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Petri NetsDefinition of Petri NetApplications of Petri NetSlide 4Slide 5Slide 6Slide 7Slide 8Slide 9Example: In a Restaurant (A Petri Net)Example: In a Restaurant (Two Scenarios)Example: In a Restaurant (Scenario 1)Example: In a Restaurant (Scenario 2)Example: Vending Machine (A Petri net)Example: Vending Machine (3 Scenarios)Example: Vending Machine (Token Games)Petri Net with TimeReferences1Petri Nets2Definition of Petri NetC = ( P, T, I, O)PlacesP = { p1, p2, p3, …, pn}TransitionsT = { t1, t2, t3, …, tn}Input I : T  Pr (r = number of places)OutputO : T  Pq (q = number of places)marking µ : assignment of tokens to the places of Petri net µ = µ1, µ2, µ3, … µn3Applications of Petri NetPetri net is primarily used for studying the dynamic concurrent behavior of network-based systems where there is a discrete flow.Petri Nets are applied in practice by industry, academia, and other places. -reference4Basics of Petri NetsPetri net consist two types of nodes: places and transitions. And arc exists only from a place to a transition or from a transition to a place. A place may have zero or more tokens. Graphically, places, transitions, arcs, and tokens are represented respectively by: circles, bars, arrows, and dots. p2 p1 t15Basics of Petri Nets -continuedBelow is an example Petri net with two places and one transaction. Transition node is ready to fi re 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 p2 p1 t16Properties of Petri NetsSequential ExecutionTransition t2 can fire only after the firing of t1. This impose the precedence of constraints "t2 after t1." SynchronizationTransition t1 will be enabled only when a token there are at least one token at each of its input places.MergingHappens when tokens from several places arrive for service at the same transition. p2 t1 p1 p3 t2 t17Properties of Petri NetsConcurrency t1 and t2 are concurrent. - with this property, Petri net is able to model systems of distributed control with multiple processes executing concurrently in time. t1 t2-continued8Properties of Petri NetsConflictt1 and t2 are both ready to fire but the firing of any leads to the disabling of the other transitions. t1 t2-continued t1 t29Properties of Petri NetsConflict - continued the resulting conflict may be resolved in a purely non-deterministic way or in a probabilistic way, by assigning appropriate probabilities to the conflicting transitions.there is a choice of either t1 and t2, or t3 and t4-continuedt1t2t3t410Example: In a Restaurant (A Petri Net)WaiterfreeCustomer 1Customer 2TakeorderTakeorderOrdertakenTellkitchenwaitwaitServe foodServe foodeating eating11Example: 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; takes order from customer 2; serves customer 2; serves customer 1.12Example: In a Restaurant (Scenario 1)WaiterfreeCustomer 1Customer 2TakeorderTakeorderOrdertakenTellkitchenwaitwaitServe foodServe foodeating eating13Example: In a Restaurant (Scenario 2)WaiterfreeCustomer 1Customer 2TakeorderTakeorderOrdertakenTellkitchenwaitwaitServe foodServe foodeating eating14Example: Vending Machine (A Petri net)5cTake 15c barDeposit 5c0cDeposit 10cDeposit 5c10cDeposit 10cDeposit5cDeposit 10c20cDeposit5c15cTake 20c bar15Example: 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.16Example: Vending Machine (Token Games)5cTake 15c barDeposit 5c0cDeposit 10cDeposit 5c10cDeposit 10cDeposit5cDeposit 10c20cDeposit5c15cTake 20c bar17Petri Net with Time1962 - Carl Adam Petri originally proposed Petri without any notion of time. Concept of time was intentionally avoided because addition of time restricts the behavior of the net. 1970s ~ - Addition of time has been discussed in order to analyze the performance of the modeled system. Many properties are still undecided for Petri nets extended with data and time.18ReferencesFishwick, Paul(1995) – Simulation Model Design and ExecutionPetri Nets World Ling,Chris(2001) – Lecture on Petri Nets MethodChapman, Nick(1997) – Surprise97 journal on Petri Nets


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