Download - Principles of Engineering System Design
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Principles of
Engineering System Design
Dr T Asokan
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Principles of
Engineering System Design
Dr T Asokan
GRAPHICAL MODELLING TECHNIQUES
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Asokan T ED 309
Behavioural Properties
• Reachability • “Can we reach one particular state from
another?”• Boundedness
• “Will a storage place overflow?”• Liveness
• “Will the system die in a particular state?”
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Asokan T ED 309
Multiple Local States
• In the real world, events happen at the same time.
• A system may have many local states to form a global state.
• There is a need to model concurrency and synchronization.
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Asokan T ED 309
Example: In a Restaurant (A Petri Net)
WaiterfreeCustomer 1 Customer 2
Takeorder
Takeorder
Ordertaken
Tellkitchen
wait wait
Serve food Serve food
eating eating
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Asokan T ED 309
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; takes order
from customer 2; serves customer 2; serves customer 1.
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Asokan T ED 309
Example: In a Restaurant (Scenario 1)
WaiterfreeCustomer 1 Customer 2
Takeorder
Takeorder
Ordertaken
Tellkitchen
wait wait
Serve food Serve food
eating eating
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Asokan T ED 309
Example: In a Restaurant (Scenario 2)
WaiterfreeCustomer 1 Customer 2
Takeorder
Takeorder
Ordertaken
Tellkitchen
wait wait
Serve food Serve food
eating eating
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Asokan T ED 309
Net Structures
• A sequence of events/actions:
• Concurrent executions:e1 e2 e3
e1
e2 e3
e4 e5
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Asokan T ED 309
Net Structures
• Non-deterministic events - conflict, choice or decision: A choice of either e1, e2 … or e3, e4 ...
e1 e2
e3 e4
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Asokan T ED 309
Net Structures
• Synchronization
e1
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Asokan T ED 309
Net Structures
• Synchronization and Concurrency
e1
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Asokan T ED 309
Another Example
• A producer-consumer system, consist of one producer, two consumers and one storage buffer with the following conditions:• The storage buffer may contain at most 5 items;• The producer sends 3 items in each production;• At most one consumer is able to access the storage
buffer at one time;• Each consumer removes two items when accessing the
storage buffer
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Asokan T ED 309
A Producer-Consumer System
readyp1
t1produce
idle
send
p2
t2
k=1
k=1
k=5
Storage p3
3 2 t3 t4
p4
p5
k=2
k=2
accept
accepted
consume
ready
Producer Consumers
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Asokan T ED 309
A Producer-Consumer Example
• In this Petri net, every place has a capacity and every arc has a weight.
• This allows multiple tokens to reside in a place to model more complex behaviour.
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Asokan T ED 309
Other Types of Petri Nets
• High-level Petri nets• Tokens have “colours”, holding complex
information.• Timed Petri nets
• Time delays associated with transitions and/or places.
• Fixed delays or interval delays.• Stochastic Petri nets: exponentially distributed
random variables as delays.
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Petri Net Referencesi Murata, T. (1989, April). Petri nets: properties, analysis and
applications. Proceedings of the IEEE, 77(4), 541-80.i Peterson, J.L. (1981). Petri Net Theory and the Modeling of
Systems. Prentice-Hall.i Reisig, W and G. Rozenberg (eds) (1998). Lectures on Petri
Nets 1: Basic Models. Springer-Verlag.i The World of Petri nets:
http://www.daimi.au.dk/PetriNets/