© SERG
Software Design (Behavioral)
Petri Nets
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Petri Nets-Object Oriented Design and Analysis-Lecture Slides, Slides of Object Oriented Analysis and Design
Dr. Abhidhya Yudhajit delivered this lecture at Islamic University of Science and Technology for Analysis And Design Using Object Orientation course. It includes: Petri, Nets, Software, Design, Marked, Firing, Behavioral, Transitions, Arrangement, State
Typology: Slides
2011/2012
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© SERG
Software Design (Behavioral)
Petri Nets
© SERG
Software Design (Behavioral)
A Simple Petri Net
P
P
t
t
t
P
P
© SERG
Software Design (Behavioral)
A Marked Petri Net
After Firing t
P
P
t
t
t
P
P
© SERG
Software Design (Behavioral)
Definition of a Petri Net
PNet = (P, T, A, M0)
P
is a finite set of
places
(labeled circles),
where a place holds tokens.
T
is a finite set of
transitions
(bars), where a
transition represents an activity.
A
is a finite set of directed
arcs
, where an arc
connects a place and a transition.
M
is the initial
marking
of
PNet
, where a
marking is an arrangement of tokens in placesrepresenting state.
© SERG
Software Design (Behavioral)
Petri Net
Execution Model (Cont’d)
•^
Firing a Transition:
An enabled transition
is non deterministically selected and
fired
by removing one token from each of itsinput places and depositing one token ateach of its output places.
-^
Firing Sequence:
A firing sequence
<t0,t1, …, tn>
such that
t
is enabled and
fired in
M
,^
t
is enabled and fired in
M
© SERG
Software Design (Behavioral)
Petri Net Firing
© SERG
Software Design (Behavioral)
A Marked Petri Net Semaphore
IN
IN
CR
CR
SEM
OUT
OUT
IN = Input of ProcessOUT = Output of ProcessCR = Critical Region
SEM = Semaphore
© SERG
Software Design (Behavioral)
Enabled Transitions IN
IN
CR
CR
SEM
OUT
OUT
© SERG
Software Design (Behavioral)
Enabled Transition
IN
IN
CR
CR
SEM
OUT
OUT
© SERG
Software Design (Behavioral)
After Firing
IN
IN
CR
CR
SEM
OUT
OUT
© SERG
Software Design (Behavioral)
Deadlock and Starvation
- A Petri Net with a given marking is in
deadlock
iff no transition is enabled in that
marking.
- A Petri Net with a given marking is in
starvation
iff one or more transitions have
been permanently disabled.
- A Petri Net is
live
if every transition can
eventually be fired.
© SERG
Software Design (Behavioral)
A Deadlocked Petri Net
© SERG
Software Design (Behavioral)
A Deadlocked Petri Net
© SERG
Software Design (Behavioral)