MECS 18. Extensions of Petri Nets

MECS 18. Extensions of Petri Nets - > @ @ @ @ : > @...

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Unformatted text preview: > @ @ @ @ : > @ :18 Modeling and Evaluation of Computer Systems (MECS) @ : (Mohammad Abdollahi Azgomi) [email protected] @ @ @ > > > @ @ @ @ @ @ @ @ @ @ (timed Petri nets) (stochastic Petri nets) (generalized SPNs) (stochastic activity networks) (high-level Petri nets) @ MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 2 < @ ( <> . > @ @ ) >@ > . > > @ > @ > > @ > > . @ . @ (model construction) < . @ @ @ <> > @ MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 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 - IUST-CE 4 .> @ @ <@ @ < < < > > < > . @ : @ @ @ @ @ @ @ @ @ @ > > > > > > . @ > 5 MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE @ : < @ @ @ @ @ > > <(multiple arc) (arc multiplicity) <(inhibitor arc) <(priority level) .(guard) (enabling function) @ @ > . . > > (infinitely reproducible property) @ @ MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 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 - IUST-CE 7 > @ @ > pi > > <> > > . > tk @ pj > . > (inhibitor arcs) > > . > < @ > @ > pi tk .> > > > @ 16 @ > > .> @ @ . > pj @ > @ <@ @ > > .> > > @ @ < @ 8 MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE > @ = @ @ > MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 9 > t5 < p6 t2 p2 @ > > <t5 : t4 > t2 t1 > <> p2 . @ > >> MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 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 - IUST-CE > : 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 - IUST-CE 12 > <> < @ @ @ > > @> (priority level) . @ > . > < >< @ > > (prioritized Petri net) > @ > @ > .> > > > (2 @ < ) > 2 @ < @ > < > > > > .(3 > ) . @ > > 3 .> .> > > > <2 @ > > @ @ >> @ : @ > @ @ @ > @ <[1] > . [1] http://www.informatik.uni-hamburg.de/TGI/PetriNets/tools/complete_db.html MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 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 - IUST-CE 14 > < @ >> > @ . > . : > . > k >> > > . @ p1 K1 < > >< PAR={K} 15 PRED = {K 1} : MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE @ (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 - IUST-CE @ @ > . > (timeless) @ @ @ @ @ @ @ . : > > . > . @ > @ @ @ > < > @ @ < @ > > > > (temporal concepts) (synchronization) @ . @ @ @ (parallelism) @ < @ (global) @ > (casual dependencies) > > 17 <(independency) < . (concurrency) @ MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE @ @ > > > > > @ @> @ > > @ < @> <> > > . @ . @ >@ @ > MIT > (C. Ramchandani) >> @ > @ . . 1974 @ < > > 18 (general approach) (delay) > ( . > ) (stochastic) . ) (deterministic) ( MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE @ @ : @ @ @ @ @ < < < .( ) @ . @ @ > > MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 19 <> > >> > (time-stamp) @ : < .> . @ > theta1 > >> @ delta theta i t1 @ > > p1 .> . >> theta2 p1 > . > > t1 p2 > . @ > > > (coloured Petri nets) @ @ . @ > > @ 20 MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE .> > (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 - IUST-CE (t) (delay attribute) > .> @ : > @ > @ (p) > > >> > .> @ t @ t1 p t2 @ @ p > p > >> >> t > t > <p > > @ > t2 . > >< > < < > . MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 22 < : @ (activity) . . > .> < > : > MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 23 : (Ramchandani's approach) (Merlin's approach) @ > MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 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 - IUST-CE 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. 89-96 (1980) MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 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 - IUST-CE 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 - IUST-CE 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 - IUST-CE 29 @ @ @ (timed transition) >> @ > @ < @ @ @ .> @ < @ > > > > : > p1 < T <> .> p1 > > > < <> .> @ > (timer) > .> p2 30 MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE @ : @ > <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 - IUST-CE @ . :> 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 - IUST-CE 32 @ .> < <3 > M1 > . @ > T2 @ T3 > > > 1 2- 1 . T1 T2 > <M2 @ >> >. > < > @ > > T1 @ > > : .> > <> T1 <> > .