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:18 Modeling and Evaluation of Computer Systems (MECS)
@ : (Mohammad Abdollahi Azgomi) [email protected] @ @ @ > > > @ @ @ @ @ @ @ @ @ @ (timed Petri nets) (stochastic Petri nets) (generalized SPNs) (stochastic activity networks) (highlevel Petri nets) @ MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 2 < @ ( <> . > @ @ ) >@ > . > > @ > @ > > @ > > . @ . @ (model construction) < . @ @ @ <> > @ MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 3 @ @ @
> @ : @ > > @ < @ @ . > @ @ @ :(modeling power) @ > @ @ @ @ > (inhibitor arc) > @ @ < . > (Turing machine) > @ @ > <(times Petri nets) . > @ @ : > @ @ > @ (stochastic Petri nets) > . > @ @ :@ @ > > @ (coloured Petri nets) @ .> @ @ @ @ @ MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 4 .> @ @
<@ @ < < < > > < > . @ :
@ @ @ @ @ @ @ @ @ @ > > > > > > . @ >
5 MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE @
: < @
@ @ @
@
> > <(multiple arc) (arc multiplicity) <(inhibitor arc) <(priority level) .(guard) (enabling function) @ @ > . . > > (infinitely reproducible property) @ @ MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 6 @ @> < @ > <(arc cardinality) <> 16 <@ @ > @ . :
t2 > p n <t2 > > m > . @ @ . . >> <@ @ > > @ > > > m t1 > n > .> > p t2 p n > t1 p MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 7 >
@ @ > pi > > <> > > . > tk @ pj > . > (inhibitor arcs) > > . > < @ > @ > pi tk .> > > > @ 16 @ > > .> @ @ . > pj @ > @ <@ @ > > .> > > @ @ < @
8 MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE >
@ = @ @ > MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 9 >
t5
< p6 t2 p2 @ > > <t5 :
t4 > t2
t1 > <> p2 . @
> >> MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 10 >
> > < :
n m t1 >> . n . > >> p1 p1 p1 > > > p p1 > m > p t2 > <> > t1 < < >. > > . > . > @ > @> > < >< > > > t2 > @ @ @ > .> > > > 16
11 MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE >
:
2 t1 p1 p3 p2 > p3 > > p1 > > . > p2 > (3 t1 ) <> > > > > p2 @> :> > t1 > p1 t1 p2 2 p3 MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 12 > <> < @ @ @ > > @> (priority level) . @ > . > < >< @ > > (prioritized Petri net) > @ > @ > .> > > >
(2 @ < ) > 2 @ < @ > <
> > > > .(3 > ) .
@ > > 3 .> .> > > > <2 @ > > @ @ >> @ : @ > @ @ @ > @ <[1] > . [1] http://www.informatik.unihamburg.de/TGI/PetriNets/tools/complete_db.html MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 13 > @
. . . > @
> @ : @ :1
:P :T <@> . @ >> @ .> PN = (P, T, I, O, H, , PAR, PRED, MP) :I, O, H
:: T N (N) @ :PAR > > > > . > > @ @ (priority function) > .> @ > (predicate) . @ :PRED > :MP : T N PAR MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 14 >
< @
>> > @ . > . : > . > k >> > > . @ p1 K1 < > >< PAR={K}
15 PRED = {K 1} : MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE @
(guard) @ <> (enabling function) @ <(Boolean expression) > <> ( < < )@ .> @ > > :
p1 tk p2 @ . > @ @ @ (tk) = #p3<2 & #p4=0 : > > > tk >
16 (#p1>0 & #p2=0) & (#p3<2 & #p4=0) = True
MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE @
@ > . > (timeless) @ @ @
@ @ @ @ . : >
> . > . @ > @
@ @ > < > @
@ < @ > > > > (temporal concepts)
(synchronization) @ . @ @ @ (parallelism) @ < @ (global) @ > (casual dependencies) > >
17 <(independency) < . (concurrency) @ MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE @
@ > > > > > @
@> @ > > @ < @> <> > > . @ . @ >@ @ > MIT > (C. Ramchandani) >> @ > @ . . 1974 @ <
> >
18 (general approach) (delay) >
( . >
) (stochastic) . ) (deterministic) ( MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE @ @
: @ @ @
@ @
< < < .( ) @ . @ @ > > MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 19 <> > >> > (timestamp) @ : < .> . @ > theta1 > >> @ delta theta i t1 @ > > p1 .> . >> theta2 p1 > . > > t1 p2 > . @ > > > (coloured Petri nets) @ @ . @ > > @
20 MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE .> > (t) (traveling delay) > <@> . : > > > < > >< @ max(t1, t2) > > .> > p2 p1 @> p3 @ > > t3 > max(t1, t2)+t3 : > > > .
