University of Southern California Dissertations and Theses

A framework for worst-case performance evaluation of MAC protocols for wireless adhoc networks

(USC Thesis Other)

A framework for worst-case performance evaluation of MAC protocols for wireless adhoc networks

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RTS Transmit, RTS Receive Transmit Backoff timer expire Backoff 11 Start Backoff time Backoff RTS Recv start Receive 10 Start Backoff timer Backoff WCTS timer expire WCTS 9 Start Defer timer Defer RTS overhear end Receive 8 Receive RTS overhear start Idle 7 Data Transmit , Data Receive Transmit CTS Recv end WCTS & Receive 6 WCTS & Receive CTS Recv start WCTS 5 CTS Transmit, CTS Receive Transmit RTS Recv end Receive 4 Receive RTS Recv start Idle 3 Start WCTS timer WCTS End of RTS Transmit 2 RTS Transmit, RTS Receive Transmit Packet Idle 1 Output event End state Input event Start state Successful Data(row 6) Successful CTS (row 4) Successful RTS (row 1) Necessary transitions (Increase throughput) 0, œ ¶v¿F•;$†`–A‡F–L·\(‡`•‚-„L” ·)• ¯oº )[ ¯ ˙-¿F·‡`·|´·\„] · ”„-·v$”z‡M˚l·¿X¸ ‡`·˙·;„L·‰ ¨ m?0ol’Qwk=’w0knw0+=w 88n8+8QŒı~ $M0ow5w8=8?0{?%’Q&\]=Sz088+0?8 ı)8S,’M0owW0ZQZ8S?01 /0knQwQn’08˛w8 [’Q^I]SR08[88ı)8Sk’w0woU=Æ8Q8,0S?8o 8_ oQ0Roı)w8QŒı~[L8)88ı8Q$\_‘ba Zc U’\0‘da`U c U\9‘Ta U c U 0e\ < ‘TaF c U$0)^f_‘ga U$ c Uh^'0‘Ta`U$U c U8^I9‘ia`U U c U 0+^ < ‘da U; c · ”„L†l·$”z‡N˚n·;¿F¸Z$· ”[†Q‡`•8‡F”z†n• ˙¿X·0‡`·|´R·;„u”?††•0‰;”z† ¨ 8Q1’mm?0 w0’S)o(WıØ0.Q08.m08x0’’ ’w0w0l8 mw Q’ w0oØnuo`N=S[8 ’’,’M0o’’Q ı)0SQ0…`iN\S85’’R’00˛SQ0[0_SQM)0 `QM88)mw +8QQLIUzı~8Sm=’)_0’S;mwz’5%’w0s owl0mSQ 0?8’M0o’88)mwP`w00~’’+ı)8 0+’w0kUo0o8’’v85’M0o~0oM08 ~’’.ı)8k 088’w0o +8QQLIUzı~L8w8Q8Sm=’ ’w0wo.01SQ˛z’mS’=008/D‚‚…§I‚=0>[˝˛§[‚ ?o8 Q~ Qz»Awt8wSm881 ’˛0’0 88j)Qœlkm]on pørqœtsFuwv)ı)8Qw 8mQz,&s2GU’quQ0’zmm’oı)0M 0o8,A 8’w0w.0+S’G[U<u Q’z8’Q88EN=S’[Æz +0 ’’1D~%m88]\8w8n=Qw yxCUyz 08’˛Æ?68{D4‚|x#‚|z~} 8Sł8mIU= ’x+X?8’s?0)mwnLt88» R’00L8?0 j,m8_A`ı)01QzQœn-]on pS$wos?w»’x]n pNC)_m]_?U ]on pSw0os0’x]n pN+–)v‹9‘˜_ 5h U0]on pS+SS?G’x]n pS )n140‘ _ 5 0(]n pS)SS ’x]n pS)l» < ‘ _ 5/5F 08’_mwo0;W8` h 88’_8mmo5’[’w0s o4+FwS5 [mw 8 ª 0’’M’85’kRQQz ø 0oSw’=000’’’w00L$=l&…’x8 ) ~m_88PF 0’C+5SłM08ı)o88GK )8+Qz~Q0R’.Qœ%-0An_w ’x2)a Zc[ U}0tn_N’ ) 0 U%-0An_w)‰’ )a Zc[ 0Z0tn_N)‰’ Q5 ) G0 ?8(FM08ol’’[L Ł ˝ƒYn’ Œ [m_.ı)8l’m’M0o’88 km 0U88~l05’S8n-omw0.M088 ’’A Ł ˝MƒW%’G… %*9UR0?8 8’wow5mw08~%’’ L Œ ’º3‚ ?8, 00~wS?8m8,mw5+ < ı)0˛+w8) ’’5Aafi,’ Œ ?8nlw08’’5Aw…_’ ı †+*< +8’’$l88~8$8A`ı)8_Œı~mŒz=Qœ\’ )~0’IU8,’ )4`Q„ ¸}w˝,’’ &s˛0,’’IU=o88,=QLwo0.8_L0S[ı)0>wI`/¸[·*˝ ’’_\QwAwkm0[0,L0S 8Słm;IU…5o0’’,ı)0 º £ Œ B ¢ …/’LısL’?0S?)v~mS5Æ8’’,kı)wl88ı 0.S8mo 0’S\QR+~8 8LFı)85ıvnŒz=Qœ ’ )8mQ;U?0˘’ )mQ oQ~Qz~.QzvLvı)0M.5S’=008 mQw008oı)0˛88 om?0$8wQ5Œz=oQw ’ )) D4‡?¿¿*D„ D4§,mQl5w80’ ıv_Ln’okQzn’?QQ0n0Z5800w’ ı)8 8lQz,?QQ0w[U| UGº £ Œ B[mQ ’ ),P„D‡;¿2¿“DwD·§ImQMo80’ Sz’8mQS’[8mw088U= U ı †+mQ ’ ),\[48˝8oQU= U mQ l8SwÆ=8w0o)8m0w’?S Æ U k 0’z)8 8SM0k’m’’U8QR+.mXwÆ~$80’S8U’=S z?