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Modeling computer networks by colored Petri nets

D
DmitryZaitsev5

The document discusses modeling computer networks using colored Petri nets, highlighting the use of specific tools and techniques for simulating various network protocols such as Ethernet and IP. It describes the components of Petri nets, like color sets and hierarchical structures, and provides guidance for building and evaluating network models. Additionally, it offers resources for further reading and example nets that can be downloaded for practical use.

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Performance Evaluation
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Modeling computer networks by colored Petri nets Dmitry A. Zaitsev http://member.acm.org/~daze
How it looks Statistics i03 PBBseg bavail o03 PBBseg bavail i04 PBBseg bavail o04 PBBseg bavail i01 PBBseg bavail o01 PBBseg bavail i02 PBBseg bavail o02 PBBseg bavail i06 seg avail o06 seg avail io5 seg avail o05 seg avail i07 seg avail o07 seg avail i09 seg avail o09 seg avail i10 seg avail o10 seg avail i33 seg avail o33 seg avail i32 seg avail o32 seg avail i34 seg avail o34 seg avail i35 seg avail o35 seg avail i36 seg avail o36 seg avail i37 seg avail o37 seg avail i38 seg avail o38 seg avail i08 seg avail o08 seg avail o31 seg avail i31 seg avail i11 seg avail 011 seg avail i12 seg avail o12 seg avail i13 seg avail o13 seg avail i14 seg avail o145 seg avail i15 seg avail o15 seg avail i16 seg avail o16 seg avail i17 seg avail o17 seg avail i18 seg avail o18 seg avail o19 seg avail i19 seg avail i20 seg avail o20 seg avail i21 seg avail o21 seg avail i22 seg avail o22 seg avail i23 seg avail o23 seg avail i24 seg avail o24 seg avail i25 seg avail o25 seg avail i41 seg avail o41 seg avail i42 seg avail o42 seg avail i43 seg avail o43 seg avail o44 seg avail i44 seg avail o45 seg avail i45 seg avail i46 seg avail o46 seg avail i48 seg avail o48 seg avail i49 seg avail o49 seg avail i50 seg avail o50 seg avail i51 seg avail o51 seg avail i52 seg avail o52 seg avail i53 seg avail o53 seg avail i54 seg avail o54 seg avail i55 seg avail o55 seg avail i56 seg avail o56 seg avail i57 seg avail o57 seg avail i58 seg avail o58 seg avail i59 seg avail o59 seg avail a31 mac 31 a32 mac 32 a33 mac 33 a34 mac 34 a35 mac 35 a36 mac 36 a41 mac 41 a42 mac 42 a43 mac 43 a44 mac 44 a45 mac 45 a46 mac 46 a47 mac 47 a48 mac 48 a49 mac 49 a4a mac 50 a4b mac 51 a4c mac 52 a11 mac 11 a12 mac 12 a13 mac 13 a14 mac 14 a15 mac 15 a16 mac 16 a21 mac 21 a22 mac 22 a23 mac 23 a24 mac 24 a25 mac 25 a26 mac 26 a27 mac 27 a28 mac 28 a29 mac 29 a37 mac 37 a38 mac 38 i61 seg avail o61 seg avail o60 seg avail i60 seg avail a2a mac 30 i26 seg avail o26 seg avail ab0 mac 80 ab3 mac 83 ab4 mac 84 ab2 mac 82 ab1 mac 81 SndFrmT sfT INT 0 sfT RcvFrmT rfT INT 0 rfT DrpFrmNw dfN INT 0 dfN DrpFrmT dfT INT 0 dfT PBB0 SWB4SWB4 PBB3 SWB1-2SWB1-2 PBB4 SWB1-2SWB1-2 PBB1 SWB1-2SWB1-2 PBB2 SWB1-2SWB1-2 SW11 SW4SW4 SW12 SW4SW4 SW21 SW4SW4 SW22 SW4SW4 SW23 SW4SW4 SW42 SW4SW4 SW41 SW4SW4 SW45 SW4SW4 SW43 SW4SW4 SW44 SW4SW4 SW31 SW4SW4 SW33 SW4SW4 SW24 SW4SW4 SW32 SW4SW4 c11 SS c12 WSWS c13 WSWS c14 WSWS c15 WSWS c16 MWSMWS c21 WSWS c22 WSWS c23 WSWS c24 WSWS c25 WSWS c26 MWSMWS c27 SS c28 WSWS c29 WSWS c31 SS c32 WSWS c33 WSWS c34 WSWS c35 WSWS c36 MWSMWS c41 WSWS c42 WSWS c43 WSWS c44 SS c45 WSWS c46 WSWS c47 WSWS c48 WSWS c49 MWSMWS c4a SS c4b WSWS c4c WSWS c37 SS c38 SS c2a SS 1 1`bavail@0 1 1`bavail@0 1 1`bavail@0 1 1`bavail@0 1 1`bavail@0 1 1`bavail@0 1 1`bavail@0 1 1`bavail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 11`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`31 1 1`32 1 1`33 1 1`34 1 1`35 1 1`36 1 1`41 1 1`42 1 1`43 1 1`44 1 1`45 1 1`46 1 1`47 1 1`48 1 1`49 1 1`50 1 1`51 1 1`52 1 1`11 1 1`12 1 1`13 1 1`14 1 1`15 1 1`16 1 1`21 1 1`22 1 1`23 1 1`24 1 1`25 1 1`26 1 1`27 1 1`28 1 1`29 1 1`37 1 1`38 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`30 1 1`avail@0 1 1`avail@0 1 1`80 1 1`83 1 1`841 1`82 1 1`81 1 1`0 1 1`0 1 1`0 1 1`0
