Petri Nets Chapter 4 Sections 4.3.3 & 4.3.4 - - PowerPoint PPT Presentation

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Petri Nets Chapter 4 Sections 4.3.3 & 4.3.4 - - PowerPoint PPT Presentation

Petri Nets Chapter 4 Sections 4.3.3 & 4.3.4 Definition of a Petri net It is a bipartite directed graph with components < P , T , In , Out > Two types of nodes P are


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SLIDE 1

Petri Nets

  • Chapter 4
  • Sections 4.3.3 & 4.3.4
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SLIDE 2

Definition of a Petri net

PN–2  It is a bipartite directed graph with components


  • < P , T , In , Out >

 Two types of nodes

 P are places  T are transitions


  •  Two types of edges

 In are input to transitions  Out are output from transitions

In ! P "T Out ! T " P

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SLIDE 3

PN–3

Components of a Petri Net p1, p2 ∈ P t1 ∈ T

  • (p1 , t1) ∈ In
  • (t1 , p2) ∈ Out
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SLIDE 4

Marked Petri net

 It is a Petri net augment with a marking M

 A marking is a mapping M from places to integers

 Designated by tokens in a diagram

PN–4

M : P ! "

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SLIDE 5

PN–5

Example of a Petri net transition firing

LP needed LP available LP allocated Allocate LP LP needed LP available LP allocated Allocate LP A before firing B after firing

 A transition can fire when

 Every input place has at least one token

 When a transition fires

 One token is removed from every input place  One token is added to every output place

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SLIDE 6

PN–6

Schematic for modeling semaphores

Semaphore for get resource Want resource Resource available Allocate resource Resource allocated Have resource Free resource Resource available Process does not want resouce Semaphore for free resource

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SLIDE 7

PN–7

Modeling Mutual Exclusion

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SLIDE 8

Definition of an event-driven Petri net

PN–8  It is a Petri net augment with two additional types of

nodes

 I – Input ports  O – Output ports

 In and Out include ports

In ! (P ! I)"T Out ! T "(P !O)

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SLIDE 9

PN–9

Model for a Single Server A marked event-driven Petri net