= Œ U{B Œ U0cLB Œ 88’8mQU)000wSmQU0488 80SmQU’=S ’˛0 Ł ˝ƒYmlØ0’’0•‚~m 0QR m801’’U/º £ Œ B ¢ …15S_Æ;8’ º £ Œ B mQ 1800w˛mQ[[kQ˛w800w’(Æ?(SQ058 S’=008 t 0 t 1 =t 0 +d t 2 =t 0 +a r t 3 =t 0 +d+a r RTS 1,0 -TS RTS 1,0 -RS RTS 1,0 -RE RTS 1,0 -TE Event: Timeline State of Node 1: State of Node 0: Tx Idle Tx Wait Idle Tx Rx Rx Event History: RTS 1,0 -TS @ t 0 , RTS 1,0 -RS @ t 1 , RTS 1,0 -RS @ t 2 , RTS 1,0 -RE @ t 3 State History: Node 1: { <Idle, _, t 0 >, <Tx, t 0 , t 2 >, <Wait, t 2 , _> }, Node 0: { <Idle, _, t 1 >, <Rx, t 1 , t 3 >, <Tx, t 3 , _> }, Node 2: { <Idle, _, t 1 >, <Rx, t 1 , t 3 >, <Defer, t 3 , _> } Time relations: 1. t 1 =t 0 +d 2. t 2 =t 0 +a r 3. t 3 =t 0 +d+ a r State of Node 2: Idle Defer Rx Rx 8_ ª œ º ”u•\‡F–L´†m·•˙-¿F·‡`·|´·;„u”?††•0‰;” £ Œ B 05 ’z)mw+’w0[Æ,8_0’S &Œ+ıv) L`ıQœ%8=kS?0lnwQ+L08Q`Q+A+0?8jU0?8Q;’w0ov Œ B8’8Am88j4U%M800nº £ Œ B mQn’ınAn8 £ Œ B Lj #\˛S8m8 Œ B8’0A[U88j’w0k+ £ Œ B˘’’?0) ’88( Ø`Qw0w8u8 Œ BCUu8?0˘•8QLQwoQSwk’u8w08+Æ? 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" Q[Æ=n8mm0zmm1SQ ’=00v[0QSL0oS8l`?(’x02)0<q Æ=0’ m8’M0o’’Q ’=00n0S8 M’l’w0ou0=00’’M0ol8˛U~8ıv˛8 0 ‡ ˘ ¿X·;‰ ˘ ˙ ‡ œ )48088‘ q ’ ) &k8~m88Um88’~8)o~~L.z’08oSQ’nw0QS’x0nS )0WwQ 818kSł8m0’S\-]UØm ÆzwÆł0R’ ØÆ; ? q480’o8˛zm’M0o’’Q.’=00lL 8’o w -n’w0kl’58)o|0QSL00SQ0k 8`ı)8mz )’0~= 8`ı)8mz%’%wXz0w8Q’w0woU8m%Aw0QS’x0SQ8 [%Q’wo’’0k08`ı8mz+S00Q˛øq 8+ÆMsSn+’ 8Qw’n85)*SwkoXł8oWVQ?q +?08QM8kıvw’Q’n888;8 S0wR 0088[)iSwn,’ 81kXłn0œq o88 S0w+0+ıv8Qw’ ¯ •;–A¿”z†† ¨ (o8 0 •–L¿$”?†† 0)’?S--Æ’?Q’ 8)w08;Æ08ı)83*¶‡‚2¸[ƒG ª 8 0)_Sw_’nSł80Æxw8w|00?8 08o000w0)QX?00=00Œ’1’M0o0 l0 851S0M.’ Sł0Æ]‡†[·}DwD5010001500QSL0Alm’n81+88?0_0 0’n000w0m 8mS0w[0 0n,ol~8m88oQS’x0 &s08Sł -00LM88 0˛Qœ &s08Sł.%00LM8?‘ _Æ=Q+88+00w0QS’x0=[000 $?0_Æ=Q880)0’000 ’ ) )’n0 00SłVQQw.Q’zk\QwASxwS0w 08Sł[ ’k’ Q0’z_L_S0w588,8[000kw.00w0QS’x0 &00Sł Æ\QŒı~Qm0 L)owS0wm0)Sł0Æ08xw8w BDCFEDCFE GÆV%ßO~N‰M!&J˜MfO˘C Q MIRTG Q C Q N%O -8 0’z8Q_Sm=8zl8AMmQı~w oQ’wU,0M 888;8[U8)Æ’Sn’k8QM’5S0M+0˛’o0,ı~M’)Q’5X0,A 8_mQ’w nw0Q50ÆMsSl08l8_LFı)8m’’Q ’ )888;8[U Implication Algorithms Search Algorithms Topology Search Tree Consistency report State, event State, event, time relation State, event, time relation Wanted_states Initial partial scenario Target event identification Performance Objective Function Target events Wanted_state generation Protocol Transition Table Wanted_state Generation Test Scenario Generation MAC Scenarios -8_ œ ”z‡`•–x„~´·;u˙·\$”\‡`†o·;·\$¿1¿X•u”R˚l·¿X¸ ı~ w’’w0AwJ+z’km0’S$S0[+ı~5oXłoWVQ,˛’Q’’Q)[w8Q ’10Qw’oS0w’[o0n08w888 .’= mQAQ 8oS0000,mQQ,85’08ÆsSo/‚w˝ D‚‚D ˝ˇ•\‡F” †‡`•8‡`”?†[‰”|— ”z¿X•8‡F–L·; 0w?S00m’w0’Lwo_8o0w’?S~=QAMo0SoÆ’S1R’ıvz’ ’’ ’ ) 1’QıR’ ’’1’=IU=8 ‡`”z†‡1†´R”?•0¿–A· ‰”$”?¿F•0‡F–L·; w0J8Qw’,Sw0oXłoWVQn8’08[Æ’SIU|ı)w 8wU=o0oWVQ 888;88’\ ˝ˇ•\‡`” †Q‡`•8‡`”?