Tools and models • Download and install modeling system CPN Tools from http://cpntools.org • Download and unpack example nets modeling networks: Ethernet, IP, MPLS, Bluetooth, PBB
Books and textbooks • Zaitsev D.A. Clans of Petri Nets: Verification of protocols and performance evaluation of networks, LAP LAMBERT Academic Publishing, 2013, 292 p. – free download a draft from http://daze.ho.ua/daze-clans-covered-draft.djvu • Zaitsev D.A., Shmeleva T.R. Simulating computer networks by CPN Tools, Odessa: ONAT, 2006, 65 p. – free download from http://daze.ho.ua/cpnmp2.pdf
Colored Petri net concept • A Petri net graph – directed bipartite graph • Functional programming language ML to load elements of the graph • Tokens as elements of abstract data types (color sets) • Hierarchical structure with the transition substitution • Time delays associated with transitions and arcs
What to do with CPN models • Watch tokens game – for understanding and debugging • Build the model State Space – for model checking (verification) • Simulate on prolonged interval of time – for performance evaluation
After starting CPN Tools
Palettes and tools
A Place Name Color set Initial Marking
A Transition Name [Guard predicate] @+Timed Dealay input (); output (); action (A Program);
Arcs pattern constructor@+ Time_delay
Declarations • Colset – a color set • Val – a constant • Var – a variable • Fun – a function
Model of switched Ethernet Switch (SWI) Server 1 (S1, MAC=1) Server 2 (S2, MAC=3) Workstation 1 (WS1, MAC=2) Workstation 2 (WS2, MAC=4) Workstation 3 (WS3, MAC=5) Workstation 4 (WS4, MAC=6) Workstation 5 (WS5, MAC=7) HUB1 HUB2 HUB3 Port 1 Port 2 Port 3 Scheme of sample switched LAN
Main page of Ethernet model Model of LAN p1out seg avail p1in seg avail p2in seg availp2out seg avail p3out seg avail p3in seg avail aS1 mac 1`1 aS2 mac 1`3 aWS1 mac 1`2 aWS2 mac 1`4 aWS3 mac 1`5 aWS4 mac 1`6 aWS5 mac 1`7 SWI SWISWI S1 SS S2 SS WS1 WSWS WS2 WSWS WS3 WSWS WS4 WSWS WS5 MWSMWS
Declarations colset mac = INT timed; colset portnum = INT; colset nfrm = INT; colset sfrm = product nfrm * INT timed; colset frm = product mac * mac * nfrm timed; colset seg = union f:frm + avail timed; colset swi = product mac * portnum; colset swf = product mac * mac * nfrm * portnum timed; colset remsv = product mac * nfrm timed; var src, dst, target: mac; var port: portnum; var nf, rnf: nfrm; var t1, t2, s, q, r: INT; colset Delta = int with 1000..2000; fun Delay() = Delta.ran(); colset dex = int with 100..200; fun Dexec() = dex.ran(); colset dse = int with 10..20; fun Dsend() = dse.ran(); colset nse = int with 10..20; fun Nsend() = nse.ran(); fun cT()=IntInf.toInt(!CPN'Time.model_time)
Ethernet Switch Port1 Text Text Text Port2 Port3 Model of Switch Port1InIn/Out seg In/Out Port1OutIn/Out seg In/Out Port2InIn/Out seg In/Out Port2OutIn/Out seg In/Out Port3InIn/Out seg In/Out Port3OutIn/Out seg In/Out SwTa1 SwitchTable swi 1`(1,1)++1`(2,1)++1`(3,2)++1`(4,2)++1`(5,3)++1`(6,3)++1`(7,3) SwitchTable Bu1 Buffer swf Buffer SwTa2 SwitchTable swi 1`(1,1)++1`(2,1)++1`(3,2)++1`(4,2)++1`(5,3)++1`(6,3)++1`(7,3) SwitchTable SwTa3 SwitchTable swi 1`(1,1)++1`(2,1)++1`(3,2)++1`(4,2)++1`(5,3)++1`(6,3)++1`(7,3) SwitchTable Bu2 Buffer swf Buffer Bu3 Buffer swf Buffer In1 @+5 [dst=target] Out1 @+5 In2 @+5 [dst=target] Out2 @+5 In3 @+5 [dst=target] Out3 @+5 f(src,dst,nf) f(src,dst,nf) (target,port) f(src,dst,nf) f(src,dst,nf) (src,dst,nf,port) (src,dst,nf,1) f(src,dst,nf) f(src,dst,nf) (target,port) (target,port) (src,dst,nf,port) (src,dst,nf,port) (src,dst,nf,2) (src,dst,nf,3) avail avail avail avail avail avail 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 1 1`avail@0 7 1`(1,1)++ 1`(2,1)++ 1`(3,2)++ 1`(4,2)++ 1`(5,3)++ 1`(6,3)++ 1`(7,3) 7 1`(1,1)++ 1`(2,1)++ 1`(3,2)++ 1`(4,2)++ 1`(5,3)++ 1`(6,3)++ 1`(7,3) 7 1`(1,1)++ 1`(2,1)++ 1`(3,2)++ 1`(4,2)++ 1`(5,3)++ 1`(6,3)++ 1`(7,3)
Switch port Port1In In/Out seg In/Out Port1Out In/Out seg In/Out SwTa1 SwitchTable swi 1`(1,1)++1`(2,1)++1`(3,2)++ 1`(4,2)++1`(5,3)++1`(6,3)++1`(7,3) Bu1 Buffer swf Buffer In1 @+5 [dst=target] Out1 @+5 f(src,dst,nf) f(src,dst,nf) (target,port) (src,dst,nf,port) (src,dst,nf,1) avail avail SwitchTable
