Chapter 2: Non-hierarchical Coloured Petri Nets. 1`(1,"COL")++ 1`(2,"OUR")++ 1`(3,"ED ")++ 1`(4,"PET")++ 1`(5,"RI ")++ 1`(6,"NET") (n,d) AllPackets
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1 Modellig ad Validatio of ocurret Systems hapter 2: No-hierarchical Kurt Jese & Lars Michael Kristese lls s To Sed Sed NextSed 6 `(,"OL")++ `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") the ` Trasmit Trasmit the ` NextRec if = the + else `"" data if = the + else ata d `"" T if = the data^d else data epartmet of omputer Sciece Kurt Jese Lars M. Kristese
2 `(,"OL " )++ `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") Simple protocol s To Sed s d Sed Trasmit NextSed + Trasmit 2 epartmet of omputer Sciece Kurt Jese Lars M. Kristese
3 `(,"OL " )++ `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") Iformal descriptio s To Sed s d Sed Trasmit NextSed No loss of pacets No overtaig + Trasmit Seder Networ r 3 epartmet of omputer Sciece Kurt Jese Lars M. Kristese
4 `(,"OL " )++ `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") oloured Petri Net Place s To Sed s d rc Trasitio Sed Trasmit NextSed Net iscriptios + Trasmit 4 epartmet of omputer Sciece Kurt Jese Lars M. Kristese
5 Places represet the state of the system Name (o formal meaig; large impact o readability) `(,"OL " )++ `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") s To Sed Iitial marig (multiset of toes) Each toe i the iitial marig must have a colour that belogs to the colour set efiitio of colour sets: colset = it; (* itegers *) colset T = strig; (* text strigs *) colset = product * T; olour set (type) Each place cotais a umber of toes. Each toe carries a colour (data value). Sed Trasmit The colour set specifies the set of allowed toe colours. epartmet of omputer Sciece 5 Kurt Jese Lars M. Kristese
6 urret marig durig simulatio Type: olour set (set of allowed toe colours) `(,"OL " )++ `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") ircle: 6 toes s To Sed 6 `(,"OL ")++ `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") Values: Toe colours (multiset of actual toe colours) Square: etailed toe values The thic border lie idicates that the trasitio is eabled (ready to occur) Sed Trasmit Iformatio about curret marig (chages durig simulatio) NextSed Oe toe with value Rece Pac 6 epartmet of omputer Sciece Trasmit Kurt Jese Lars M. Kristese
7 `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") Trasitios ad arcs s To Sed rc expressio The type of the arc expressio must be equal to the colour set of the attached place (or a multiset over the colour set) Name (o formal meaig) Sed eclaratio of variables: var : ; (* itegers *) var d : T; (* strigs *) Trasmit idig of variables: <=3,d="PN"> (,d NextSed Evaluatio of expressios: (3,"PN") : 3 : R 7 epartmet of omputer Sciece Kurt Jese Lars M. Kristese
8 `(,"OL " )++ `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") Eablig of trasitios s To Sed? 6 `(,"OL ")++ `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") Two variables: var : ; (* itegers *) var d : T; (* strigs *) s d x Sed Trasmit idig: < =?, d=? > T? NextSed Trasitio is eabled if we ca fid a bidig so that each iput arc expressios evaluates to a multi-set of colours that is preset o the correspodig iput place + Trasmit oloured Petri Nets epartmet of omputer Sciece 8 Kurt Jese Lars M. Kristese
9 `(,"OL " )++ `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") Eablig of Sed s To Sed 6 `(,"OL ")++ `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") idig: < =, d=? > s d x rc expressio Sed NextSed Trasmit We wat to fid a bidig for the variable such that the arc expressio evaluates to a colour which is preset o the place NextSed Oe toe with value + Trasmit oloured Petri Nets epartmet of omputer Sciece 9 Kurt Jese Lars M. Kristese
