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CLASSIFICATION OF PETRI NETS

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APPLICATIONS OF PETRI NET

Petri net is primarily used for studying thedynamic concurrent behavior of network-based systems where there is a discrete flow.

Petri Nets are applied in practice by industry,academic, and other places.

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Basics of Petri Nets

Petri net consist two types of nodes: placesandtransitions. And arc exists only from a place toa transition or from a transition to a place.

A place may have zero or more tokens.

Graphically, places, transitions, arcs, andtokens are represented respectively by: circles,bars, arrows, and dots.

p2p1t1

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Basics of Petri Nets

Below is an example Petri net with two placesand one transaction.

Transition node is ready to fire if and only if there

is at least one token at each of its input placesstate transition of form (1, 0) (0, 1)

p1 : input place p2: output place

p2p1t1

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PROPERTIES

Reachability Boundedness Liveness

a PN is live if, no matter what marking has been reached, it

is possible to fire any transition with an appropriate firingsequence

Reversibility Coverability

a marking is coverable if exists M reachable from M0

Persistence for any two enabled transitions, the firing of one of them

will not disable the other

Synchronic distance

Fairness

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PROPERTIES OF PETRI NETS

Synchronization

Concurrency

p2t1p1 p3t2t1

t1

t2

Merging

Sequential Execution

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Properties of Petri Nets

Conflict

t1

t2

t1

t2

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Example: In a Restaurant (A Petri Net)Waiter

freeCustomer 1 Customer 2

Take

order

Take

order

Order

taken

Tell

kitchen

wait wait

Serve food Serve food

eating eating

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Example: In a Restaurant(Two Scenarios)

Scenario 1:

Waiter takes order from customer 1; servescustomer 1; takes order from customer 2;

serves customer 2.

Scenario 2:

Waiter takes order from customer 1; takes

order from customer 2; serves customer 2;serves customer 1.

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Example: In a Restaurant (Scenario 1)Waiter

freeCustomer 1 Customer 2

Take

order

Take

order

Order

taken

Tell

kitchen

wait wait

Serve food Serve food

eating eating

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Example: In a Restaurant (Scenario 2)Waiter

freeCustomer 1 Customer 2

Take

order

Take

order

Order

taken

Tell

kitchen

wait wait

Serve food Serve food

eating eating

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12

Example: Vending Machine (A Petri net)

5c

Take 15c bar

Deposit 5c

0c

Deposit 10c

Deposit

5c

10c

Deposit 10c

Deposit

5c

Deposit 10c20c

Deposit

5c

15c

Take 20c bar

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13

Example: Vending Machine (3 Scenarios)

Scenario 1: Deposit 5c, deposit 5c, deposit 5c, deposit 5c,

take 20c snack bar.

Scenario 2: Deposit 10c, deposit 5c, take 15c snack bar.

Scenario 3: Deposit 5c, deposit 10c, deposit 5c, take 20c

snack bar.

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Example: Vending Machine (Token Games)

5c

Take 15c bar

Deposit 5c

0c

Deposit 10c

Deposit

5c

10c

Deposit 10c

Deposit

5c

Deposit 10c20c

Deposit

5c

15c

Take 20c bar

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A B

concurrency

A B

synchronisation

A B

communication

A B

conflict/choice

A B

multiplicity/resources

A B

individuality/data

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1.Marked Graph:

A marked graph is a Petri-net in whicheach place have one i/p and one o/ptransitions. |.p|=|p.|=1 :for all p P

t2

t3

t1 t4

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p1

p1 p7

P6p2 p4

p5p3

t2

t3

t4

t1

Marked Graph

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p1

p1 p7

P6p2 p4

p5p3

t2

t3

t4

t1

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2.State machines:

A State machine is a Petri-net

in which each transition

Has exactly one input

and one output place.

|.t|=|t.|=1:for all t T

510

vend 15 candy

10

5

5

10

5

vend 20 candy

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p1

p1

p7P6

p2

p4

p5

p3t2 t3t1

p1

t6t7 t8

t4

t5

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3.Free-Choice Nets:

This model provide a mechanism for conflict

resolution. The below net is example for free-choicenet. This class of nets allowed controlled conflict.

p1

p2

p3

t2

t1

Conflict or decision making structure

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Free choice net:

A free-choice net is an ordinary Petri-net such that an arc a place is the only

out going arc or it is the only input to atransition.

tj P and pi.tj

.tj={pi} or pi={tj}

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p3p2

p1

t1

t2

p4p5

t3t4

The diagram is not a Free-choice NetIn this example presence in token p1,p2 involved in

the choice of t1,t2.

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4.Extended free-choice

If two places have some common outputtransition, then they have all their outputtransitions in common

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5.Asymmetric or Simple Nets

A net is called simple if no two transitions

t1 and t2have the same sets of input and output

places. Example (not a simple net)

Def: Simple nets with no isolated elements meeting some additional restrictions

are called condition/event nets (C/E nets).

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Classes of Petri Nets

PN

PN

AC EFC FC SM MG