Workstation LANout In/Out seg In/Out Own In/Out mac In/Out Remote mac 1`1++1`3 LANin In/Out seg In/Out Receive @+10 [dst=target] Send @+10 avail f(src,dst,1) target src dst dst@+Delay() f(src,dst,nf) avail
Server LANout In/Out seg In/Out Own In/Out macIn/Out Remote remsv Reply frm LANin In/Out seg In/Out Receive @+10 [dst=target] Send @+Dsend() Exec @+Dexec() avail f(src,dst,nf) target (src,nf) (dst,nf) src Nsend()`(src,dst,nf)(src,dst,nf) f(src,dst,nf) avail
Measuring workstation Avarage Network Responce Time Network Responce Times for Requests Own In/Out mac In/Out LANoutIn/Out seg In/Out LANinIn/Out seg In/Out return sfrm Remote mac 1`1++1`3 num nfrm 1`1 nSnd sfrm NRTs sfrm new BOOL sum INT 1`0 quan INT 1`0 NRTime INT 1`0 Send @+10 Receive @+10 [dst=target] IsFirst [rnf=nf] Culc avail f(src,dst,nf) dst dst@+Delay() src nf nf+1 f(src,dst,rnf) target (nf,cT()) (rnf,cT()) (rnf,t2) (nf,t1) (nf,t2-t1) avail true s s+(t2-t1) q q+1 q s true r s div q
Avarage Network Responce Time Network Responce Times for Requests Own In/Out mac In/Out LANoutIn/Out seg In/Out LANinIn/Out seg In/Out return sfrm Remote mac 1`1++1`3 num nfrm 1`1 nSnd sfrm NRTs sfrm new BOOL sum INT 1`0 quan INT 1`0 NRTime INT 1`0 Send @+10 Receive @+10 [dst=target] IsFirst [rnf=nf] Culc avail f(src,dst,nf) dst dst@+Delay() src nf nf+1 f(src,dst,rnf) target (nf,cT()) (rnf,cT()) (rnf,t2) (nf,t1) (nf,t2-t1) avail true s s+(t2-t1) q q+1 q s true r s div q 1 1`7@235684 1 1`avail@235535 1 1`avail@235684 4544 2 1`1@236718+++ 1`3@236161 1 1`311 1 1`(310,235520)@235530 309 1`(1,861)@886+++ 1`(2,696)@781+++ 1`(3,266)@1730+++ 1`(4,335)@1989+++ 1`(5,262)@3411+++ 1`(6,253)@3591+++ 1`(7,213)@4928+++ 1`(8,213)@5021+++ 1`(9,430)@6458+++ 1`(10,267)@6383+++ 1`(11,347)@8099+++ 1`(12,336)@8365+++ 1`(13,444)@9606+++ 1`(14,415)@9951+++ 1`(15,342)@10964+++ 1`(16,218)@11172+++ 1`(17,305)@12105+++ 1`(18,334)@13215+++ 1`(19,678)@14284+++ 1`(20,488)@15348+++ 1`(21,290)@15385+++ 1`(22,291)@16291+++ 1`(23,381)@16645+++ 1 1`108233 1 1`309 1 1`350 Model state
Time scaling
Model of IP network
Main page R1P1In pkt R1P1Out pkt R1P2In pkt R1P2Out pkt R1P3In pkt R1P3Out pkt R1P4In pkt R1P4Out pkt R2P1In pkt R2P1Out pkt R2P2In pkt R2P2Out pkt R2P3In pkt R2P3Out pkt R2P4In pkt R2P4Out pkt R3P1Out pkt R3P1In pkt R3P2Out pkt R3P2In pkt R3P4Out pkt R3P4In pkt R3P3Out pkt R3P3In pkt R4P1In pkt R4P1Out pkt R4P4In pkt R4P4Out pkt R4P2Out pkt R4P2In pkt R4P3Out pkt R4P3In pkt R5P1In pkt R5P1Out pkt R5P2Out pkt R5P2In pkt R5P3In pkt R5P3Out pkt R5P4In pkt R5P4Out pkt R6P1In pkt R6P1Out pkt R6P2Out pkt R6P2In pkt R6P3Out pkt R6P3In pkt R6P4In pkt R6P4Out pkt R7P3Out pkt R7P3In pkt R7P4In pkt R7P4Out pkt R7P2In pkt R7P2Out pkt R7P1In pkt R7P1Out pkt Traffic Traffic INT 1`0 Traffic France Router1Router1 Sweden Router2Router2 Transmit @+2 Receive @+2 Spain Router3Router3 Germany1 Router4Router4 Germany Router5Router5 Ukraine Router6Router6 Finland Router7Router7 Receive1 @+2 Transmit1 @+2 Transmit2 @+2 Receive2 @+2 Transmit3 @+2 Receive3 @+2 Transmit4 @+2 Receive4 @+2 Transmit7 @+2 Receive7 @+2 Transmit6 @+2 Receive6 @+2 Receive5 @+2 Transmit5 @+2 Receive9 @+2 Transmit9 @+2 Transmit8 @+2 Receive8 @+2 Terminal1 Terminal1Terminal1 Terminal3 Terminal3Terminal3 Terminal2 Terminal2Terminal2 Terminal Terminal6Terminal6 Terminal6 Terminal5Terminal5 Terminal5 Terminal4Terminal4 a a a a a a a a a a a a a a a a a a a a a a a a a a aa a a a a a a a a a a a a a a a a a a a a a a a a
Basic declarations colset ip=product INT*INT*INT*INT timed; colset mask=INT; colset nwt=product ip*mask timed; colset b=INT timed; colset pkt=record ipsrc:ip*ipdst:ip*data:b timed; colset nif=int; colset interf=product ip*nif; colset gw=ip; colset rtr=record nw:nwt *gw:ip*ifc:interf timed ; colset buf=product pkt*ip; fun pow(x,0)=1 | pow(x,y)=pow(x,y-1)*x; colset aux=INT timed; var q:nwt; var r:rtr; var p,src,dst:ip; var a:pkt ; var v:aux; var i,c,k:INT; var tr:buf;
