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Petri Nets

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Definition of Petri Net

C = ( P, T, I, O) Places

P = { p1, p2, p3, , pn}

TransitionsT = { t1, t2, t3, , tn}

InputI : T Pr(r = number of places)

Output

O : T

Pq

(q = number of places)

marking : assignment of tokens to the places ofPetri net = 1, 2, 3, n

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Applications of Petri Net

Petri net is primarily used for studying the dynamicconcurrent behavior of network-based systemswhere there is a discrete flow.

Petri Nets are applied in practice by industry,academia, and other places. -reference

http://www.informatik.uni-hamburg.de/TGI/PetriNets/applications/http://www.informatik.uni-hamburg.de/TGI/PetriNets/applications/

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Basics of Petri Nets

Petri net consist two types of nodes:

places and transitions. And arc exists onlyfrom a place to a transition or from atransition 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.

p2p1 t1

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Basics of Petri Nets -continued

Below is an example Petri net with two

places and one transaction. Transition node is ready to fire if and only

if there is at least one token at each of itsinput places

state transition of form (1, 0) (0, 1)

p1 : input place p2: output place

p2p1 t1

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Properties of Petri Nets

Sequential ExecutionTransition t2 can fire onlyafter the firing of t1. Thisimpose the precedence

of constraints "t2 after t1."

SynchronizationTransition t1 will beenabled only when atoken there are at leastone token at each of its

input places. Merging

Happens when tokensfrom several places arrive

for service at the sametransition.

p2t1p1 p3t2

t1

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Properties of Petri Nets

Conflictt1 and t2 are both ready tofire but the firing of anyleads to the disabling of the

other transitions.

t1

t2

-continued

t1

t2

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Properties of Petri Nets

Conflict - continued

the resulting conflict may be resolved in apurely non-deterministic way or in a

probabilistic way, by assigning appropriateprobabilities to the conflicting transitions.

there is a choice of either t1 and t2, or t3 and t4

-continued

t1 t2

t3 t4

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t1, t4 are forking transitions, t3 is a joining (synchronizing transition)

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Example: In a Restaurant

(Two Scenarios)

Scenario 1:

Waiter takes order from customer 1; serves

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

Scenario 2:

Waiter takes order from customer 1; takesorder from customer 2; serves customer 2;serves customer 1.

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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 (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