21 MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE (t) (delay attribute) > .> @ :
> @ > @ (p) > > >> > .> @ t @ t1 p t2 @ @ p > p > >> >> t > t > <p > > @ > t2 . > >< > < < > .
MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 22 < : @ (activity)
. . > .> < > : > MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 23 :
(Ramchandani's approach) (Merlin's approach) @ > MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 24 .[1] (t) (firing duration) > :>
. > .> 1974 .> >
(t) > > > @ >
> > > [1] Ramchandani, C.: Analysis of Asynchronous Concurrent Systems by Timed Petri Nets, Ph.D. Thesis , MIT, Department of Electrical Engineering (1974) MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 25 @
. > @ > > > @
> @ . @ > > > > (W. M. Zuberek) >> > @ >> .[1] (Memorial) . . > @ @ > > > > [1] Zuberek, W.M.: Timed Petri Nets and Preliminary Performance Evaluation, Proc. 7th Annual Symposium on Computer Architecture, La Baule, France, pp. 8996 (1980) MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 26 1974 @
.> > @ >. > (P. M. Merlin) @ .[1] b a> > > 0ab :
> :a > (deadline) :b >
> .> <b :
0 a >>
b > [1] P. M. Merlin and D. J. Farber, "Recoverability of Communication Protocols: Implications of a Theoretical Study," IEEE Transactions on Communications, 24(9), pp.10361043 (1976)
MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 27 (workflow modeling) > (W. van der Aalst) . > > @ @ . @ >> (K. van Hee) > < (workflow nets) > @ > (yet another workflow language) YAWL . MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 28 @
> > @ . > <( .> > @ <> @ @ @ @
@ > @ >@ @ [1] > @ @ @ ) > > @ @ . > @ @ > [1] Ajmone Marsan, M., Balbo, G., Conte, G., Donatelli, S. and Franceschinis, G.: Modelling with Generalized Stochastic Petri Nets, John Wiley & Sons (1995) MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 29 @
@ @ (timed transition) >> @ > @ < @
@ @ .> @ < @ > > > > : > p1 < T <> .> p1 > > > < <> .> @ > (timer) > .> p2
30 MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE @
: @ > <T4 T3 <T2 <T1 . @ p3 p2 <p1 @ 4 3 <2 <1 > @ > @ > @
31 M1 = (1, 0, 0) : MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE @
. :> T2 T1
< .> @
@ <
T1 T2 @ <
< 1< 2 > :
. . p2 > .> > p1 M2 = (0, 1, 0) .> > > 1< 2
@ > T1 @ <> T2 < > > > (disable) MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 32 @
.> < <3 > M1 > . @ > T2 @
T3 >
> > 1 2 1 . T1 T2 > <M2 @ >> >. > < > @ > > T1 @ >
> :
.> > <> T1 <> > .> T2 > > MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 33 @
@ > < > @ > @ @ > . @
@ > @> @ . < @ @ @ @ @ @ > >
. @ @ < . @ <
> > @ (SPN: stochastic Petri nets) MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 34 >
@ > @ @ < < > @
@ @ @
. @
(SPN: stochastic Petri nets) > > @ < > @ >> . > @ @ . @ > > @ @
CTMC > > @ > 1981 (state process) (isomorphic) .[1]
@ @ . > (M. K. Molloy) @ @ (marking process) @ CTMC < @
. > [1] Molloy, M.K.: "Performance Analysis Using Stochastic Petri Nets", IEEE Trans. Computers 31(9), pp. 913917 (1982) MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 35 CTMC
:
. > SPNs
SPNs @
: >
@ > > @
. @ @ > . :
> @ > > > . . SPNs CTMC > > < > > > . CTMC > @ @ (CTMC generation methods) CTMC @ < > @ @ < > .> .> CTMC > >
36 MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE CTMC
@ @ > SPNs . @ .> SPN SPNs
@ < @ SPNs @ ... > > > < > @ CTMC CTMC > MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 37 CTMC
> SPN
/ @ t1 p2 p1 .