10 `(,"OL " )++ `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") Eablig of Sed rc expressio s To Sed 6 `(,"OL ")++ `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") Six differet toes s d x Sed Trasmit idig: < =, d=? d="ol" > > NextSed We wat to fid a bidig for the variable d such that the arc expressio evaluates to a colour which is preset o the place stosed + Trasmit oloured Petri Nets epartmet of omputer Sciece 0 Kurt Jese Lars M. Kristese
11 `(,"OL " )++ `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") Eablig of Sed s To Sed 6 `(,"OL ")++ `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") (,"OL") We have foud a bidig so that each iput arc expressio evaluates to a colour that is preset o the correspodig iput place s d x Sed NextSed Trasmit idig: < =, d="ol" > Trasitio is eabled (ready to occur) + Trasmit oloured Petri Nets epartmet of omputer Sciece Kurt Jese Lars M. Kristese
12 Occurrece of Sed i bidig <=,d= OL > `(,"OL " )++ `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") s To Sed Sed 6 `(,"OL ")++ `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") (,"OL") (,"OL") Remove: (,"OL") Trasmit dd a ew toe: (,"OL") Pace Receiv ( NextSed Remove: + Trasmit oloured Petri Nets epartmet of omputer Sciece 2 Kurt Jese Lars M. Kristese
13 New marig after occurrece of Sed i bidig <=,d= OL > Trasitio is o loger eabled (thi border lie) `(,"OL " )++ `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") s To Sed Sed 5 `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") `(,"OL ") The first pacet has bee removed Trasmit copy of the first pacet has bee put o P R NextSed No toe o this place 3 + epartmet of omputer Sciece Trasmit Kurt Jese Lars M. Kristese
14 `(,"OL " )++ `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") s To Sed Sed NextSed 5 `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") `(,"OL ") New marig M Trasmit Trasitio eabled + s d Trasmit 4 epartmet of omputer Sciece Kurt Jese Lars M. Kristese
15 acets o Sed d) Sed 5 idig of Trasmit `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ urret marig `(5,"RI ")++ `(6,"NET") `(,"OL ") Trasmit s d extsed rc expressio idig: < =? =, d="ol" d=? > > + eceive Trasmit epartmet of omputer Sciece 5 Kurt Jese Lars M. Kristese
16 OL " )++ UR")++ ")++ ET")++ I ")++ ET") T s To Sed Sed Occurrece of Trasmit i bidig <=,d= OL > 5 `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ Remove: (,"OL") `(5,"RI ")++ `(6,"NET") `(,"OL ") Trasmit dd a ew toe: (,"OL") s d NextSed (, "OL") (, "OL") + 6 epartmet of omputer Sciece Trasmit Kurt Jese Lars M. Kristese
17 `(,"OL " )++ `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") s To Sed Sed 5 `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") New marig M 2 Trasmit `(,"OL ") s d NextSed + Trasmit 7 epartmet of omputer Sciece Kurt Jese Lars M. Kristese
18 Simulatio emo i PN Tools 8 epartmet of omputer Sciece Kurt Jese Lars M. Kristese
19 Secod versio of protocol ostat lls s To Sed 6 `(,"OL")++ `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") `"" ata d `"" T Sed Trasmit the ` data if = the data^d else data NextSed the ` Trasmit NextRec if = the + else if = the + else 30 epartmet of omputer Sciece Kurt Jese Lars M. Kristese
20 eclaratio of costats We use the followig costat to specify the iitial marig of stosed. val lls = (,"OL") ++ (2,"OUR") ++ (3,"E ") ++ (4,"PET") ++ (5,"RI ") ++ (6,"NET"); Saves a little bit of space i the diagram. Ehaces readability. a be reused (at other places). 3 epartmet of omputer Sciece Kurt Jese Lars M. Kristese
21 ouble-headed arcs lls s To Sed Sed NextSed 6 `(,"OL")++ `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") ouble-headed arc the ` Trasmit Trasmit the ` epartmet of omputer Sciece We o loger remove the toes from the iput places ouble-headed arc Retrasmissio becomes possible double-headed arc is a shorthad for two oppositely directed arcs with the same arc expressio NextRec if = the + else `"" data if = the + else ata d `"" T if = the data^d else data 32 Kurt Jese Lars M. Kristese