> T2 > > MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 33 @ @ > < > @ > @ @ > . @ @ > @> @ . < @ @ @ @ @ @ > > . @ @ < . @ < > > @ (SPN: stochastic Petri nets) MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 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. 913-917 (1982) MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 35 CTMC : . > SPNs SPNs @ : > @ > > @ . @ @ > . : > @ > > > . . SPNs CTMC > > < > > > . CTMC > @ @ (CTMC generation methods) CTMC @ < > @ @ < > .> .> CTMC > > 36 MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE CTMC @ @ > SPNs . @ .> SPN SPNs @ < @ SPNs @ ... > > > < > @ CTMC CTMC > MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 37 CTMC > SPN / @ t1 p2 p1 . p1 @ t1 p2 . t2 > t1 10 t2 MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE t2 CTMC 01 10 01 38 CTMC SPN > MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 39 CTMC SPN MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 40 SPN @ : > :SPN t p RG = CTMC 0 1 2 ....... ....... MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 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 - IUST-CE (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 - IUST-CE (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 - IUST-CE > .> . 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 - IUST-CE SPN SPN RG @ :1 CTMC (t1)= #P1 MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 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 - IUST-CE 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 - IUST-CE k@ > :> > > < (t1) = #P1 (t2) = @ :3 > :> > CTMC > > MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 49 k@ > :> > (t1) = #P1 (t2) = #P2 2 if #P2 < 2 otherwise @ > > :3 > < :> > CTMC > > MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 50 > < < @ @ @ @ @ > > < @ : @ @ < > @ >> @ <> @ @ >@ > > > @ .> <> <@ @ @ > @ . < > > if-else . @ @ >> >@ < < (instantaneous) > > MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 51 > @ @ > .> @ @ .> > @ @ @ @ > > @ > @ > > @ @ > > > > 1981-1980 @ > <> > @ > @ < @ > @ (M. Ajmone Marsan) @ >< CTMC .> > .> < @ > > @ MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 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 - IUST-CE 53 > @ @ > GSPNs @ @ > > @ SPNs @ @ < @ > :> > > . .> : < @ >> > > > :(timed transition) :(immediate transition) @ p : > . >> . (firing probability) > .> @ <@ > > > > @ @ < @ @ @ > @ > MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 54 > : @ >@ < @ @ @ > @ :> > @ @ @ > T p1 t > > p t1 1-p p1 t2 p2 p1 < : @ @ @ T t @ p t1 1-p p1 t2 p2 p3 p3 > > p2 p2 p3 p3 55 MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 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 - IUST-CE GSPNs @ @ . < > . < . . >> >> @ > @ @ GSPN @ > < > < <> > @ > > > (vanishing markings) . > > @ > (tangible marking) < > @ @ > < @ > @ (temporal behavior) . > > CTMC < > > > > SPNs > > @ MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 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 - IUST-CE @ > @ > > >@ @ > > > ) @ > > @ @ > < @ @ .> > > @ ( > . ) @ < @ >@ @ @ @ <( > MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 59 GSPNs @ GSPNs @ @ @ > .> @ > > @ > < > @ > @ @ . > @ > > < @ > < (ERG: extended reachability graph) > ERG = >> @ (ERG) . CTMC 60 CTMC . @ (RG) @ .> > > = <> .> > > CTMC @ @ > MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE @ @ . . . @> @ @ @ :1 :2 :3 @ : @ > ...> > > @ MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 61 @ :1 GSPN .> > RG = CTMC @ > 62 MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE @> @ :2 GSPN . > >> ERG @ CTMC > 63 MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE @ :3 GSPN . > >> ERG @ CTMC > 64 MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE GSPNs @ GSPNs @ <CTMC > @ RG .> < > <SPNs ERG CTMC @ . CTMC @ MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 65 GSPNs @ > @ <> > > < GSPN > @ > :CTMC >> ) @ .> ( > > .> < @ < CTMC MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 66 GSPNs @ > > @ :> <@ <@ < .( ) @ > > .> > @ @ @ >> > > < > @ @ > > >> SHARPE GreatSPN > > @> . @ @ GSPNs SPNs MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 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 Real-Time Systems Symp., Austin, TX, USA (1984) 215-224 [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) 303-311 MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 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 - IUST-CE 69 > . : GSPNs . @ @ @ @ (parallelism) @ ) > @ > @ :(place) :(timed activity) (activity time ( ) (enabling rate) @ (reactivation predicate) > GSPNs . <distribution function) ( @ .