Invariant–based performance analysis of timed Petri net models

In timed Petri nets, temporal properties are associated with transitions as transition firing times (or occurrence times). For net models which can be decomposed into a family of place invariants, performance analysis can be conveniently performed on the basis of its components. The paper presents an approach to finding place invariants of net models and proposes an incremental method which, for large models, can significantly reduce the required amount of computations

Modeling and Performance Analysis of Priority Queuing Systems

The paper presents the results of modeling and analysis of data performance on systems that support QoS (Quality of Service). In order to evaluate the performance of the modeled systems used were TPN (Timed Petri Nets). Studied were mechanisms of traffic shaping systems based on PQS (Priority Queuing System). Tested was the impact of the mechanism of generating traffic using TPN. Moreover, discussed were the basic mechanisms and queuing systems occurring in QoS structures. It is shown that models can be effectively used in the modeling and analysis of the performance of computer systems

Modelling reconfigurable manufacturing systems with coloured timed Petri nets

International audienceReconfigurable manufacturing systems (RMSs) have been acknowledged as a promising means of providing manufacturing companies with the required production capacities and capabilities. This is accomplished through reconfiguring system elements over time for a diverse set of individualized products often required in small quantities and with short delivery lead times. Recognizing the importance of dynamic modeling and visualization in decision-making support in RMSs and the limitations of current research, we propose in this work to model RMSs with Petri net (PN) techniques focusing on the process of reconfiguring system elements while considering constraints and system performance. In view of the modeling challenges, including variety handling, production variation accommodation, machine selection, and constraint satisfaction, we develop a new formalism of colored timed PNs. In conjunction with colored tokens and timing in colored and timed PNs, we also define a reconfiguration mechanism to meet modeling challenges. An application case from an electronics company producing mobile phone vibration motors is presented. Also reported are system analysis and application results, which show how the proposed formalism can be used in the reconfiguration decision making process

Decision systems: the relation between problem specification and mathematical analysis

In this paper it is demonstrated that automated support for decision making of a tactical or strategic nature requires a solver-independent medium for describing decision situations. Such a medium may be specific for one environment, but it is also possible to develop media for certain types of environments. By using such a medium one obtains a decoupling of problem formulation and method of analysis. This makes it possible to use (parts of) the problem formulation as input for different types of models. Such problem formulations may provide mathematical models themselves, although they might also contain some less formal features. The decoupling makes it possible to choose problem formulations which are much closer to the original decision situation than would otherwise be possible with formulations in terms of a preselected solver. The argumentation is illustrated by treating a language for specifying goods flow problems in some detail. This language is based on timed colored Petri-nets

DISCRETE-TIME MARKOVIAN STOCHASTIC PETRI NETS

We revisit and extend the original definition of discrete-time stochastic Petri nets, by allowing the firing times to have a “defective discrete phase distribution”. We show that this formalism still corresponds to an underlying discrete-time Markov chain. The structure of the state for this process describes both the marking of the Petri net and the phase of the firing time for of each transition, resulting in a large state space. We then modify the well-known power method to perform a transient analysis even when the state space is infinite, subject to the condition that only a finite number of states can be reached in a finite amount of time. Since the memory requirements might still be excessive, we suggest a bounding technique based on truncation

System Modelling With Petri Nets

Petri Nets (PN) are a graphical formalism which is gaining popularity in recent years as a tool for the representation of complex logical interactions (like synchronization, sequentiality, concurrency and conflict) among physical components or activities in a system. This notes are devoted to introduce the formalism of Petri nets with particular emphasis on the application of the methodology in the area of the performance and reliability modelling and analysis of systems. The quantitative analysis of the behaviour of systems in time requires the superposition of a stochastic timing mechanism to the classical representation of PN. Timed Petri nets and, in particular, Stochastic Petri nets (SPN) are the object of the second part of the notes. Finally, some fully developed examples enlighten peculiar aspects which di#erentiate PNs from other modelling techniques usual in reliability analysis. In few words, the goal of these notes is to show that the proposed methodology based on the PN formalism can be conveniently used as a user-friendly language to represent and evaluate complex stochastic systems