22 More complicated arc expressio lls s To Sed 6 `(,"OL")++ `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") More complicated arc expressio (if-the-else expressio) `"" ata d `"" T Sed Trasmit the ` data if = the data^d else data NextSed the ` Trasmit NextRec if = the + else if = the + else 33 epartmet of omputer Sciece Kurt Jese Lars M. Kristese
23 6 `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") If-the-else expressio `"" at Rece ` O `(,"OL") New variable: Trasmit var success : OOL; the ` NextRec b + = <=, d="ol", success=true> if = the + b = <=, d="ol", success=false> else Trasmit success = true epartmet of omputer Sciece `(,"OL") `(,"OL") data Successful trasmissio over the etwor if = the + else 34 Kurt Jese Lars M. Kristese
24 6 `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") If-the-else expressio `"" at Rece ` O `(,"OL") Trasmit var success : OOL; the ` NextRec b + = <=, d="ol", success=true> if = the + b = <=, d="ol", success=false> else Trasmit success = false epartmet of omputer Sciece empty No pacet is added data is lost durig trasmissio if = the + else 35 Kurt Jese Lars M. Kristese
25 New ame ad ew type New ame lls s To Sed 6 `(,"OL")++ `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") Iitial marig: empty text strig `"" ata d `"" T Sed Trasmit the ` New type data if = the data^d else data NextSed the ` Trasmit NextRec if = the + else if = the + else 36 epartmet of omputer Sciece Kurt Jese Lars M. Kristese
26 New place: NextRec lls s To Sed Sed NextSed 6 `(,"OL")++ `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") Plays a similar role as NextSed otais the umber of the expected pacet the ` Trasmit Trasmit the ` New place epartmet of omputer Sciece NextRec if = the + else `"" data if = the + else ata d `"" T if = the data^d else data 37 Kurt Jese Lars M. Kristese
27 orrect pacet arrives ss pty Empty text strig o arrivig Trasmit Trasmit the ` o expected `2 2 NextRec if = the + else `2 `"" `(,"OL") data if = the + else ata d `"" T if = the data^d else data 2 `"OL" idig: <=, d="ol", =, data=""> "OL" ^ is the cocateatio operator Update NextRec (from to 2) Sed acoweledgemet (with sequece umber of ext pacet) dd received data: "OL to atad 38 epartmet of omputer Sciece Kurt Jese Lars M. Kristese
28 Wrog pacet arrives ss pty o arrivig Trasmit Trasmit the ` NextRec o 3 expected `3 `3 3 if = the + else `3 `"OLOUR" `(,"OLOUR") `"" `(,"OL") `(,"OL") data if = the + else ata d `"" T if = the data^d else data 3 idig: <=, d="ol", =3, data="olour"> "OLOUR" o ot chage NextRec Sed acowledgemet (with sequece umber of ext pacet ) No data is added to atad 39 epartmet of omputer Sciece Kurt Jese Lars M. Kristese
29 owledgemets ca be lost lls s To Sed 6 `(,"OL")++ `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") `"" ata d `"" T Sed Trasmit the ` data if = the data^d else data NextSed the ` lso possible to loose acowledgemets Trasmit NextRec if = the + else if = the + else 40 epartmet of omputer Sciece Kurt Jese Lars M. Kristese
30 NextSed is updated lls s To Sed Sed NextSed 6 `(,"OL")++ `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") the ` Trasmit Trasmit the ` NextSed is updated with sequece umber from acowledgemet epartmet of omputer Sciece NextRec if = the + else `"" data if = the + else ata d `"" T if = the data^d else data 4 Kurt Jese Lars M. Kristese
31 Two eabled trasitios lls s To Sed Sed 6 `(,"OL")++ `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") `(,"OL") These bidig elemets eed the same toe They are i coflict with each other Trasmit the ` data ata d `"" T if = the data^d else data NextSed NextRec if = the + else if = SP = (Sed, <=, d="ol">) the + else TP = (Trasmit, Trasmit <=, d="ol", success=true>) the ` TP = (Trasmit, <=, d="ol", success=false>) `"" 42 epartmet of omputer Sciece Kurt Jese Lars M. Kristese