SameNW function fun sameNW(a1:ip,a2:ip,m:INT)=if (32-m) < 8 then ( if ((#1 a1) = (#1 a2)) andalso ((#2 a1) = (#2 a2)) andalso ((#3 a1) =(#3 a2)) andalso ((((#4 a1) div pow(2,(32-m)))*(pow(2,(32-m)))) = (#4 a2)) then true else false ) else if (32-m)<16 then ( if ((#1 a1) = (#1 a2)) andalso ((#2 a1) = (#2 a2)) andalso ((((#3 a1) div pow(2,((32-m)-8))) * pow(2,((32-m)-8))) = (#3 a2)) then true else false) else if (32-m)<24 then (if ((#1 a1)=(#1 a2)) andalso ((((#2 a1) div pow(2,((32-m)-16)))*pow(2,((32-m)-16)))=(#2 a2)) then true else false) else if ((((#1 a1) div pow(2,((32-m)-24)))*pow(2,((32-m)-24)))=(#1 a2)) then true else false;
Router port RT1 rt rtr [{nw=((194,79,128,0),19),gw=(212,225,128,1),ifc=((212,225,128,1),2)}, {nw=((212,225,128,0),17),gw=(212,225,128,1),ifc=((212,225,128,1),2)}, {nw=((194,98,0,0),19),gw=(212,225,128,1),ifc=((212,225,128,1),2)}, {nw=((217,13,48,0),20),gw=(212,225,128,1),ifc=((212,225,128,1),2)}, {nw=((195,100,0,0),16),gw=(85,68,0,2),ifc=((85,68,0,1),4)}, {nw=((62,220,160,0),19),gw=(85,68,0,2),ifc=((85,68,0,1),4)}, {nw=((83,218,64,0),19),gw=(85,68,0,2),ifc=((85,68,0,1),4)}, {nw=((82,99,0,0),18),gw=(85,68,0,2),ifc=((85,68,0,1),4)}, {nw=((82,223,0,0),16),gw=(213,9,128,2),ifc=((213,9,128,1),3)}, {nw=((85,155,0,0),16),gw=(213,9,128,2),ifc=((213,9,128,1),3)}, {nw=((213,171,224,0),19),gw=(213,9,128,2),ifc=((213,9,128,1),3)}, {nw=((80,81,96,0),20),gw=(213,9,128,2),ifc=((213,9,128,1),3)}, {nw=((62,117,0,0),19),gw=(213,9,128,2),ifc=((213,9,128,1),3)}, {nw=((82,119,0,0),19),gw=(213,9,128,2),ifc=((213,9,128,1),3)}, {nw=((212,60,192,0),18),gw=(213,9,128,2),ifc=((213,9,128,1),3)}, {nw=((217,146,144,0),20),gw=(213,9,128,2),ifc=((213,9,128,1),3)}, {nw=((82,207,0,0),17),gw=(85,68,0,2),ifc=((85,68,0,1),4)}, {nw=((195,5,0,0),19),gw=(85,68,0,2),ifc=((85,68,0,1),4)}, {nw=((62,16,0,0),19),gw=(85,68,0,2),ifc=((85,68,0,1),4)}, {nw=((212,1,64,0),18),gw=(85,68,0,2),ifc=((85,68,0,1),4)}, {nw=((195,134,224,0),19),gw=(85,68,0,2),ifc=((85,68,0,1),4)}, {nw=((85,23,0,0),16),gw=(85,68,0,2),ifc=((85,68,0,1),4)}, {nw=((84,34,0,0),16),gw=(85,68,0,2),ifc=((85,68,0,1),4)}, {nw=((62,71,0,0),16),gw=(85,68,0,2),ifc=((85,68,0,1),4)} ] rt p1IN In pkt p1OUT Out pkt Buf Buffer1 buf Buffer1 IP1 ip 1`(194,62,10,19) get1 @+18 sameNW(#ipdst a,#1 (#nw r) ,#2 (#nw r)) put1 @+1(#2 tr)=p r tr p a (#1 tr) (a,(#1 (#ifc r))) In Out
Terminal network Out Out pkt Out ownNW nwt 1`((212,225,128,0),17)++ 1`((194,79,128,0),19)++ 1`((194,98,0,0),19)++ 1`((217,13,48,0),20) allNW nwt 1`((62,117,0,0),19)++ 1`((82,119,0,0),19)++ 1`((212,60,192,0),18)++ 1`((217,146,144,0),20)++ 1`((195,134,224,0),19)++ 1`((85,23,0,0),16)++ 1`((84,34,0,0),16)++ 1`((62,71,0,0),16)++ 1`((62,220,160,0),19)++ 1`((83,218,64,0),19)++ 1`((195,100,0,0),16)++ 1`((82,99,0,0),18)++ 1`((85,155,0,0),16)++ 1`((213,171,224,0),19)++ 1`((82,223,0,0),16)++ 1`((80,81,96,0),20)++ 1`((82,207,0,0),17)++ 1`((195,5,0,0),19)++ 1`((62,16,0,0),19)++ 1`((212,1,64,0),18) Data INT 1`64 In In pkt In ipsrc ip ipdst ip 1 aux 1`5 Traffic Traffic INT 1`0 Traffic Pkt pkt 2 INT 1`1 3 INT 4 INT 1 @+2 IpGenerate1 @+2 IpGenerate2 @+2 Counter {ipsrc=src,ipdst=dst,data=i} i qp p src dst q q @+5 q @+5 v v@+1 a k+1 k a c c c c c c
Program to generate IP address input (q); output (p); action (if (#2 q)>=24 then let val i=pow(2,8-((#2 q)-24))-1 val p=(#1 (#1 q),#2 (#1 q),#3 (#1 q),discrete((#4 (#1 q)),(#4 (#1 q))+i)) In (p) end else if (#2 q)>=16 andalso (#2 q)<24 then let val i=pow(2,8-((#2 q)-16))-1 val p=(#1 (#1 q),#2 (#1 q),discrete((#3 (#1 q)),(#3 (#1 q))+i),discrete(1,254)) In (p) end else if (#2 q)>=8 andalso (#2 q)<16 then let val i=pow(2,8-((#2 q)-8))-1 val p=(#1 (#1 q),discrete((#2 (#1 q)),(#2 (#1 q))+i),discrete(1,254),discrete(1,254)) In (p) end else let val i=pow(2,8-((#2 q)))-1 val p=(discrete((#1 (#1 q)),(#1 (#1 q))+i),discrete(1,254),discrete(1,254),discrete(1,254)) In (p) end);
MPLS label switching