> @ :(instantaneous activity) (non-determinism) @ @ > : <(case probability function) > . MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 70 > 1 2 . . @ @> @> @> @ :(input gate) @> : @> > >> > @ @> > n @ .> > 1 2 . . @> > >> :(output gate) : @ > @ > n MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 71 > @ @ > @ > (non-determinacy) @ @ : (parallelism) > (non-deterministic) (probabilistic) (activity networks) @ @ (probabilistic activity networks) > @ (stochastic) > (SANs: stochastic activity networks) < < . > @> > > > > > > > > 72 (probabilistic verification) MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE > @ @ > > @ @ > @> > @ 73 MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE > :> 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 - IUST-CE > 74 @ :> <> <> < < . @ @ @> @ > > > @> @ @> @ @> @> > @> > @ @ @ > > > > @> .> > >> @ > @> > e(x):x1 > () > .> @ > @ @ f(x) = x - 1 > >> .> 75 f(x) = x + 1 @ > > MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE @ . @ > > @ @ @ . . .> > > @ @ ) . ( @ @ @ > @ > > . @ @ (unstable marking) > < > MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 76 @ > > @ : < . @ > . > > @> @ @ > @> > > @ @ @ > > @ @ . > @ > @ . < @ > MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 77 > @ @ :(activate) > > .> > @ @ : > @ > @ > >@ @ @ @ > @ @ > @ (reactivation predicate) > > < (potential completion time) . (aborted) <> . <> MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 78 > SANs < @ GSPNs @> @ >@ @ >@ . > @ @ @ @ > > > > > @ SANs @ > @ GSPNs > > . @ . >> @ >< @ 79 @ .> (GSPNs @ @ @ > > >) SANs @ @ SANs @ @ .> @> @ SANs @ > > > @ @ > . > > @ > MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE @ < > @ @ @ <(high-level Petri nets) : @ @ < < : @ @ @ . @ > HLPNs = PNs + Colour + Hierarchy >> > @ @ > @ > @ > @ . @ > @ > < : > . . . @ (computational power) (modeling power) @ <@ > > > <@ @ > > MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 80 @ . . @ @ @ 1978 Genrich & Lautenbach (Pr/T-nets: predicate/transition nets) (CPNs: coloured Petri nets) K. Jensen @ @ @ 1980 :(WNs: well-formed nets) WNs = simple CPNs (SWNs: Stochastic WNs) SWNs = WNs+GSPNs > :HLPN > . ISO/IEC 2003 MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 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 - IUST-CE 82 @ @ @ . > @ @ @ @ @ @ > @ @ CPNs > .> > @ > > (classes) < @ ( 83 @ > (chains) > . . > > @ ( char <integer . ) (multiset) )(atomic) @ >> @ >> . MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE @ > > @ @ @ > @> > (guards) .> ( @ @ .> @ > >@ . @ ML @ > >> > > > (arc expressions) > > @ > @ . )> @ MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 84 @ @ . @ (object-oriented Petri nets) OOPNs = CPNs+OO @ @ @ @ > (structuring capabilities) . > > @ (composition) @ @ @ > : (C. Lakos) . @ @ < > >> .> > > MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 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 - IUST-CE @ OPNs > (encapsulation) @ @ . CPNs @ .> @ @ > > @ > .> @ CPNs @ > > .> > OPNs @ OPNs @ > > OPNs @ @ . 87 (read-only) > . CPNs OPNs @ > @ UML (compositionality) (hierarchical) (incremental) MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE @ > @ @ : @ @ @ @ > > > > @ @ >> > > @ @ @ @ @ > (SRNs: stochastic reward nets) (MRSPNs: Markov regenerative SPNs) (FSPNs: fluid stochastic Petri nets) (high-level SANs) MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 88 (SRNs) > @ @ @ > < @ > SPNs > > > @ .> > GSPNs @ (rate rewards) > > .> @ > @ > . @ @ > MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 89 (MRSPNs) . . @ @ @ > > . > @ SPNs @ @ @ > (iid: independent identical distribution) @ > MRSPNs MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 90 (FSPNs) < . .> (state space explosion) > > @ >< . > @ @ > @ > @ @ > @ > > GSPNs @ @ > @ . MECS#18 - Analysis of Petri Nets - By: M. Abdollahi Azgomi - IUST-CE 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., High-Level 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 - IUST-CE 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 - IUST-CE 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.

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