p1 @ t1 p2 . t2 > t1 10 t2
MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE t2 CTMC 01 10 01 38 CTMC SPN > MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 39 CTMC SPN MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 40 SPN @
: > :SPN t p RG = CTMC 0 1 2 ....... ....... MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 41 SPN M/M/1 t1 p @ :M/M/1 t2 :SPN RG = CTMC 0 1 2 ....... n ....... 42 MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE (1 ) SPN M/M/1/n @
:M/M/1/n n t1 n
p t2 :SPN RG = CTMC 0 1 2 ....... n 43 MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE (2 ) SPN M/M/1/n @
:M/M/1/n n p1 t1 n
p2 t2 :SPN RG = CTMC 0 1 2 ....... n 44 MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE >
.> . p
(firing rate) >
SPN > t2 n > >
2
(t2)= #p > (marking dependent) @ > < > : @ @ >
1 t1 :p @
>) <> <> p >
t2 > @ 1 21 > n > < t2 t2
t2 > < t2 > < n1 >
p >
>@ p@ >p@ t2 > > > >
45 <( @ . p @ MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE SPN
SPN RG @ :1
CTMC (t1)= #P1 MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 46 SPN M/M/n/n+m n m t1 @
1 2 :2 :M/M/n/n+m n
p (t2)= #p :SPN t2
> > MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 47 k@ >
(repairable components) @
: @ :3
SPN k@ > :
> k p1 < > t2 > @ > > . > > . @ t1 > p2 p1 > > > > >< > ... > t2 t1 @
48 MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE k@ >
:> > > <
(t1) = #P1 (t2) = @ :3
> :> > CTMC > > MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 49 k@ >
:> >
(t1) = #P1 (t2) = #P2 2 if #P2 < 2 otherwise @
> > :3 > < :> > CTMC > > MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 50 >
<
< @
@ @ @
@
> > < @ : @
@ < > @ >> @
<> @ @
>@ > > >
@ .> <> <@ @ @ > @ . < > > ifelse . @ @ >> >@ < < (instantaneous) > > MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 51 >
@ @ > .> @ @
.> > @
@ @ @ > > @ > @ > > @ @ > > > > 19811980 @ > <> > @ > @ < @ > @ (M. Ajmone Marsan) @ >< CTMC .> > .> < @ > > @ MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 52 >
< > > @ @ .[1] > @ > @ > @
1984 @
> > >
GSPNs > (GSPN: generalized stochastic Petri net) > @ > > .> @ > @
GSPNs > > > . @ [1] Ajmone Marsan, M., Balbo, G., and Conte, G.: "A Class of Generalized Stochastic Petri Nets for the Performance Analysis of Multiprocessor Systems," ACM Transactions on Computer Systems 2(1) (1984) MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 53 > @ @
> GSPNs @
@
> > @ SPNs @ @ < @ > :> > >
. .> : < @ >> > > > :(timed transition) :(immediate transition) @
p : > . >> . (firing probability) > .> @ <@ > > > > @ @ < @ @ @
> @ > MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 54 >
:
@ >@ < @ @ @
>
@ :> > @ @ @
> T p1 t > > p t1 1p p1 t2 p2 p1 < : @ @ @ T t @ p t1 1p p1 t2 p2 p3 p3 > > p2 p2 p3 p3
55 MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE GSPNs :
R @ @
> @
@ @
. < (T) (1) :2 PN = (P, T, I, H, O, , W, PAR, PRED, MP)
P, T, I, H, O, , PAR, PRED, MP :W : T R . > > ( >> @ wk . > GSPN GSPN @ ) W(t, M) > > < :( > @ . <tT W < @ < < > > W .> .tkT
tk (rate) > < (weight) < W > > W(tk) > wk ) W(t, M)
tk @ tk
56 . . M@ M@ > > tk MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE GSPNs @
@ . < > .
< . . >> >> @
> @ @
GSPN @ > < >
< <> > @ > > > (vanishing markings) . > > @ > (tangible marking) <
> @ @ > < @ > @ (temporal behavior)
. > > CTMC < > > > > SPNs > > @ MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 57 @ @ @ > > < > (sojourn time)
: @ @ :>
@ @ < > @ @ @ > > @ (1) [1] (negative exponential) > > @ > (2) > > (pdf) < pdf @
pdf @ > .