†‰””z¿X•8‡F–L·; ¨ +01ız’ ’m8QwØw0 wn0 ı ‚6fiw4§m50˘‚I¥[‚G[§‚ÆuWSq u#Xz0 )’[0 8kQmQz ı I‚3fiw4§n_8’;8nWFı ø +81’w0wWÆ;.’z’Z -8 ? +8w0 8[0’lÆwzıw[’wM[’w0YX?8’n0Qw’,8’w 0)8S(’LFı) ø U ª U\0 [8 8?)v’1’wQ8_wQQz ’50 Inputs to test generation Node 0 in BOCOL Node 0 in Defer2 Node 0 In BOFT Node 1 in Defer1 Node 1 in BOCOL Node 0 in Defer1 State descriptions: Node 0: starts in Defer1 at time t 1 , ends at time t 2 Event descriptions: Relations between time variables: t 1 < t 2 Initial partial scenario E 1 (E 2 ) (E 3 ) (E 4 ) (E 5 ) (E 6 ) Node 3 in BOFT (E 16 ) … 0_ ø œ ;-–‡X–A•;„~˙-•0¿F‡F–L•„~†´”$•0¿–L·†.·¿.‡ ˘ ¿F·\$‰ ˘ ˙$‡ 8’w008Sw.’o’MQ+8 ı I‚]fiw4§QRz ~8+’8kÆ’S ’x0’’oQQ8k0_Æ’S?) ?8oL8_’w0w0[U805w08 05Lıw1’ww1’M00YX?8’58QM’I‚*˝ ‚‹CD4‚CD zo|8’ıR’ ’w00+MkQz)’.8Qw’m1S00˛0oQQ8Æ’S 8wn ’x) 0’zıR’ ’’[U; U’Ø0 ı 8†[[~0)00S8w888Æ?10S0q ¯ †´R”?•0¿–A·4‰;”?”z¿X•8‡F–L·\ ¨ `ı ı) 8k?8Fı)8kvız’ ’_05=S 0WVQ5888;8[U;0%’8Qw’m8l8Q~1) S0w.0’ ı~w+Q’_8QŒı~8w888[=1&v0w8n8,’’+0Qw˛M0 +0 88,’81’’l8QwZw0£’ )’=IU‰’ )_’wÆ.˜’ ) ıvz’ ’’ w’S0’w0S,0$;S0w1ı~o08,8lz 8?05~8m’wwW’Q eD4[o8 8 ’Qwov8Qıv 8?0l’[U 0’ S|QR0mw0Æ=QıvQ˛0QR0˛’’,’M00Q0R+ Æ=S00_8Qıv +81’’m8QwØw0 wnS0’w0Smv=Æ;k0wS0w 08k8_ıR’ ’005’= 8l ø ’z)8l’Q0| S0w 0vSł8mIUR8Q ø ’QM0w8S~$88’5Æ=)k8|8)Œı~ ıvz’ ’’_ı8 8oÆ’S1’ooWVQl8Qıv8w8888m’= )’0’%;0Q8Q88-;0v’=l8’=Q 5l?S0w ,8Qo’Æ=k’=Q Æ?’Q5’’Q;,8kM0 m0˛8’1w8SU8 w0 0SQ0_ı8 w’5w8S˘’L~S0w6.,0)ı)0M,8.Q’1ı)8 8?0K~<’’ ’ww01mQ0\’x0SwÆ=k’Qv?S0 ? 0 ? 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Search procedures 2. Implication procedures create_tree enumerate create_pred check_exist test_exist specify_scenario bk_implication fw_implication succ_rx supp_timer non_supp_timer -81 œ –L”?¿F•¿F´ ˘ ·o˙-¿F·|´R” $¿X”?†W$†” –xi‡`”z†‡ †`´”?•0¿–L·‰””z¿X•8‡F–L·;i•„L‰·8— ¿X–A‡ ˘ @ ’w0˛Æn8n0’S’x-8m )005=QLwo0SnmQ’w5z’Q’[U 0m8w888˛’x8[ ’x2)“) +0.QlQzon8z D‡Cw4DwD†4‡ƒ…˝I‚ “w4”¿‚l2X’x8[ ’LÆ})“) &su0nQ’IU81QmQzo8z uz0 +8’08Æ’S 30SIU\85M0 w’8Qw’8n0zıvz’’M0 0Z8Ø8Qw’k8ıvz’(’M0 8˛ ’x;)m0’zm8’[’M0 8,Sł8mIUz2>’xw0QS’x0%22)4U%?0z m0Qw’W,0zıR’ ’w00-~ı)wn0’Æ=m ’[’wQ,8mwQ,QRn2X) #+ ’x000QSw’L\)4U0#+0˛2’x8w˛-)v,8Qw’ ıR’’w0 0Rı)0MwMkQz’[mQQ8’8[Æ’Sl~ooWV0m888;8 -8 ’x)~0’zv88’8v$0vız’ ’8Qw[M0 +8Æ -8 ’x)n’zoıR’ ’w00nı)8ow’?Q’ 0zıvz’(0 ıvz’S00 ’k05 0Sł8mIU8mıR’ ’’.8Qww0 8Qw’L8ıR’˛S00U?0oIUW £ UW Œ U ı †[F0 ı † R. 8’,S000n0’Æ=, ˛w8Q)’kmQQ+8’08.ÆsS «v 3CzPyQ…|*~yQ|z*~‰y‰~\|“zÆ> -8 ’z8Æ;?wk0M $8’’8QwLwmQıv &8;8’l8 AwoQı~ow)8’w0oÆ]U8Qıvo’=<\QUz8’Qv|ıvz’S00 0’M0[U|0 85w0Æ=QıvQ 8lıvz’0 0zıvz’ ’w0w0 +0 ’Œı~oSo\0R8’0ıvz’ ’’8QwM0 +8’’8Q’ w 0’8’’,Sw0,mQQ8,08˛Æ’S +8nLwmQıv 08QlÆ008lÆQœQ’ )’wwU’ )mQU;h’ )80w’Q ww w0t?0mQw’nw0880WS’n0WkR08o’MwW’wQ &smQ w0e0Qw88o’’10 0’S%Qz50’ı)wQÆ\m0YXz08Q’Q’ o8.Aw 0’[U0Qz+01m0wQ0’z’Æz1n’Q,881M8 S0’’S185’Q50?8 &s0S0’R+’wQ588)w_0w8 )8,mQ0 0’ ’[00Sl8oSoSł8v’Mw )QQw8[U$ı~wsQ’kwRonSm;Sł =zk’Mw1w000Qw’ •„x„-†´”$•0¿–L·† ’xm8nı)0woıv0Qo’ 0m8 ı~w+Q’?))ıv`?m0MSQk 80’U0ı~58QoQ+%88wQ ’nS’)08??l0v8’wM1w08Qw’8ı~wvQ’Sw5 0wSQ;m 0Q80w’Q~1S[ ßz l~’M00YX?8~’5w00S8ww SmSł8 0’zv.`Qw?Qı$8’v0Qww k0v’S 5’Q vız’S000,0W’w00[U$ıv M’,SRQw58’[;Sw˛0 Q0’z.8QŒı~wS0085’= &0’’QU\ı~l0˛88wQ ’o0885’ww’k8QM’5S000’kmQQ8)’8kÆ’S _80 ’ww0Wm;Q00_8Q,’8oıvw’1’L_Æ=’4)Q.S0M[,0w8 Æ\Q’˛,0S’’0S 8.’Mw/0 oQ w0koıv(kLFı)o’ 8Qw’8ı~wwS0w 1z1.5;SwMUı~’’m0’m8Qw 00YX?8m8Lwou00[Æ?