32 Two eabled trasitios lls s To Sed Sed 6 `(,"OL")++ `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") `(,"OL") These bidigs elemets use differet toes They are cocurretly eabled `"" ad ca occur cocurretly Trasmit the ` data ata d `"" T if = the data^d else data NextSed NextRec if = the + else if = SP = (Sed, <=, d="ol">) the + else TP = (Trasmit, Trasmit <=, d="ol", success=true>) the ` TP = (Trasmit, <=, d="ol", success=false>) 43 epartmet of omputer Sciece Kurt Jese Lars M. Kristese
33 Three eabled trasitios lls These bidig elemets are i coflict s To Sed Sed NextSed 6 `(,"OL")++ `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") SP = (Sed, `(,"OL") Trasmit ll other bidig elemets are cocurretly eabled the ` NextRec Trasmit TP = (Trasmit, <=, d="ol", success=false>) the ` if = the + else `(,"OL") `"" data ata d `"" T if = the data^d else data if = <=, d="ol">) the + else TP + = (Trasmit, <=, d="ol", success=true>) RP = (, <=, d="ol", =, data="">) 44 epartmet of omputer Sciece Kurt Jese Lars M. Kristese
34 Three eabled trasitios lls s To Sed Sed 6 `(,"OL")++ `(2,"OUR")++ `(3,"E ")++ `(4,"PET")++ `(5,"RI ")++ `(6,"NET") 2 2`(,"OL") Trasmit ll other bidig elemets are cocurretly eabled the ` data ata d if = the data^d else data NextSed `2 NextRec if = the + SP = (Sed, <=, d="ol">) else if = the + TP + = (Trasmit, <=, d="ol", success=true>) `2 else Trasmit TP = (Trasmit, <=, d="ol", success=false>) T + = (Trasmit, the ` <=2, success=true>) T = (Trasmit, 35 differet eabled steps `"OL" <=2, success=false>) `"" T 45 epartmet of omputer Sciece Kurt Jese Lars M. Kristese
35 Simulatio emo i PN Tools 46 epartmet of omputer Sciece Kurt Jese Lars M. Kristese
36 Trasitios ca have a guard oolea expressio which must evaluate to true for the bidig elemet to be eabled. dditioal eablig coditio. ata d `"" T data data^d Wrog pacets [<>] iscard NextRec + Next [=] orrect pacets Guard (<> is the Iequality operator) + Guard (tests whether ad are equal) 5 epartmet of omputer Sciece Kurt Jese Lars M. Kristese
37 Guard must evaluate to true [<>] iscard `(,"OL")++ `(2,"OUR") 2 `2 NextRec + `"OL" `"" Next data [=] [=] ata d `"" data^d T + false true RN = (Next, <=, =2, d="ol", data="ol">) RN 2 = (Next, <=2, =2, d="our", data="ol">) 52 epartmet of omputer Sciece Kurt Jese Lars M. Kristese
38 Guard must evaluate to true [<>] [<>] iscard `(,"OL")++ `(2,"OUR") 2 `2 NextRec + `"OL" `"" Next data [=] ata d `"" data^d T + true false P = (iscard, <=, =2, d="ol" ) P 2 = (iscard, <=2, =2, d="our") 53 epartmet of omputer Sciece Kurt Jese Lars M. Kristese
39 Editig emo i PN Tools 54 epartmet of omputer Sciece Kurt Jese Lars M. Kristese
40 Questios 55 epartmet of omputer Sciece Kurt Jese Lars M. Kristese
41 ssigmet 3 Tas I the lectures you have see a stop-ad-wait protocol. The seder eeps sedig the same pacet util a matchig acowledgemet is received. I a slidig widow protocol it is possible for the seder to trasmit several pacets to the receiver before receivig a acowledgemet. The seder has a widow cotaiig a umber of data pacets which are curretly uder trasmissio ad for which acowledgemets have ot yet bee received. Tas : Modify the PN model such that it models a Go-ac-N Widow Protocol. I a Go-ac-N protocol, the seder seds all data pacets i the curret widow ad the waits for acowledgemets. If o acowledgemet is received (withi a certai amout of time), the data pacets i the widow are all retrasmitted. The PN model of the stop-ad-wait protocol ca be dowloaded from: It should oly be ecessary to modify the Seder part of the PN model. You should chage the colour set ad the iitial marig of the NextSed place, so that it cotais iformatio about the start ad ed of the widow. Havig doe this you should chage the arc iscriptios of the surroudig arcs so that they implemet a slidig widows strategy. Use simulatio to validate the correctess of your protocol. It may be useful to chage the iitial marig of ToSed so that you get more pacets to wor with. 56 epartmet of omputer Sciece Kurt Jese Lars M. Kristese
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