. @ > > > @ .> > @ @ pdf > >
exp() < > @ >
>0 pdf @ >
exp() [1] 58 MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE @ > @ > > >@ @ > > > ) @ > > @ @ > < @ @ .> > > @ ( > . ) @ < @ >@ @ @ @ <( > MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 59 GSPNs @
GSPNs @ @ @ > .> @ > > @
> < > @ >
@ @ . > @ > > < @ > < (ERG: extended reachability graph) > ERG =
>> @ (ERG) . CTMC
60 CTMC
. @ (RG) @ .> > > =
<> .> > > CTMC
@ @ > MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE @
@
. . . @> @ @ @ :1 :2 :3 @ : @ > ...> > > @ MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 61 @ :1 GSPN .> > RG = CTMC @ >
62 MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE @> @ :2 GSPN . > >> ERG @ CTMC >
63 MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE @ :3 GSPN . > >> ERG @ CTMC >
64 MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE GSPNs @
GSPNs @ <CTMC > @ RG .> < > <SPNs ERG CTMC @ . CTMC @ MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 65 GSPNs @
> @ <>
> > < GSPN > @ > :CTMC
>> ) @ .> ( > > .> < @ < CTMC MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 66 GSPNs @
> > @ :>
<@ <@ < .( ) @ > > .> > @ @ @
>> > > < > @ @ > > >> SHARPE GreatSPN > > @> . @ @ GSPNs SPNs MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 67 >
@ @ @ > < @ > @
> (J. F. Meyer) .[1, 2] > @ >
SANs (SANs: stochastic activity networks) > 1984 @ > GSPNs @ SANs @ > > > @ 2001 . @ @> @ > @ . .[3] > @ > [1] Movaghar, A. and Meyer, J.F.: "Performability Modeling with Stochastic Activity Networks," Proc. of the 1984 RealTime Systems Symp., Austin, TX, USA (1984) 215224 [2] Movaghar, A., Performability Modeling with Stochastic Activity Networks, Ph.D. Dissertation, The University of Michigan (1985) [3] Movaghar, A.: "Stochastic Activity Networks: A New Definition and Some Properties," Scientia Iranica 8(4) (2001) 303311 MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 68 >
@ > <(W. H. Sanders) @
UltraSAN @
@ . > . > >> @ @ @
SANs < >> @ @ > SANs > > >
[1] Mbius @ @ < @ @ . > > [1] http://www.crhc.uiuc.edu MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 69 >
. :
GSPNs . @
@ @ @
(parallelism) @ ) > @ >
@ :(place) :(timed activity) (activity time ( ) (enabling rate) @ (reactivation predicate) > GSPNs . <distribution function) ( @ .> @ :(instantaneous activity)
(nondeterminism) @ @ > : <(case probability function) > . MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 70 >
1 2
. . @
@> @>
@> @ :(input gate) @> :
@> > >> > @ @> > n @ .> >
1 2
. . @>
> >> :(output gate) :
@ > @ > n MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 71 >
@ @ > @
> (nondeterminacy)
@ @ : (parallelism) >
(nondeterministic) (probabilistic) (activity networks) @ @ (probabilistic activity networks) > @ (stochastic) > (SANs: stochastic activity networks) < < . > @> > > > > > > > >
72 (probabilistic verification) MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE >
@ @
> > @ @ > @> > @
73 MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE >
:>
Gate ig1 Predicate
(MARK(Fast) != 0)  (MARK(Slow) != 0) >
Gate Table SAN
Function @ if (MARK(Fast) != 0) { MARK(Fast) = 0; MARK(WhichSel) = 0; } else { MARK(Slow) = 0; MARK(WhichSel) = 1; } if (MARK(WhichSel) == 0) MARK(FastAlloc) = 1; else MARK(SlowAlloc) = 1; if (MARK(Jobs) < 10) MARK(Jobs) = MARK(Jobs)+1; og1 og2 C/C++
MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE > 74 @
:>
<> <> < < . @ @ @> @ > > > @> @
@> @
@> @> > @> > @ @ @ > > > > @> .> > >> @ > @> > e(x):x1 > () > .> @ > @ @ f(x) = x  1 > >> .>
75 f(x) = x + 1 @ > > MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE @
. @ > > @ @ @ . . .> > > @
@ ) . ( @ @ @ > @ > > . @ @ (unstable marking) > < > MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 76 @
> > @ :
< . @
> . > >
@> @ @ > @> > > @ @ @ > >
@ @ . > @ > @ . < @ > MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 77 >
@ @ :(activate) >
> .> > @ @
:
> @
> @ >
>@ @ @ @ > @ @ > @ (reactivation predicate) > > < (potential completion time) . (aborted) <> . <> MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 78 >
SANs < @ GSPNs @> @ >@ @
>@ . > @
@ @ @ > > > > > @ SANs @ > @ GSPNs > > . @ . >> @ >< @
79 @ .> (GSPNs @ @ @ > > >) SANs @ @ SANs @ @ .> @> @ SANs @ > > > @ @ > . > > @ > MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE @
< > @
@ @ <(highlevel Petri nets) : @ @ < < : @ @ @ . @
> HLPNs = PNs + Colour + Hierarchy >> > @ @
> @ > @ > @ . @
> @ > < : > . . . @ (computational power) (modeling power) @ <@ > > > <@ @ > > MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 80 @
. . @
@ @
1978
Genrich & Lautenbach (Pr/Tnets: predicate/transition nets) (CPNs: coloured Petri nets)
K. Jensen @ @ @ 1980 :(WNs: wellformed nets)
WNs = simple CPNs (SWNs: Stochastic WNs)
SWNs = WNs+GSPNs > :HLPN >
. ISO/IEC 2003 MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 81 @
> > @
1980 . > @ @ (K. Jensen) >> . @ @ > CPN Tools . > > @ @ > (Aarhus) > Design/CPN @ .