ıvMu0uLıvMm;Q00kz 80So8 8Qw[0Awkoz+81Sł’+18_Sw3’x08’.’m8Q)Q|X Implication Algorithms Search Algorithms Topology G Transition table F Search Tree T MAC Scenarios O Consistency State, event State, event, time relation State, event, time relation Search Heuristics Wanted/unwanted transitions, Relations between wanted and unwanted transitions Initial partial scenario -8_ œ ¶ ˘ ”˙-¿F·;˙·†`” ‡`”?†Q‡o‰””z¿X•8‡F–L·;•„L‰·;¿X–A‡ ˘ ª 04)4Uıv+w0mı)8Q0Q%8+8Qı)58Qw’.8Lwol05Sł8’%l0+S0w ,088Lwo18Swm$ıvQ˛S M 08z0+8.Sł o8Sw 40)08588Lwok’n0SwMUı~M8.Az.SS )0S0w’’0S.Æ\QŒı~QSł’8m0˛0Qı).8˛8Lwo &ŒoSSSł[U8ı~ 0w088,S0M 8Qı’IU[[zIUı~,M8[$z1-v0w8S’w+Sł 8S0w %ł8’’0S.)˛0w8S’\’’ _8kzuW81S0w &Œ8 RŒm8z80`)Rl0w8S’vl8)SwMUıv)n0’0’L5 _8_MUzl8 ’wwo’QIURıv)S’w0n0?8;8+wS0w,Æ?lS8QQl=Æw8S);8 08SvLQQ0E0’ oz118S0w )z0v80w?Sv-mQ 0zmQw[Sz?8+0z=\R+18,Swm0’ &s80w?S Słw8ow8S)[’MwU;ı~_’_88M’Qv’kw00S8_ww ’S,’1mQQ+8 ’08.ÆsS ?S0~ ? 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’x2)0R8n08Sw’w8’m0’0 [zQ8w0 Æ? ´¿X”?•8‡`”R—w˙¿X” 0S08 ’oLfi8m’w0w Æ3’x0k )0_ z0Œı~[0w8S’wœ0w8S’,Fı Q0’z’w0k ı)8 0o8?0mS_;Q_L 8QQ;U08S’5 `ı wQ0’z,˛wQ’w0o + +?00’kŒı~08Sw,w0 w[88QœD8_00+8_“98Fı)˛-8_ ? ’LÆ}) v08Q8,’Q58?0’_0 8o ø? +8o88m[x0’=Q S0w˛,z, 0kS0w #0’ U?08Svl-88 -88’z5’+S0wl0 0+’o8Q8Qıv[’’ ø RTS-TS 1,2 @ t 3 Pkt 1,2 @ t 3, 1: <Idle, _, t 3 > 1: <Tx, t 3 , _> BOTE 1 @ t 3, 1: <BOFT, _, t 3 > 1: <Tx, t 3 , _> T 0 T 01 : Adds to T 0 : Pkt 1,2 @ t 3 , 1: <Idle, _, t 3 > 1: <Tx, t 3 , _> T 02 : Adds to T 0 : BOTE 1 @ t 3 , 1: <BOFT, _, t 3 > 1: <Tx, t 3 , _> a) Predecessors of unjustified entities of tree node T 0 b) Enumeration of T 0 creates 2 branches rooted at T 0 8w_ œ |-”?¿F•0‡F–x$‰´ ˘ –x„ $· ”?†I H e : RTS-RE 1,2 @ t 1 , RTS-RS 1,2 @ t 2 , RTS-TS 1,2 @t 3 RTS-TE 1,2 @ t 4 , WCTST-TS 1 @t 4 , Pkt 1,2 @ t 3 , SOI: t 1 = t 0 – q r t 2 = t 1 – a r t 3 = t 2 – d, t 4 = t 3 + a r d < a r PL s : PL e : PL SOI : T 01 H s : 0: <Defer1, t 1 , t 0 > 0: <Rx, t 2 , t 1 > 1: <Tx, t 3 , t 4 > 1: <WCTS, t 4 , _> 1: <Idle, _, t 3 > 8w_ ø œ „L”z•0$· ” ¨ ·;$‡`˙ ‡o†´R”?•0¿–A·„L”z• –x‰W‡`· . 0 –x(…)–L‰\$¿X” Ł ˜z X •8Y; kz0nSw’,o80M0880&=8’’~Sw0R’ u-81 ø? ’1n0w8˛81o80M ıv1QZQ8QM’10.’’ S0Ml0n’ 01wQo0~S0w 050’.8[Sw u 8QŒı~.n0’U U0sŒ1 ø? 0’0& •„x„ oSw~’nSm;)8 8088,w00Su)8S0M[U0u8Z8’858[S0w0m0 ’[8oıvw’0880 +?08QM8[8mıvw’,Sw˛00’5, X?0’oSł0’1Sł85SmQ’,’Mw ’S ˝e–‡ ˘ ˘ ”$¿–L†Q‡F–L´† ¨ n808[UF8’’8Qwlw0 w’-S0’’w0S -=Æ;5 ;%S0MÆz 00180w’Q -8o ` 0R8 w-M8S+0%0w0ˇ’S%’8Qw’)nS0M &Œ;8w0 0nX.wS0wnÆzkSł?w850vw8SIU8vQ=v8S0wl08 ’ı~M’08808[X 8Qı)IU\SRz8ı0n’S M8SIU 0˛m m0’nA`ı)8kŒı~˛80w’Q)ı)0_w8?00|;-S0w108Q 1’’.0_ıvw’Q’nwS0w -w’[U;o81’Qw0nıvz’ ’’[U ıvw0z’ 8 ’’. ’u8 oXł85 k,m2’x4) #w8W0 88M’Q[Uo8_ıR’1’’[U?ıv)0SQoım8 w’M8S £ ?N 0U|m0’Qw0o88[U=ıvmw8?’o885ı 08Q88n0QQm`Q_ 88ı)˛`ıvQ)88,8QQ 8 `z ’x2) 0R|0w8S L808=’+’’$8Qw5w0 &Œ 0’38w ’,M8?’8 £ ’’+8ıR’mS0l0m38w l’kM8?’588 )8S8o0?8IU0)0+88_88ı[08 880QQm8n8M8S$0?8U U8n0 ? 