MPLS router port p2IN In pkt In rec2 rtr p2 pkt Buf1 buf Ltable2 LT1 lt 1`{ininterf=2,L1=2,outinterf=4,L2=5}++ 1`{ininterf=2,L1=3,outinterf=3,L2=1}++ 1`{ininterf=2,L1=4,outinterf=3,L2=2}++ 1`{ininterf=2,L1=5,outinterf=4,L2=6}++ 1`{ininterf=2,L1=6,outinterf=4,L2=7}++ 1`{ininterf=3,L1=3,outinterf=2,L2=0}++ 1`{ininterf=3,L1=6,outinterf=2,L2=0}++ 1`{ininterf=4,L1=2,outinterf=2,L2=0}++ 1`{ininterf=4,L1=3,outinterf=2,L2=0}++ 1`{ininterf=4,L1=4,outinterf=2,L2=0} LT1 p2OUT Out pkt Out RT2 rtr [{nw=((194,79,128,0),19),gw=(212,225,128,1),ifc=((212,225,128,1),2),label=1}, {nw=((212,225,128,0),17),gw=(212,225,128,1),ifc=((212,225,128,1),2),label=1}, {nw=((194,98,0,0),19),gw=(212,225,128,1),ifc=((212,225,128,1),2),label=1}, {nw=((217,13,48,0),20),gw=(212,225,128,1),ifc=((212,225,128,1),2),label=1}, {nw=((195,100,0,0),16),gw=(85,68,0,2),ifc=((85,68,0,1),4),label=2}, {nw=((62,220,160,0),19),gw=(85,68,0,2),ifc=((85,68,0,1),4),label=2}, {nw=((83,218,64,0),19),gw=(85,68,0,2),ifc=((85,68,0,1),4),label=2}, {nw=((82,99,0,0),18),gw=(85,68,0,2),ifc=((85,68,0,1),4),label=2}, {nw=((82,223,0,0),16),gw=(213,9,128,2),ifc=((213,9,128,1),3),label=3}, {nw=((85,155,0,0),16),gw=(213,9,128,2),ifc=((213,9,128,1),3),label=3}, {nw=((213,171,224,0),19),gw=(213,9,128,2),ifc=((213,9,128,1),3),label=3}, {nw=((80,81,96,0),20),gw=(213,9,128,2),ifc=((213,9,128,1),3),label=3}, {nw=((62,117,0,0),19),gw=(213,9,128,2),ifc=((213,9,128,1),3),label=4}, {nw=((82,119,0,0),19),gw=(213,9,128,2),ifc=((213,9,128,1),3),label=4}, {nw=((212,60,192,0),18),gw=(213,9,128,2),ifc=((213,9,128,1),3),label=4}, {nw=((217,146,144,0),20),gw=(213,9,128,2),ifc=((213,9,128,1),3),label=4}, {nw=((82,207,0,0),17),gw=(85,68,0,2),ifc=((85,68,0,1),4),label=5}, {nw=((195,5,0,0),19),gw=(85,68,0,2),ifc=((85,68,0,1),4),label=5}, {nw=((62,16,0,0),19),gw=(85,68,0,2),ifc=((85,68,0,1),4),label=5}, {nw=((212,1,64,0),18),gw=(85,68,0,2),ifc=((85,68,0,1),4),label=5}, {nw=((195,134,224,0),19),gw=(85,68,0,2),ifc=((85,68,0,1),4),label=6}, {nw=((85,23,0,0),16),gw=(85,68,0,2),ifc=((85,68,0,1),4),label=6}, {nw=((84,34,0,0),16),gw=(85,68,0,2),ifc=((85,68,0,1),4),label=6}, {nw=((62,71,0,0),16),gw=(85,68,0,2),ifc=((85,68,0,1),4),label=6} ] InterfaceNr2 INT 1`2 Buffer2 Buffer1 buffer Buffer1 get2 @+18 sameNW(#ipdst a,#1 (#nw r) ,#2 (#nw r)) 2 @+1 Intermed @+1 (#label (#1 tr))=(#L1 entry) andalso (#2 tr)=(#ininterf entry) Out2 @+1 (#2 buff)=k a r a a r ({label=(#label r),ipsrc=(#ipsrc a),ipdst=(#ipdst a),data=(#data a)},i) tr entry r i ({label=(#L2 entry),ipsrc=(#ipsrc (#1 tr)),ipdst=(#ipdst (#1 tr)),data=(#data (#1 tr))},#outinterf entry) buff({ipsrc=(#ipsrc (#1 buff)),ipdst=(#ipdst (#1 buff)),data=(#data (#1 buff))}) k
Comparison of IP and MPLS
Bluetooth piconetworks
Air rf availmaster pma1 addr 11 pma2 addr 21 pma3 addr 31 pma4 addr 41 pma5 addr 51 pma6 addr 61 pma7 addr 71 pma8 addr 81 M1 MasterMaster Keyboard slaveslave Mouse slaveslave Mobile slaveslave Printer slaveslave Kamera slaveslave Scaner slaveslave Printer 2 slaveslave Mobile2 slaveslave 1 1`availmaster@0 1 1`11 1 1`21 1 1`31 1 1`41 1 1`51 1 1`611 1`71 1 1`81
Basic declarations colset addr=INT; colset ptype=INT; colset pkt = record srcama:addr*dstama:addr*mtype:ptype*pma:addr; colset rf=union r:pkt+availmaster+availslave timed; colset lpkt=list pkt; colset amatab=record ama:addr*pma:addr*t:INT; colset lamatab=list amatab; colset npkt=int with 10..20; fun NSend()=npkt.ran(); colset clc=unit with c timed; colset Interval=int with 500..1000; fun Delay()=Interval.ran(); fun eqpma v (rr:amatab)=((#pma rr)=v); fun eqt v (rr:amatab)=((#t rr)=v); fun grec prd [] = zero | grec prd (y::z) = if prd(y) then y else grec prd z; fun prec prd [] pm ti= [] | prec prd (y::z) pm ti= if prd(y) then ({ama=(#ama y),pma=pm,t=ti}::z) else y::(prec prd z pm ti); fun cT()=IntInf.toInt(!CPN'Time.model_time) fun mint [] = (cT()) | mint ((y::z):lamatab) = Int.min((#t y),(mint z));
Master outbuf lpkt [] InBuf pkt AllocBuf pkt TabAMA lamatab [{ama=1,pma=0,t=0}, {ama=2,pma=0,t=0}, {ama=3,pma=0,t=0}, {ama=4,pma=0,t=0}, {ama=5,pma=0,t=0}, {ama=6,pma=0,t=0}, {ama=7,pma=0,t=0}] Release pkt C1 INT 0 C2 INT 0 air In/Out rf In/Out Listen @+2 #dstama p=0 t1 #mtype p=1 t2 #mtype p=2 t3 #mtype p=3 AllocAma List.exists (eqpma 0) al RlsAma send @+2 x=availmaster orelse x=availslave check SwapAMA not (List.exists (eqpma 0) al) p p p p p p al prec (eqpma 0) al (#pma p) (cT()) pl^^[{srcama=0, dstama=(#ama (grec (eqpma 0) al)), mtype=1, pma=(#pma p)}] p p al prec (eqpma (#pma p)) al 0 (cT()) pl^^[{srcama=0, dstama=(#srcama p), mtype=2, pma=(#pma p)}] i i+1 i+1 i pl r(p) pl availmaster p::pl pl x r(p) [] availmaster availslave al p pl pl^^[{srcama=0, dstama=(#ama (grec (eqt (mint al)) al)), mtype=2, pma=(#pma (grec (eqt (mint al)) al))}, {srcama=0, dstama=(#ama (grec (eqt (mint al)) al)), mtype=1, pma=(#pma p)}] prec (eqt (mint al)) al (#pma p) (cT()) 1 1`[] 1 1`[{ama=1,pma=0,t=0},{ama=2,pm a=0,t=0},{ama=3,pma=0,t=0},{ama =4,pma=0,t=0},{ama=5,pma=0,t=0} ,{ama=6,pma=0,t=0},{ama=7,pma= 0,t=0}] 1 1`0 1 1`0 1 1`availmaster@0