http://www.daimi.au.dk/CPnets/ CPNs @ MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 82 @
@ @ . > @ @
@ @ @ @ > @ @ CPNs > .> > @ > > (classes) < @ (
83 @ > (chains) > . . > > @ ( char <integer . ) (multiset) )(atomic) @ >> @ >> . MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE @
> > @ @ @ > @> > (guards) .> ( @ @ .> @
> >@ . @ ML @ > >> > > > (arc expressions) > > @ > @ . )> @ MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 84 @
@ . @
(objectoriented Petri nets) OOPNs = CPNs+OO @
@ @ @ > (structuring capabilities) . > > @ (composition) @ @ @ > : (C. Lakos) . @ @ < > >> .> > > MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 85 @
@ @ (data fields) @ > > @
OPNs > . (attributes) @ @ . CPNs :> > >
.> . . > @ >> > @ OPNs > (class) > >
> > OPNs @> (inheritance) > (instantiation) @ <( <Boolean <Real <Integer . ) > @ >> >
86 MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE @
OPNs > (encapsulation) @ @ . CPNs @ .> @ @ > > @
> .> @ CPNs @ > > .> > OPNs @ OPNs @ > > OPNs @ @ .
87 (readonly) > . CPNs OPNs @ > @ UML (compositionality) (hierarchical) (incremental) MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE @
> @
@ : @ @
@ @
> > > > @ @ >> >
> @ @ @ @ @ > (SRNs: stochastic reward nets) (MRSPNs: Markov regenerative SPNs) (FSPNs: fluid stochastic Petri nets) (highlevel SANs) MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 88 (SRNs) > @ @ @ > < @ > SPNs >
> > @
.> > GSPNs @ (rate rewards) > > .> @ > @ > . @ @ > MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 89 (MRSPNs) . . @ @ @ > > . >
@ SPNs @ @
@ > (iid: independent identical distribution) @ > MRSPNs MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 90 (FSPNs) < . .>
(state space explosion) >
> @ >< . > @ @
> @ > @ @ > @ > > GSPNs @ @ > @ . MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 91 >
>
SANs @
@ >> @ > <
> > > . :[1]
@ @ @ @ @ (HSANs: hierarchical SANs)
HSANs = Hierarchy + SANs (CSANs: coloured SANs)
CSANs = Hierarchy + Colour + SANs (OSANs: object SANs)
OSANs = Hierarchy + Colour + OO + SANs [1] Abdollahi Azgomi, M., HighLevel Extensions for Stochastic Activity Networks: Theories, Tools and Applications, Ph.D. Dissertation, Department of Computer Engineering, Sharif University of Technology (2005) MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 92 @ @
Pr/TNs CPNs @
HCPNs MCPNs OBPNs OOPNs > PNs WNs SWNs GSPNs TPNs SPNs SANs SANs*
Hierarchy Colour ObjectOrientation ... Hybrid PNs Fuzzy PNs FSPNs HSANs
Queueing Disciplines CSANs OSANs Queueing Models * A new definition of SANs : : MECS#18  Analysis of Petri Nets  By: M. Abdollahi Azgomi  IUSTCE 93 ...
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This note was uploaded on 04/08/2010 for the course COMPUTER E 409232 taught by Professor Mohammadabdolahiazgomiph.d during the Spring '10 term at Islamic University.
 Spring '10
 MohammadAbdolahiAzgomiPh.D

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