8 `z ’LÆ})~0w’R–. = U 8 M’+0;;|S0Mmı)0M[+08v’o8,’’)8Qww0 Input to test generation Node 1 in BOCOL Initial partial scenario E 3 Apply Heuristic 1 fi BOCOL Apply Heuristic 2 fi Node 1 Node 0 in BOCOL Input to test generation Node 0 in Defer Node 0 in BOFT Node 1 In Defer Node 3 in Defer Node 1 in BOCOL (a) Choices from the input (b) Initial partial scenario with heuristics State descriptions: Node 1: starts in BOCOL at time t 1 , ends at time t 2 Event descriptions: Relations between time variables: t 1 < t 2 (E 1 ) (E 2 ) (E 3 ) (E 4 ) (E 5 ) (E 12 ) … -8_ ` œ ¯ ·;†Q‡`¿$´‡X–L‰–L-–A‡F–L•„~˙•0¿F‡F–L•„v†´”•0¿X–L· X ˚.–A‡ ˘ ˘ ”$¿–L†Q‡F–L´†IY; +8w w’~S;v80\S0w5’$ _ U8?~ 0ww ’Q10’z’01 ? ’x2) SwMUı~1=QLw mQA QQ[Qz0’’n8k)8_oQ?S8008Qı8Lwo z’01Sw ˛’’ı)8ZmQ058 0n0z8Qı8Lwo 0’z0oQw81w8S 8n ? ’LÆ}))0’z)0 M’)885ı)0M v8Qw’˛A 8wz88A’Q+w000~-mQ001?0mQw & 0nS0MMU SwWfl–'* _ n 0 †m 9 n <.o0?8 0l ’n m_0+ı0˛08w8’_nO0Um0n_U;0‡fl·2_nO0 )’50)ı888 88M’Q8oM0e8Q0’8Qw’k Sw,0Som8 ’˛8QM’k8mıvw’_QkS0w /l8k80w’Q8˛0,0wz’Qk0 8 w’S0wkı)|Æ=_0k8Uıvm0nÆ’Q 0oz˛8nQ’ı~ 0`_’00 H s : 1: <BOCOL, t 1 , t 0 > 1: <WData, t 3 , t 1 > 2: <WData, t 2 , _> 2: <Tx, t 6 , t 2 > 1: <Tx, t 7 , t 3 > 3: <WCTS, t 8 , t 4 > 3: <WCTARx, t 4 , t 1 > 3: <Tx, t 1 , _> 2: <Rx, t 10 , t 6 > 1: <Rx, t 11 , t 7 > 3: <Tx, t 12 , t 8 > 0: <Tx, t 13 , t 9 > 0: <WCTS, t 9 , t 5 > 0: <WCTARx, t 5 , t 14 > 0: <Tx, t 14 , _> SOI: t 1 = t 0 – B c t 2 = t 1 – d, t 3 < t 1 , t 4 = t 1 - a c , t 5 = t 3 + d - a c , t 6 = t 4 – d, t 7 = t 5 – d, t 8 = t 6 – d, t 9 = t 7 – d, t 10 = t 6 - a r , t 11 = t 7 - a r , t 12 = t 8 - a r , t 13 = t 9 - a r , PL s : PL e : RTS-RS 2,3 @t 0 , RTS-RE 2,3 @t 1 , CTS-RS 2,3 @t 2 , CTS-RE 2,3 @t 3 , Data-RS 2,3 @t 4 , Data-RE 2,3 @t 5 , PL SOI : t 11 £ t 0 £t 7 , t 11 £ t 1 £t 7 , t 11 £ t 2 £t 7 , t 11 £ t 3 £t 7 , t 11 £ t 4 £t 7 , t 11 £ t 5 £t 7 , H s : 1: <BOCOL, t 1 , t 0 > SOI: t 1 = t 0 - B c PL s : PL e : PL SOI : T h 0 (a) Tree root node T h 01 (b) First valid scenario reported as an output scenario H e : CTS-RE 2,3 @t 1 , CTS-TE 2,3 @t 2 , WDataT-TS 2 @t 2 , CTS-TE 1,0 @t 3 , WData-T-TS 1 @t 3 , CTS-RS 2,3 @t 4 , CTS-RS 1,0 @t 5 , CTS-TS 2,3 @t 6 , RTS-RE 3,2 @t 6 , CTS-TS 1,0 @t 7 , RTS-RE 0,1 @t 7 , RTS-TE 3,2 @t 8 , WCTST-TS 3 @t 8 , RTS-TE 0,1 @t 8 , WCTST-TS 0 @t 9 , RTS-RS 3,2 @t 10 , RTS-RS 0,1 @t 11 , RTS-TS 3,2 @t 12 , RTS-TS 0,1 @t 13 , CTS-RE 1,0 @t 14 , Data-TS 1,0 @t 14 , 8_ œ º ´R”?•0¿–A·Z‰””z¿X•8‡`” Œ¿F·\ ‡ ˘ ”†`”z•0¿X´ ˘ ‡F¿F”?”¿X·|·0‡.†`–x‰ ˘ ”?¿–A†‡F–L´†I ø «v* ˆ˜…} ,zQ¶·• x8‚„‚‚ ”y»,«vwu‰u ;~\| 5 *|w}…/ÆQ~L‰ z¿ @˜~‰|87L &~ -Æ’low8w0885QS~w8o +8w088QS Æ’WÆ=z?wQ%00QwQ_0’ 1S00Q8o0’Sow0X 0o˛2,Øı)0w˛)88˛A08,8QıvÆ;’˛ +8+ ~w 8?05oz0JG‚4• ¢ ƒƒWwI‚8*;‚’x!,))mQ’[m0’0lM008’X 0 /0k88K)|$=m&%ız’n’w0k0_’n88GFIU?~’0’~8M008 ’0 &08+w0880L08 05=Qw?˛’x2&C)4U%’0-5’1F00Q8 8+=Qw Œ A~ı)0MmSł=S’,Q)8w0000=-C+l%0QS’x0 ?8 K1w80l mQl’Wk,8=Qw)m’ ıvlL. 488?0 FkwSl-}U+5$!JmQl505w008MU-_wQ_ı)Z wQoW8 8Sł?_Awo. 0Qı)’IU-_0Qw00k wQ 40k008}U 886F w80%,42_mQ’_o8+=Qwl=m’5ıvA 08Q~88 8_w0_%’w0wo’’QSQ8|0’_8!