Starts with a brief review of the history and the application areas considered in the literature. The author then proceeds with introductory modeling examples, behavioral and structural properties, three methods of analysis, subclasses of Petri nets and their analysis. In particular, one section is devoted to marked graphs, the concurrent system model most amenable to analysis. Introductory discussions on stochastic nets with their application to performance modeling, and on high-level nets with their application to logic programming, are provided. Also included are recent results on reachability criteria. Suggestions are provided for further reading on many subject areas of Petri nets. >

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Petri nets: Properties, analysis and applications

[서평]「The Unified Modeling Language User Guide」

This book proposes a unified mathematical treatment of a class of 'linear' discrete event systems, which contains important subclasses of Petri nets and queuing networks with synchronization constraints. The linearity has to be understood with respect to nonstandard algebraic structures, e.g. the 'max-plus algebra'. A calculus is developed based on such structures, which is followed by tools for computing the time behaviour to such systems. This algebraic vision lays the foundation of a bona fide 'discrete event system theory', which is shown to parallel the classical linear system theory in several ways.

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Synchronization and Linearity: An Algebra for Discrete Event Systems

An attack graph is a succinct representation of all paths through a system that end in a state where an intruder has successfully achieved his goal. Today Red Teams determine the vulnerability of networked systems by drawing gigantic attack graphs by hand. Constructing attack graphs by hand is tedious, error-prone, and impractical for large systems. By viewing an attack as a violation of a safety property, we can use off-the-shelf model checking technology to produce attack graphs automatically: a successful path from the intruder's viewpoint is a counterexample produced by the model checker In this paper we present an algorithm for generating attack graphs using model checking as a subroutine. Security analysts use attack graphs for detection, defense and forensics. In this paper we present a minimization analysis technique that allows analysts to decide which minimal set of security measures would guarantee the safety of the system. We provide a formal characterization of this problem: we prove that it is polynomially equivalent to the minimum hitting set problem and we present a greedy algorithm with provable bounds. We also present a reliability analysis technique that allows analysts to perform a simple cost-benefit trade-off depending on the likelihoods of attacks. By interpreting attack graphs as Markov Decision Processes we can use the value iteration algorithm to compute the probabilities of intruder success for each attack the graph.

Two Formal Analyses of Attack Graphs

This paper surveys recent research on the application of Petri net models to the analysis and synthesis of controllers for discrete event systems. Petri nets have been used extensively in applications such as automated manufacturing, and there exists a large body of tools for qualitative and quantitative analysis of Petri nets. The goal of Petri net research in discrete event systems is to exploit the structural properties of Petri net models in computationally efficient algorithms for computing controls. We present an overview of the various models and problems formulated in the literature focusing on two particular models, the controlled Petri nets and the labeled nets. We describe two basic approaches for controller synthesis, based on state feedback and event feedback. We also discuss two efficient techniques for the on-line computation of the control law, namely the linear integer programming approach which takes advantage of the linear structure of the Petri net state transition equation, and path-based algorithms which take advantage of the graphical structure of Petri net models. Extensions to timed models are briefly described. The paper concludes with a discussion of directions for future research.

http://www.mne.psu.edu/ray/me597DESandSymbolicDyn/hollowayKroghGiua97.pdf

A Survey of Petri Net Methods for Controlled Discrete EventSystems

Performance evaluation of concurrent systems using Petri nets

A System-Theoretic Accident Model and Process with Human Factors Analysis and Classification System taxonomy

Timing analysis of safety properties using fault trees with time dependencies and timed state-charts

Estimating the mean completion time of PERT networks with exponentially distributed durations of activities

In order to make computer-aided control systems as safe as possible, a number of analysis techniques have been developed. One of these is fault tree analysis. A fault tree (FT) represents causal and generalisation relations between events (e.g. a hazard and its causes). However, it can express neither time relations between events nor detection and protection times. Time Petri nets (TPNs) can model all the above aspects. Thus, TPNs can be used for analysing and verifying time-dependent fault trees (FTs). One of the limitations of classical TPN analysis is the large number of TPN states. Even for a small FT this number can turn out to be vast. The authors introduce a new method for analysing such TPNs that model FTs. We do not consider all states that are reachable from the initial marking in classical TPN analysis but only those that lead to the occurrence of a hazard. Such an approach simplifies the procedure and results in cleaner final conclusions. If the hazard is reachable there is a need for safety measures to be taken. FT analysis and modelling of protection using TPNs will be illustrated using an example.

Jan Magott

Papers

Performance evaluation of concurrent systems using Petri nets

A System-Theoretic Accident Model and Process with Human Factors Analysis and Classification System taxonomy

Timing analysis of safety properties using fault trees with time dependencies and timed state-charts

Estimating the mean completion time of PERT networks with exponentially distributed durations of activities

Method of time Petri net analysis for analysis of fault trees with time dependencies