Slave Air In/Out rf In/Out myAMA addr 1`8 myPMA In/Out addr In/Out InBuf pkt outbufs lpkt [] clock clc 1`c@+Delay() data pkt Listen @+2 #dstama p=ama, #mtype p=3 AlloAMA @+2 pl<>nil FreeAMA @+2ama <> 8 SetAMA @+2 #mtype p=1, #pma p=tpma, #srcama p<>8 DelAMA @+2 #mtype p=2, #pma p=tpma, #srcama p=0 SendData inque send @+2 ama<>8 r(p) ama p 8 tpmar({srcama=8, dstama=0, mtype=1, pma=tpma}) ama r({srcama=ama, dstama=0, mtype=2, pma=tpma}) r(p) tpma #dstama p r(p) tpma 8 tpma cc cc@+Delay() NSend()`{srcama=0,dstama=0, mtype=3,pma=tpma} p pl^^[p]pl p::plpl r({srcama=ama,dstama=0, mtype=(#mtype p),pma=(#pma p)}) availslave availmasteravailmaster availslave availslave availmaster ama pl [] tpma ama 1 1`availmaster@0 1 1`8 1 1`51 1 1`[] 1 1`c@823
Efficiency of address space sharing
Provider Backbone Bridge
Example PBB network
Main pageStatistics i03 PBBseg bavail o03 PBBseg bavail i04 PBBseg bavail o04 PBBseg bavail i01 PBBseg bavail o01 PBBseg bavail i02 PBBseg bavail o02 PBBseg bavail i06 seg avail o06 seg avail io5 seg avail o05 seg avail i07 seg avail o07 seg avail i09 seg avail o09 seg avail i10 seg avail o10 seg avail i33 seg avail o33 seg avail i32 seg avail o32 seg avail i34 seg avail o34 seg avail i35 seg avail o35 seg avail i36 seg avail o36 seg avail i37 seg avail o37 seg avail i38 seg avail o38 seg avail i08 seg avail o08 seg avail o31 seg avail i31 seg avail i11 seg avail 011 seg avail i12 seg avail o12 seg avail i13 seg avail o13 seg avail i14 seg avail o145 seg avail i15 seg avail o15 seg avail i16 seg avail o16 seg avail i17 seg avail o17 seg avail i18 seg avail o18 seg avail o19 seg availi19 seg avail i20 seg avail o20 seg avail i21 seg avail o21 seg avail i22 seg avail o22 seg avail i23 seg avail o23 seg avail i24 seg avail o24 seg avail i25 seg avail o25 seg avail i41 seg avail o41 seg avail i42 seg avail o42 seg avail i43 seg avail o43 seg avail o44 seg avail i44 seg avail o45 seg avail i45 seg avail i46 seg avail o46 seg avail i48 seg avail o48 seg avail i49 seg avail o49 seg avail i50 seg avail o50 seg avail i51 seg avail o51 seg avail i52 seg avail o52 seg avail i53 seg avail o53 seg avail i54 seg avail o54 seg avail i55 seg avail o55 seg avail i56 seg avail o56 seg avail i57 seg avail o57 seg avail i58 seg avail o58 seg avail i59 seg avail o59 seg avail a31 mac 31 a32 mac 32 a33 mac 33 a34 mac 34 a35 mac 35 a36 mac 36 a41 mac 41 a42 mac 42 a43 mac 43 a44 mac 44 a45 mac 45 a46 mac 46 a47 mac 47 a48 mac 48 a49 mac 49 a4a mac 50 a4b mac 51 a4c mac 52 a11 mac 11 a12 mac 12 a13 mac 13 a14 mac 14 a15 mac 15 a16 mac 16 a21 mac 21 a22 mac 22 a23 mac 23 a24 mac 24 a25 mac 25 a26 mac 26 a27 mac 27 a28 mac 28 a29 mac 29 a37 mac 37 a38 mac 38 i61 seg avail o61 seg avail o60 seg avail i60 seg avail a2a mac 30 i26 seg avail o26 seg avail ab0 mac 80 ab3 mac 83 ab4 mac 84 ab2 mac 82 ab1 mac 81 SndFrmT sfT INT 0 sfT RcvFrmT rfT INT 0 rfT DrpFrmNw dfN INT 0 dfN DrpFrmT dfT INT 0 dfT PBB0 SWB4SWB4 PBB3 SWB1-2SWB1-2 PBB4 SWB1-2SWB1-2 PBB1 SWB1-2SWB1-2 PBB2 SWB1-2SWB1-2 SW11 SW4SW4 SW12 SW4SW4 SW21 SW4SW4 SW22 SW4SW4 SW23 SW4SW4 SW42 SW4SW4 SW41 SW4SW4 SW45 SW4SW4 SW43 SW4SW4 SW44 SW4SW4 SW31 SW4SW4 SW33 SW4SW4 SW24 SW4SW4 SW32 SW4SW4 c11 SS c12 WSWS c13 WSWS c14 WSWS c15 WSWS c16 MWSMWS c21 WSWS c22 WSWS c23 WSWS c24 WSWS c25 WSWS c26 MWSMWS c27 SS c28 WSWS c29 WSWS c31 SS c32 WSWS c33 WSWS c34 WSWS c35 WSWS c36 MWSMWS c41 WSWS c42 WSWS c43 WSWS c44 SS c45 WSWS c46 WSWS c47 WSWS c48 WSWS c49 MWSMWS c4a SS c4b WSWS c4c WSWS c37 SS c38 SS c2a SS