ˇı)˛0_85 [8 -C+[Q 20w8o05=Qw˛ı888n0!iw008MU8QLQwQS ’58w08 488?0QK)S+oÆ=QAw~kmQvSł[U?v’w0o 0 ı)01w0000 )fimQl’ ıvnLo) &))fiLC88(F8zl8 wlı) 0=QwU|883KnÆ,NØ0WSz’00,A,0ow000 #\ SQ0[0mL0?8»KU881F’0+˛)ˇÆ;[’k881K & ’SU ıvm0R,0;Q v8_)ˇS0w8QMLwmQıv 08m&s~ 2(0’S l’_80=’ )8QM’’.8QM’l ’Q~)/wS0wv1=QLwo0SmQ’wQU?LSłoIU88Qıv.888;8~0 LM8 +8))S0w8QwmLwmQıvm’wQ\w-0+’Q=S0wı)0M Qk’nı~M’v0Qıvk0k888;8 ?S ? Q0%80m0 0’00 ø 0 2 1 3 (a) Four node chain 0 2 1 3 4 (b) 3+3 cross 0 2 1 3 (c) 2x2 grid 0_ ?œ ¶v·˙·;„L·‰\–A”?†.†” Œ·¿ ¯ †´”•0¿X–L·Z‰”$”?¿X•8‡F–L·; BDC C C Q M!N”ß—RTG Q C Q N%O #8)8%)ZS0w8Qw5LwmQıv}Uı~8’kQ,0Qw’Q-\) QSwlm’= &sm)\0 ł,& PUıv0’z%8’’Q%%ı~+0v’ Æ0.888;8~0.xw8~l)S0M 8 50’zv8’= ,05ı~10’o’ 8Qw’18.ı~w5Q’)S0w 10kw0’= A,Æ=W?w8Qıv 8088,0WLM8[U$0`ıvQQUı~k’kS_0Ww ’\0[L8n?w)~8808 -8m 0’z1Æ0w) S0w8Qw’1Æ?m8LwmQıvoo_A0~88M0k’\ &k8’wS0w[U 8w`ı)~Q0R~8Sm-)(Sł?’QM0QzL’L U0lQzo0Q’?) 8%SłoIU)ZwS0w,70Q0w’RŒı~_Qz[U8’wQw5L 88’ 8?0 0188QvL 0?8,’l88 ? +o+ 8)Qz)Sł’wS’ A858wSw0˛-05S0Mo8Qw’ Æ?8M0o 5’_88M’Q’ 8Qw’n8_ıvw’Q’5Sw.˛k˛’=[L85˛=QLwoS_mQ’w ø 0 1 2 3 Scenario M 1 0 1 2 3 Scenario M 2 0 1 2 3 Scenario M 3 0 1 2 3 Scenario M 4 0 1 2 3 Scenario M 5 0 1 2 3 Scenario M 6 -8_ œ „x–L‚-¿F•0¿ ·; ¯ †`´”?•0¿–L·†k‰;”?”?¿F•8‡F” –x Œ·;¿[$· ”´ ˘ •–x ‡F·˙·\„— ·‰ -8v ’x2)0’z-8)ZS0M08+’8vıvw’%Q’8Qıv5888;8 ª 88kM0’= 8k ’LÆ}),0R_8kS0M˛8Sw0 &sW0 S0wMU=ı)50?8FlS812f_ª0;U `Qw8M59ª < U 0 N=QwSw ı)0M[Q0’)%0QSL0kS _ª0 0 0yª _ mw 0_ ’x2) 0’zS0w˛081’˛ıvw’,Q’mxw0 $= & &s 0wS0w˛[S 1- _ª0 0[ 9ª <+0?8/F0’ [‹,888;8v8?0]F,0[oXł85 888;8)88]H 8_ ’LÆ)0w’R+8_S0Mo8Sw0 -8, 0’zv8,)/wS0wl005’l8ıvw’Q’8Qıv1888 8m 5, S’\ )’0~508Q0’w0wo5=L8lo 8?0 ’wQwSno80SIUzQ’w0kn=%08 “)888;8 A)=Qw?,Rz)88vSm-8ÆN’’ -8v ª 0’’w’$8vı~wQ’ )WS0w00’+S0 [‹8808 0?8 ,Fł8+w’= «v` yQfi¶P}w ~‰˘zÆQ=Q|?> *@c~\|87 +0n’SØ`8m 8QØ0n0oS0w 8QMØLwmQıv 0 S0w18Qww0klÆ ’Mw ’w0YX?8ı)0M ww 8nı)8 ’S’m8Qw’,’+S0w _0’’QQw=’M00YX?8’m0S8SmSł8. ø State Descriptions: Node 1: starts in BOCOL at time t 1 and end at time t 2 Node 1: starts in Rx at time t 3 and end at time t 1 …. Event Description: Data 0,1 receive start at t 1 CTS 2,3 receive start at t 3 CTS 2,3 transmit start at t 4 CTS 1,0 transmit start at t 5 …… RTS 0,1 transmit start at t 10 RTS 3,2 transmit start at t 11 Time relation: t 4 = t 3 – time to transmit CTS t 5 = t 1 – time to transmit Data t 3 £ t 1 £ (t 3 + time to receive Data) ….. t 11 £ t 10 £ (t 11 + time to receive Data) MAC external Event: MAC interval Event: 0 1 2 3 RTS 0,1 RTS 3,2 BOCOL Data 0,1 CTS 2,3 (b). Scenario description (a). Worst case MAC scenario 0_ œ ˝ˇ·¿X†Q‡1´•0†”‡ ˘ ¿F·\$‰ ˘ ˙ ‡.†´”$•0¿–L·Z–x·\$¿$· ” ´ ˘ •–x‡`·˙·\„L·‰ 0 1 2 3 (a). Worst case MAC scenario RTS 0,1 RTS 2,3 BOCOL State Descriptions: Node 1: starts in BOCOL at time t 1 and end at time t 2 Node 1: starts in Rx at time t 3 and end at time t 1 Event Description: RTS 2,3 receive start at t 1 RTS 0,1 receive start at t 3 RTS 0,1 transmit start at t 4 RTS 2,3 transmit start at t 5 Time relation: t 4 = t 3 – time to transmit RTS t 5 = t 1 – time to transmit RTS t 3 £ t 1 £ (t 3 + time to receive RTS) (b). Scenario description Rx 8_ ?