4,772 research outputs found
Petri net approaches for modeling, controlling, and validating flexible manufacturing systems
In this dissertation, we introduce the fundamental ideas and constructs of Petri net models such as ordinary, timed, colored, stochastic, control, and neural, and present some studies that emphasize Petri nets theories and applications as extended research fields that provide suitable platforms in modeling, controlling, validating, and evaluating concurrent systems, information systems, and a versatile dynamic system and manufacturing systems;We then suggest some of extensions that help make Petri nets useful for modeling and analyzing discrete event systems and manufacturing systems models based on the context of a versatile manufacturing system, and applies extended Petri nets models to several manufacturing systems such as an assembly cell, an Automated Palletized Conveyor System, and a tooling machine to show increased modeling power and efficient analysis methods;Finally, Validation methods are presented for these models and results of a performance analysis from a deterministic and stochastic model are used to reorganize and re-evaluate a manufacturing system in order to increase its flexibility
TRANSIENT ANALYSIS OF A PREEMPTIVE RESUME M/D/l/2/2 THROUGH PETRI NETS
Stochastic Petri Nets (SPN) are usually designed to support exponential distributions
only, with the consequence that their modelling power is restricted to Markovian systems.
In recent years, some attempts have appeared in the literature aimed to define SPN
models with generally distributed firing times. A particular subclass, called Deterministic
and Stochastic Petri Nets (DSPN), combines into a single model both exponential and
deterministic transitions. The available DSPN implementations require simplifying assumptions
which limit the applicability of the model to preemptive repeat different service
mechanisms only. The present paper discusses a semantical generalization of the DSPNs
by including preemptive mechanisms of resume type. This generalization is crucial in
connection with fault tolerant systems, where the work performed before the interruption
should not be lost. By means of this new approach, the transient analysis of a M/D/1/2/2
queue (with 2 customers, 1 server, exponential thinking and deterministic service time) is
fully examined under different preemptive resume policies
Petri net modeling and analysis of an FMS cell
Petri nets have evolved into a powerful tool for the modeling, analysis and design of asynchronous, concurrent systems. This thesis presents the modeling and analysis of a flexible manufacturing system (FMS) cell using Petri nets. In order to improve the productivity of such systems, the building of mathematical models is a crucial step.
In this thesis, the theory and application of Petri nets are presented with emphasis on their application to the modeling and analysis of practical automated manufacturing systems. The theory of Petri nets includes their basic notation and properties. In order to illustrate how a Petri net with desirable properties can be modeled, this thesis describes the detailed modeling process for an FMS cell. During the process, top-down refinement, system decomposition, and modular composition ideas are used to achieve the hierarchy and preservation of important system properties. These properties include liveness, boundedness, and reversibility.
This thesis also presents two illustrations showing the method adopted to model any manufacturing systems using ordinary Petri nets. The first example deals with a typical resource sharing problem and the second the modeling of Fanuc Machining Center at New Jersey Institute of Technology.
Furthermore, this thesis presents the analysis of a timed Petri net for cycle time, system throughput and equipment utilization. The timed (deterministic) Petri net is first converted into an equivalent timed marked graph. Then the standard procedure to find the cycle time for marked graphs is applied. Secondly, stochastic Petri net is analyzed using SPNP software package for obtaining the system throughput and equipment utilization. This thesis is of significance in the sense that it provides industrial engineers and academic researchers with a comprehensive real-life example of applying Petri net theory to modeling and analysis of FMS cells. This will help them develop their own applications
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
CSL model checking of Deterministic and Stochastic Petri Nets
Deterministic and Stochastic Petri Nets (DSPNs) are a widely used high-level formalism for modeling discrete-event systems where events may occur either without consuming time, after a deterministic time, or after an exponentially distributed time. The underlying process dened by DSPNs, under certain restrictions, corresponds to a class of Markov Regenerative Stochastic Processes (MRGP). In this paper, we investigate the use of CSL (Continuous Stochastic Logic) to express probabilistic properties, such a time-bounded until and time-bounded next, at the DSPN level. The verication of such properties requires the solution of the steady-state and transient probabilities of the underlying MRGP. We also address a number of semantic issues regarding the application of CSL on MRGP and provide numerical model checking algorithms for this logic. A prototype model checker, based on SPNica, is also described
A case study in model-driven synthetic biology
We report on a case study in synthetic biology, demonstrating the modeldriven
design of a self-powering electrochemical biosensor. An essential result of
the design process is a general template of a biosensor, which can be instantiated
to be adapted to specific pollutants. This template represents a gene expression network
extended by metabolic activity. We illustrate the model-based analysis of this
template using qualitative, stochastic and continuous Petri nets and related analysis
techniques, contributing to a reliable and robust design
Numerical analysis of deterministic and stochastic Petri nets with concurrent deterministic transitions
This paper introduces an efficient numerical algorithm for the steady-state analysis of deterministic and stochastic Petri nets (DSPNs) without structural restrictions on the enabling of deterministic transitions. The method rests on observation, at equidistant time points, of the continuous-time Markov process that records tangible markings of the DSPN and remaining firing times associated with deterministic transitions. This approach results in the analysis of a general state space Markov chain whose system of stationary equations can be transformed into a system of Volterra equations. The techniques of this paper are also applicable to queueing networks, stochastic process algebras, and other discrete-event stochastic systems with an underlying stochastic process which can be represented as a generalized semi-Markov process with exponential and deterministic events
From Epidemic to Pandemic Modelling
We present a methodology for systematically extending epidemic models to
multilevel and multiscale spatio-temporal pandemic ones. Our approach builds on
the use of coloured stochastic and continuous Petri nets facilitating the sound
component-based extension of basic SIR models to include population
stratification and also spatio-geographic information and travel connections,
represented as graphs, resulting in robust stratified pandemic metapopulation
models. This method is inherently easy to use, producing scalable and reusable
models with a high degree of clarity and accessibility which can be read either
in a deterministic or stochastic paradigm. Our method is supported by a
publicly available platform PetriNuts; it enables the visual construction and
editing of models; deterministic, stochastic and hybrid simulation as well as
structural and behavioural analysis. All the models are available as
supplementary material, ensuring reproducibility.Comment: 79 pages (with Appendix), 23 figures, 7 table
On Fault Diagnosis of random Free-choice Petri Nets
This paper presents an on-line diagnosis algorithm for Petri nets where a priori probabilistic knowledge about the plant operation is available. We follow the method developed by Benveniste, Fabre, and Haar to assign probabilities to configurations in a net unfolding thus avoiding the need for randomizing all concurrent interleavings of transitions. We consider different settings of the diagnosis problem, including estimating the likelihood that a fault may have happened prior to the most recent observed event, the likelihood that a fault will have happened prior to the next observed event. A novel problem formulation treated in this paper considers deterministic diagnosis of faults that occurred prior to the most recent observed event, and simultaneous calculation of the likelihood that a fault will occur prior to the next observed event
MathMC: A mathematica-based tool for CSL model checking of deterministic and stochastic Petri nets
Deterministic and Stochastic Petri Nets (DSPNs) are a widely used high-level formalism for modeling discreteevent systems where events may occur either without consuming time, after a deterministic time, or after an exponentially distributed time. CSL (Continuous Stochastic Logic) is a (branching) temporal logic developed to express probabilistic properties in continuous time Markov chains (CTMCs). In this paper we present a Mathematica-based tool that implements recent developments for model checking CSL style properties on DSPNs. Furthermore, as a consequence of the type of process underlying DSPNs (a superset of Markovian processes), we are also able to check CSL properties of Generalized Stochastic Petri Nets (GSPNs) and labeled CTMCs
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