Essential declarations colset sfrm = product nfrm * INT; colset frm = product mac * mac * nfrm timed; colset PBBfrm = product mac * mac * mac * mac * nfrm timed; colset seg = union f:frm + avail timed; colset PBBseg = union b:PBBfrm + bavail timed; colset swi = product mac * portnum; colset swita=list swi; colset PBBswi = product mac * mac * portnum; colset PBBswita = list PBBswi; colset qfrm = list frm; colset xfrm = union cf:frm + bf:PBBfrm; colset qxfrm = list xfrm; colset pqxfrm = product portnum *qxfrm;
Recursive ML functions fun eqa a (rr:swi)=((#1 rr)=a); fun eqaB a (rr:PBBswi)=((#1 rr)=a); fun eqbaB a (rr:PBBswi)=((#2 rr)=a); fun grec prd [] = (0,0) | grec prd (q::r) = if prd(q) then q else grec prd r; fun xrec prd [] = [] | xrec prd (q::r) = if prd(q) then r else q::(xrec prd r); fun grecB prd [] = (0,0,0) | grecB prd (q::r) = if prd(q) then q else grecB prd r; fun xrecB prd [] = [] | xrecB prd (q::r) = if prd(q) then r else q::(xrecB prd r);
Ethernet switch (dynamic table) Timer mact InP1 In/Out seg In/Out OutP1 In/Out seg In/Out Buf1 pqfrm 1`(1,[])++ 1`(2,[])++ 1`(3,[])++ 1`(4,[]) SwT1 swita [] qport1 INT 1`4 myport1 portnum 1`1 InP2 In/Out seg In/Out OutP2 In/Out seg In/Out myport2 portnum 1`2 InP3 In/Out seg In/Out OutP3 In/Out seg In/Out InP4 In/Out seg In/Out OutP4 In/Out seg In/Out myport4 portnum 1`4 myport3 portnum 1`3 ClrSwTa [List.exists (eqa target) x] Port1 portport Port2 portport Port3 portport Port4 portport targetx xrec (eqa target) x
Ethernet switch port SwTa In/Out swita In/Out PortIn In/Out seg In/Out Aux1 frm Buf In/Out pqfrm In/Out PortOut In/Out seg In/Out qports In/Out INT In/Out myport In/Out portnum In/Out Aux2 frm fnum INT timer Out mact Out NewSrc [not (List.exists (eqa src) x)] OldSrc [List.exists (eqa src) x] NewDst [not (List.exists (eqa dst) x)] OldDst [List.exists (eqa dst) x, i=(#2 (grec (eqa dst) x))] Out @+1 BroadC [i<=q] clean [i>q] x (src,m)::x f(src,dst,nf) f(src,dst,nf) (src,dst,nf) (src,dst,nf) (src,dst,nf) x (src,dst,nf) if i<>m then 1`(i,qu^^[(src,dst,nf)]) else 1`(i,qu) f(src,dst,nf) avail (src,dst,nf) 1 (src,dst,nf) i if i<>m then 1`(i,qu^^[(src,dst,nf)]) else 1`(i,qu) i+1 q m (src,dst,nf) i q (m,(src,dst,nf)::qu) x x avail avail m m src@+TCL (m,qu) (i,qu) (i,qu) m
PBB-port SwTa In/Out swita In/Out PBBIn In/Out PBBseg In/Out Aux1 PBBfrm Buf In/Out pqxfrm In/Out PBBOut In/Out PBBseg In/Out qports In/Out portq In/Out myport In/Out portnum In/Out Aux3 PBBfrm fnum INT timer Out mact Out Aux2 PBBfrm mymac In/Out mac In/Out dfPBB dfN INT 0 dfN NewSrc [not (List.exists (eqa bsrc) x)] OldSrc [List.exists (eqa bsrc) x] NewDst [bdst=BC orelse (not (List.exists (eqa bdst) x))] OldDst [bdst<>BC, List.exists (eqa bdst) x, i=(#2 (grec (eqa bdst) x))] Out @+1 BroadC [i<=q] clean [i>q] NotMYbdst [bdst<>mm] MYbdst [bdst=mm] x (bsrc,m)::x (bsrc,bdst, src,dst,nf) (bsrc,bdst, src,dst,nf) x if i<>m then 1`(i,qx^^[bf(bsrc,bdst,src,dst,nf)]) else 1`(i,qx) b(bsrc,bdst,src,dst,nf) bavail (bsrc,bdst, src,dst,nf) 1 (bsrc,bdst, src,dst,nf) i if i<>m then 1`(i,qx^^[bf(bsrc,bdst,src,dst,nf)]) else 1`(i,qx) i+1 q m (bsrc,bdst, src,dst,nf) i q (m,bf(bsrc,bdst,src,dst,nf)::qx) x x bavail bavail m m bsrc@+TCL (bsrc,bdst, src,dst,nf) mm mm i i+1 (i,qx) (i,qx) (m,qx) b(bsrc,bdst, src,dst,nf) b(bsrc,bdst, src,dst,nf) (bsrc,bdst, src,dst,nf) (bsrc,bdst, src,dst,nf) (bsrc,bdst, src,dst,nf) (bsrc,bdst, src,dst,nf) m
C-port SwTa In/Out PBBswita In/Out PortIn In/Out seg In/Out Aux1 frm Buf In/Out pqxfrmIn/Out PortOut In/Out seg In/Out qports In/Out portq In/Out myport In/Out portnum In/Out Aux2 frm fnum INT mymac In/Out mac 1`21 In/Out nPBBp In/Out PBBportq In/Out timer Out mact Out NewSrc [not (List.exists (eqaB src) y)] OldSrc [List.exists (eqaB src) y] NewDst [not (List.exists (eqaB dst) y)] OldDstMy [(List.exists (eqaB dst) y), (#2 (grecB (eqaB dst) y)=mm), i=(#3 (grecB (eqaB dst) y))] Out @+1 BroadC [i<=q] clean [i>q] OldDstNotMy [(List.exists (eqaB dst) y), (#2 (grecB (eqaB dst) y)<>mm), i=(#3 (grecB (eqaB dst) y))] y (src,mm,m)::y f(src,dst,nf) f(src,dst,nf) (src,dst,nf) (src,dst,nf) (src,dst,nf) y (src,dst,nf) if i<>m then 1`(i,qx^^[cf(src,dst,nf)]) else 1`(i,qx) f(src,dst,nf) avail (src,dst,nf) 1 (src,dst,nf) i if i<>m then if i<pbp then 1`(i,qx^^[cf(src,dst,nf)]) else 1`(i,qx^^[bf(mm,BC,src,dst,nf)]) else 1`(i,qx) i+1 q m (src,dst,nf) i q (m,cf(src,dst,nf)::qx) y y avail m m mm mm (src,dst,nf) y mm avail if i<>m then 1`(i,qx^^[bf(mm,#2 (grecB (eqaB dst) y),src,dst,nf)]) else 1`(i,qx) pbp mm avail src@+TCL (m,qx) (i,qx)(i,qx) (i,qx) m m