œ ˝ˇ·¿X†Q‡.´•†”Œ•–L¿X”?††o†´”•0¿X–L·–x Œ·;¿1· ” ´ ˘ •–x‡`·;˙·;„L·‰ 0 1 2 3 (a). Worst case MAC scenario RTS 0,1 RTS 2,1 State Descriptions: Node 1: starts in BOCOL at time t 1 and end at time t 2 Node 1: starts in Rx at time t 3 and end at time t 1 …. Event Description: RTS 0,1 receive start at t 1 RTS 2,1 receive start at t 3 RTS 3,1 receive start at t 4 RTS 4,1 receive start at t 5 …… (b). Scenario description BOCOL Time relation: t 3 £ t 1 £ (t 3 + time to receive RTS) t 4 £ t 3 £ (t 4 + time to receive RTS) t 5 £ t 4 £ (t 5 + time to receive RTS) ….. 4 RTS 3,1 RTS 4,1 0, œ ˝ˇ·¿X†Q‡k´R•0†”‡ ˘ ¿X·;‰ ˘ ˙ ‡1†´”$•0¿–L·u–x ´1 ´¿X·††k‡`·˙·\„L·‰ øXª State Descriptions: Node 1: starts in BOCOL at time t 1 and end at time t 2 Node 1: starts in Rx at time t 3 and end at time t 1 …. Event Description: RTS 0,1 receive start at t 1 RTS 3,1 receive start at t 3 RTS 0,1 transmit start at t 4 RTS 3,1 transmit start at t 5 …… Time relation: t 4 = t 1 – propagation delay t 5 = t 3 – propagation t 3 £ t 1 £ (t 3 + time to receive RTS) ….. 0 1 2 3 (a). Worst case MAC scenario RTS 0,1 RTS 3,1 (b). 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A(AŒ37YŒ3L,-.l#Ł_Œ : Identification of MAC Cycles MAC Scenarios MAC Cycles Success/Failure Topology Heuristics Performance Metric Sequence of MAC Cycles Comparison of High Level Scenarios Worst Case High Level Scenarios Enumeration Algorithms High Level Scenarios _ ø8Œ< =\>@?AC)D ¿ CFEGDHALK4A)N ¿@ EG eU DIC8D U\ TD-? S0¿ EGA7LD-?FD ¿XSWV EGA)?K ¿XSLR DIHYA ¿XZ ø%8º‡$0Œ%L,Wc-! ŒJŁ(AŒ ı%L $LØŁØ%Łoø%L,3Œ7Nº p$0Œ%L_nIŁ..Œ3 $0Œ7ŁØŒLŒ.Œ$0Ł,AŒpº‡ŒIŁ,Ł_Œ7.8Œ?7ŒŒIŁ.Œ.v‡yØ%Ł.Œ3 cº p$0Œ%L_ y$0 N.Œ.N#yi_8Œ3ŁQ!A(8-.8Œo.Ł%Ł.Œc8i _!º Œ"AŒ;Ł"c%.gim_dŁ_ŒyŒ&_%Ł,%‘Œ3ŁQ!Œ3Œ ŁØ8ŒbŁ%Ł.ŒNŁ.L%,Ł_%%.jº Œ"AŒIŁ ø8J‘L.Ł.¢$0Ł, #º‡r$0Œ%L,Wcævº‡ &_#AŒ3JŒ"AŒ;ŁlioŒ«W,c.Ł%ŁYŁ.LLL,ı#tNŒ %AŒc.Ł%ŁYŒ$0Œ3Ł_ # NŒ%AŒcæŒ3Ł$_ Œ3Œ.Œ;ŁJß%Ł. n$$0Ł,jŁØ%Łt$3AøL.Œ<.Ł%Ł.ŒŁ.L%,Ł_%#\8-.8Œ n ŁØŒl8Œ3Ł0! A(84 ø8G‘LŁ.L$0Ł, #?Ø, Øx&,Œ"AŒ&$0Œ%L_G%Œz‘.Œ.‡‡ ø8‘L.Ł.L$0Ł_‡#tº f $0Œ%L,"c !Œ8!p.$3øLy‘n$o$0%$0Œ3Ł #æŁØ8Œs8Œ"! ‘LŁ.L$0Ł,·ø%8<#Œ"! ŒAN)&,Œº ’ $0Œ%L," Œ3Łıø%Ł(AŒłº‡ $0Œ%L,’ # ø8x.8Œh$¢ØAŁ.A&,AA , ø8Œ[ni›I_ Ø8!4p º $0Œ%L,Wı„%!a!,ŁØg.&_n.[&_8ŒNLŒ3Œ.Œ;Łl º‡ŒŁ.Œ3 &Œ"AŒIŁ i¢¡po]Łª p_ L.ŁØ%Ł£!,ŁØ.ØŒ.P&8ŒŒ3Œ.Œ;Łyº ;Ł.Œ3 &"Œ"AŒIŁ" ŁØ6$0Œ%L,Wc C ˇZ‹”h“o‚Z¶…Z'“&T¿W•hmØF•h?“`t“fiAfl8fl%‹†fiI§†‡¶fl%“*›¤fl»¶”‰flhfl‰”»¶fiZ›‰…†›‰›‰†‹fi‹¯#¿ •h…“›‰›%¶·“&K O ˇZ‹”h“o‚Z¶…Z'“&T¿W•hmØº¿D“`“fiAfl8fl%‹†fiI§†y¶fl%“*›¤fl»¶”‰flh”%““fl%†‹fi‹¯#¿W•h?…“›‰›%¶·“&K :⁄ 1. Pkt 0.1 triggers RTS-TS 0,1 at t 1 , 2. Pkt 2,1 triggers RTS-TS 2,1 at t 2 , 3. RTS-RS 0,1 at t 3 4. RTS-RS 2,1 at t 4 , Collision at node 1 at t 4 (loss of RTS 0,1 and RTS 2,1 ) 5. RTS-TE 0,1 at t 5 , WCTST-TS 0 at t 5 6. RTS-TE 2,1 at t 6 , WCTST-TS 2 at t 6 7. WCTST-TE 0 at t 7 , BOFTT-TS 0 at t 7 11. WCTST-TE 2 at t 8 , BOFTT-TS 2 at t 8 MAC external event: MAC interval event: 0 1 2 3 Pkt 0,1 Pkt 2,1 RTS 0,1 RTS 2,1 (b). Sequence of MAC events (a). MAC scenario M 1 (c). 