful for developing models of various complex applications. Typical Petri net features are concurrency and synchronisation mechanism, hierarchical and modular construction, and natural expression of causal dependencies, in combination with graphical and analytical representations.\ud \ud The aim of this thesis is to combine the strengths of Petri net modelling formalisms and those of GSHP. First, dynamically coloured Petri nets (DCPN) are developed, and proof of equivalence is provided with piecewise deterministic Markov processes, which is a particular class of GSHP. Next, DCPN are extended to stochastically and dynamically coloured Petri nets (SDCPN), and proof of equivalence is provided with GSHP. Subsequently, SDCPN are extended to SDCPN with interconnection mapping types (SDCPNimt) and proof of equivalence is provided with both SDCPN and GSHP. It is shown with illustrative air transport examples that these three classes of Petri net are very effective when it comes to the compositional modelling of operations consisting of many distributed components that behave and interact in a dynamic way with many uncertainties. With the equivalence relations between these formalisms, the properties and strengths of the various approaches are combined. The many applications of the approach developed in this thesis, executed at NLR and beyond, show that both the approach and its combined strengths are acknowledged and supported by practice

Petri nets for systems and synthetic biology

We give a description of a Petri net-based framework for modelling and analysing biochemical pathways, which uni¯es the qualita- tive, stochastic and continuous paradigms. Each perspective adds its con- tribution to the understanding of the system, thus the three approaches do not compete, but complement each other. We illustrate our approach by applying it to an extended model of the three stage cascade, which forms the core of the ERK signal transduction pathway. Consequently our focus is on transient behaviour analysis. We demonstrate how quali- tative descriptions are abstractions over stochastic or continuous descrip- tions, and show that the stochastic and continuous models approximate each other. Although our framework is based on Petri nets, it can be applied more widely to other formalisms which are used to model and analyse biochemical networks

PETRI NET BASED APPROACHES TO MANUFACTURING SYSTEMS

This paper describes the planning in manufacturing systems. The skeleton and the functionality of a Petri Net Toolbox, embedded in the Matlab environment, are briefly presented, as offering a collection of instruments devoted to simulation, analysis and synthesis of discrete event systems. Timed Petri Nets are used to model operational and routing in production systems. A generalized multi productive machine modules is defined, adapter to system feature, repeated and connected to compose the TPN models of production systems with different levels of routing and operation. The present paper approaches the stochastic medium considered to be fundamental in describing the changes and the aleatory variations during the desertion process of machines and blocking times in the processing activity. We intend to present a simulated model according to which we can establish the time variation and the outputs process in a simple production system.Petri Nets, discrete event, manufacturing systems