Abstract
Petri Nets (PNs) are an effective structure for modeling and analyzing asynchronous systems with concurrent and parallel activities. A Petri net models the static properties of a discrete event system concentrating on two basic concepts: events and conditions. Most of the theoretical work on Petri nets is a formal definition of Petri nets structures, which consist of a set of places, representing conditions, a set of transitions, representing events, an input function and an output function. For practical purposes, a graphical representation is more useful. Two types of nodes portray places and transitions. A circle is a place and a bar is a transition. There is no inherent measure of time in a classical Petri net. To approach time-based evaluation of system performances, Timed Petri Nets (TPNs) were introduced. Modeling the notion of time is not straightforward. There are several possibilities for introducing time in PNs, among them timed transitions and timed places. This paper reviews several published examples where Petri Nets were used in different circumstances such as estimating expected utilization of processing resources at steady state in open queueing networks, verifying computerized simulations and batch planning in textile industry.
Highlights
The fundamental concepts and characteristics of Petri Nets (PNs) made them a significant tool for modeling and analyzing asynchronous systems with concurrent and parallel activities
The simulation average estimating the station utilizations were close to those calculated using Timed Petri Nets (TPNs) and their differences were no higher than 2%
The relatively low differences obtained between the numerical results of the two methods provide evidence that the TPN technique is able to verify simulation models
Summary
The fundamental concepts and characteristics of Petri Nets (PNs) made them a significant tool for modeling and analyzing asynchronous systems with concurrent and parallel activities. A Petri net is both a graphical and an analytical modeling tool. Carl Adam Petri from Bonn University, Germany, developed it as a special class of generalized graphs or nets. The chief attraction of a Petri net is the way in which it identifies the basic aspects of various systems, conceptually, through a graphical representation, and mathematically, eventually supported by formal programming languages. PNs are a visual-communication aid similar to flow charts, block diagrams, and networks. Tokens (or markers) in these nets can simulate the dynamic activities
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