B-port PortBIn In/Out PBBseg In/Out SwTa In/Out PBBswita In/Out Aux1 PBBfrm Buf In/Out pqxfrm In/Out PortOut In/Out PBBseg In/Out qports In/Out portq In/Out myport In/Out portnum In/Out fnum INT mymac In/Out mac 1`21 In/Out nPBBp In/Out PBBportq In/Out timer Out mact Out Aux2 PBBfrm Aux3 PBBfrm Aux4 PBBfrm BCcport BOOL BCbport BOOL dfcp dfN INT 0 dfN NewSrc [not (List.exists (eqaB src) y)] OldSrc [List.exists (eqaB src) y] Out @+1 BroadC[i<=q] clean [i>q] bdstMY [bdst=mm] bdstNotMY [bdst<>mm,bdst<>BC] bdstBC [bdst=BC] bdstNew [not (List.exists (eqbaB bdst) y)] bdstOld [(List.exists (eqbaB bdst) y), (#2 (grecB (eqaB dst) y)=bdst), i=(#3 (grecB (eqbaB bdst) y))] dstNew [not (List.exists (eqaB dst) y)] DstOld [(List.exists (eqaB dst) y), (#2 (grecB (eqaB dst) y)=mm), i=(#3 (grecB (eqaB dst) y))] wrong [(List.exists (eqaB dst) y), (#2 (grecB (eqaB dst) y)<>mm)] y (src,bsrc,m)::y (bsrc,bdst, src,dst,nf) (bsrc,bdst, src,dst,nf) b(bsrc,bdst,src,dst,nf) bavail i if i<>m then if (i<pbp) andalso BCc then 1`(i,qx^^[cf(src,dst,nf)]) else if (i>=pbp) andalso BCb then 1`(i,qx^^[bf(bdst,bsrc,src,dst,nf)]) else 1`(i,qx) else 1`(i,qx) i+1 q m i q (m,bf(bsrc,bdst,src,dst,nf)::qx) y m m pbp bavail src@+TCL b(bsrc,bdst, src,dst,nf) b(bsrc,bdst, src,dst,nf) (bsrc,bdst, src,dst,nf) (bsrc,bdst, src,dst,nf) (bsrc,bdst,src,dst,nf) (bsrc,bdst, src,dst,nf) (bsrc,bdst, src,dst,nf) (bsrc,bdst, src,dst,nf) (bsrc,bdst, src,dst,nf) (bsrc,bdst, src,dst,nf) (bsrc,bdst,src,dst,nf) (bsrc,bdst, src,dst,nf) if i<>m then 1`(i,qx^^[cf(src,dst,nf)]) else 1`(i,qx) if i<>m then 1`(i,qx^^[bf(bdst,bsrc,src,dst,nf)]) else 1`(i,qx) true false true true false true (bsrc,bdst, src,dst,nf) (bsrc,bdst, src,dst,nf) 1 (bsrc,bdst, src,dst,nf) BCc BCb (bsrc,bdst, src,dst,nf) BCc BCb mm y y y y m (bsrc,bdst, src,dst,nf) mm mm y mm bavail bavail 1 1 bavail ii+1 (m,qx) (i,qx) (i,qx) (i,qx) m
Dynamics of broadcasting and QoS
Influence of the record ageing time
Conclusions • Colored Petri net is a convenient and flexible tool for modeling networks • Build State Space for protocols verification • Simulate on prolonged time intervals for performance evaluation • Flexibility and vivid graphical representation • Suitable for developing new networking technology http://member.acm.org/~daze
Next step – parametric models • A model for a technology • A network topology as a parameter • A tag to represent connection with topology • The same structure for any given network • Fast evaluation without redrawing model
Additional reading • D. A. Zaitsev , T. R. Shmeleva, W. Retschitzegger, B. Pröll Security of grid structures under disguised traffic attacks, Cluster Computing, 19(3) 2016, 1183–1200. • Zaitsev D.A., Shmeleva T.R. A Parametric Colored Petri Net Model of a Switched Network, Int. J. Communications, Network and System Sciences, 2011, 4, 65-76. • Vorobiyenko P.P., Guliaiev K.D., Zaitsev D.A., Shmeleva T.R. PBB Efficiency Evaluation via Colored Petri Net Models, Communications and Network, 2010, 2, 113-124. • Zaitsev D.A., Shmeleva T.R. Parametric Petri Net Model for Ethernet Performance and Qos Evaluation. Proc. of 16th Workshop on Algorithms and Tools for Petri Nets, September 25-26, 2009, University of Karlsruhe, Germany, p. 15-28. • Bereznyuk M.V., Gupta K.K., Zaitsev D.A. Effectiveness of Bluetooth Address Space Usage. Proceedings of 20th International Conference, Software & Systems Engineering and their Applications (ICSSEA 2007), Paris 4-6 December 2007. • Zaitsev D.A., Sakun A.L. An Evaluation of MPLS Efficacy using Colored Petri Net Models. Proc. of of International Middle Eastern Multiconference on Simulation and Modelling (MESM'2008), Amman (Jordan), August 26-28, 2008, p. 31-36. • Zaitsev D.A. Switched LAN simulation by colored Petri nets, Mathematics and Computers in Simulation, Volume 65, Issue 3, 22 April 2004, 245–249.

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Modeling computer networks by colored Petri nets