A Study of Petri Nets: Modeling, Analysis and Simulation - Tamu.edu

More documents

Recommendations

Info

Let p , p , } S 1 = { 1 2 p3 ; S 2 = { p1, p2 , p4} ; S 3 = { p1, p2, p3, p4} ; 4 { p2 , p3} 5 { p2 , p3, p4} S 1 = { t1, t2 , t4} ⊆ S1• = { t1, t2 , t3, t4 S 4 • = { t1, t4} ⊆ • S 4 = { t1, t2 , t4 . Thus 4 S = and S = .Then, one can verify that • }.Thus S 1 is a siphon. Again } S is a trap. Similarly it can be shown that S 2 is a siphon, S3 is both a siphon and a trap and S5 is a trap. Also, S1 and S 2 are both minimal and basic siphons. S 3 , S 4 and S5 are basic traps, S3 and S5 are not minimal traps. 4.3.5.3 TC and SC net A PN in which the set of places in every directed circuit (DC) is a trap (siphon), is called a Trapcircuit net (Siphon-circuit net) or TC (SC) net. 4.3.5.4 TCC and SCC net A PN in which the set of places in every directed circuit (DC) contains a trap (siphon) is called TCC (SCC) net. 22
Chapter 5 Analysis of Petri Nets 5.1 Importance of analysis The objective of using Petri nets in system study is to draw important conclusions about the system without going for time and cost ineffective trial and error prototyping. To do so, the first step is to model the system. Once a model is ready, the next task is to analyze the model to draw conclusions about the properties of the model and hence about the actual system. Then only one can answer questions like what the system behavior is supposed to be under specific operational conditions, what properties are inherent to the structure of the net, what to expect and what not to expect from the system during operation and whether there is any pitfall in the system design which must be avoided in operational phase. The first step i.e. modeling has been addressed in Chapter 3. This chapter deals with analysis of the modeled system. Chapter 4 serves as a link between Chapter 3 and Chapter 5, since dealing with substructures eases both modeling and analysis. It is worthwhile to mention that some authors prefer to discuss PN properties and PN analysis separately. This approach may seem more systematic but in the process it can only introduce behavioral properties, because definition and understanding of structural properties are so closely related to structural analysis that they can not be discussed separately. Keeping this in mind, this report discusses the properties and analysis techniques together to emphasize the fact that analysis is more than a mere tool, the analysis methods themselves reveal elegance of PN model and its properties. 5.2 Analysis approaches There are three major approaches for PN analysis:(1) Behavioral approach, which is a tree based approach, (2) Structural approach, which is a matrix based approach and (3) Reduction or Refinement approach, which is a net simplification approach. These three approaches are discussed here. 5.2.1 Behavioral approach This approach deals with the behavioral properties of PN. Behavioral properties are those which are dependent on the initial marking. In the following discussion, behavioral properties are treated in detail. Then effort has been given to make conclusions about them from analysis. 5.2.1.1 Reachability 23
Page 1 and 2: A Study of Petri Nets Modeling, Ana
Page 3 and 4: 4.2.3 Simple Directed path (SDP) 15
Page 5 and 6: Acknowledgement The information pre
Page 7 and 8: Chapter 1 Introduction In the engin
Page 9 and 10: Example 2.2: T< 40 O C OFF ON SWITC
Page 11 and 12: 2.2.3 Definition of Ordinary Petri
Page 13 and 14: w ( p′ , t) = w( t, p) ; this ens
Page 15 and 16: 3.2.2 Synchronization Petri nets ca
Page 17 and 18: 3.3 Primitives for Programming Cons
Page 19 and 20: 3.3.7 Either - or (Mutual exclusion
Page 21 and 22: Fig 4.1 (a) and (b) shows source an
Page 23 and 24: 4.2.9 P-Subnet (PSN) A subnet (SN),
Page 25 and 26: 4.3.3 Inverse of a PN or Reversed P
Page 27: Properties Trap Siphon Behavioral p
Page 31 and 32: times they are fired and in which o
Page 33 and 34: Example 5.5 (contd.) T m 0 = (01001
Page 35 and 36: Mathematically, for Boundedness it
Page 37 and 38: After introducing the concept of li
Page 39 and 40: Example 5.10 (a) Safe Mode t 9 p 8
Page 41 and 42: Conservation can be effectively tes
Page 43 and 44: 5.2.1.11 Fairness Many different no
Page 45 and 46: It can be recalled that,i is index
Page 47 and 48: ⎡2⎤ ⎢ ⎥ ⇒ ⎢ 0 ⎥ ⎢0
Page 49 and 50: Moreover, both PN model and the act
Page 51 and 52: A11 y1 + A12 y2 A y + A y 21 1 22 2
Page 53 and 54: solving equation (6) and (8). These
Page 55 and 56: The support of a P-invariant x is d
Page 57 and 58: Example 5.22 5.2.2.5 Structural Con
Page 59 and 60: Conclusion This report described th
Page 61 and 62: A1. Definition of Partition Matrix
Page 63 and 64: Then, where ⎡A11 ⎢ A AB ⎢ 21
Page 65 and 66: A6. Usefulness of Jordan Canonical
Page 67 and 68: A P P E N D I X Controllability Lin
Page 69 and 70: iii. The ( n × np) controllability
Page 71 and 72: B3. Condition of Controllability fo
Page 73: [14] Javier Campos, Giovanni Chiola

A Study of Petri Nets: Modeling, Analysis and Simulation - Tamu.edu

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?