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MAC cycles from scenario M 2 Node 0: Failed, destination = 1, time length = a r + BO Node 2: Success, destination = 3, time length = a r + a c + b + a a Node 1, Node 3: Null 1. Pkt 0.1 triggers RTS-TS 0,1 at t 1 , 2. Pkt 2,3 triggers RTS-TS 2,1 at t 2 , 3. RTS-RS 0,1 at t 3 4. RTS-RS 2,3 at t 4 , Collision at node 1 at t 4 (loss of RTS 0,1 ) 5. RTS-TE 0,1 at t 5 , WCTST-TS 0 at t 5 6. RTS-TE 2,3 at t 6 , WCTST-TS 2 at t 6 7. RTS-RE 2,3 at t 7 , CTS-TS 3,2 at t 7 8. CTS-RS 3,2 at t8 9. CTS-TE 3,2 at t 9 , WDataT-TS 3 at t 9 10. CTS-RS 3,2 at t 10 11. CTS-RE 3,2 at t 11 , Data-TS 2,3 at t 11 12. WCTST-TE 0 at t 12 , BOFTT-TS 0 at t 12 13. Data-RS 2,3 at t 13 14. Data-TE 2,3 at t 14 , WAckT-TS 2 at t 14 15. Data-RE 2,3 at t 15 , ACK-TS 3,2 at t 15 16. ACK-RS 3,2 at t 16 17. ACK-TE 3,2 at t 17 , Idle at t 13 18. ACK-RE 3,2 at t 18 , Idle at t 18 _ ø8Œ<W=>¥ƒ>P§ TID? S0¿ E–A X YzS ? ¤ E V TA8? V E V NFD-? V ¥ƒ>P§T ' T U D MAC external event: MAC interval event: 0 1 2 3 Pkt 0,1 Pkt 2,1 RTS 0,1 RTS 2,1 (b). Sequence of MAC events (a). MAC scenario M 3 (c). MAC cycles from scenario M 3 Node 0: Failed, Failed, destination = 1, time length = a r + BO + a r + BO Node 2: Failed, Failed, destination = 1, time length = a r + BO + a r + BO Node 1, Node 3: Null 1. Pkt 0.1 triggers RTS-TS 0,1 at t 1 , 2. Pkt 2,1 triggers RTS-TS 2,1 at t 2 , 3. RTS-RS 0,1 at t 3 4. RTS-RS 2,1 at t 4 , Collision at node 1 at t 4 5. RTS-TE 0,1 at t 5 , WCTST-TS 0 at t 5 6. RTS-TE 2,1 at t 6 , WCTST-TS 2 at t 6 7. WCTST-TE 0 at t 7 , BOFTT-TS 0 at t 7 8. WCTST-TE 2 at t 8 , BOFTT-TS 0 at t 8 9. BOFTT-TS 0 at t 9 10. BOFTT-TE2 at t 10 11. RTS-TS 0,1 at t 11 12. RTS-TS 2,1 at t 12 13. RTS-RS 0,1 at t 13 14. RTS-RS 2,1 at t 14 , Collision at node at t 14 (loss of RTS 0,1 and RTS 2,1 ) 15. RTS-TE 0,1 at t 15 , WCTST-TS 0 at t 15 16. RTS-TE 2,1 at t 16 , WCTST-TS 2 at t 16 17. WCTST-TE 0 at t 17 , BOFTT-TS 0 at t 17 18. WCTST-TE 2 at t 18 , BOFTT-TS 0 at t 18 _ ø8Œ< ; =>¥ƒ>P§ TID? S0¿ E–A X YzS ? ¤ E V TA8? V E V NFD-? V ¥ƒ>P§T ' T U D 1. Pkt 0,1 triggers RTS-TS 0,1 at t 1 2. RTS-RS 0,1 at t 2 3. RTS-TE 0,1 at t 3 , WCTST-TS 0 at t 3 4. RTS-RE 0,1 at t 4 5. CTS-TS 1,0 at t 5 , WDataT-TS 1 at t 5 6. CTS-RS 1,0 at t 6 , 7. Pkt 3,4 triggers RTS-TS 3,4 at t 7 8. RTS-RS 3,4 at t 8 , Collision of CTS 1,0 and RTS 3,4 at node 2 at t 7 (no loss) 10. CTS-TE 1,0 at t 9 , WDataT-TS 1 at t 9 11. RTS-TE 3,4 at t 10 , WCTS-TS 3 at t 10 12. Pkt 2,1 triggers RTS-TS 2,1 at t 11 12. CTS-RE 1,0 at t 12 , Data-TS 0,1 at t 12 13. RTS-RE 3,4 at t 13 , CTS-TS 4,3 at t 13 14. RTS-RS 2,1 at t 14 15. Data-RS 0,1 at t 15 , Collision at node 1 at t 15 (loss of Data 0,1 , RTS 2,1 ) 16. CTS-RS 4,3 at t 16 , Collision at node 1 at t 16 (loss of CTS 4,3 ) 17. RTS-TE 2,1 at t 17 , WCTST-TS 2 at t 17 18. Data-TE 0,1 at t 18 , WAckT-TS 0 at t 18 19. CTS-TE 4,3 at t 19 , WDataT-TS 4 at t 19 20. WCTST-TE 2 at t 20 , BOFTT-TS 2 at t 20 21. WAckT-TE 0 at t 21 , BOFTT-TS 0 at t 21 22. WCTST-TE 3 at t 22 , BOFTT-TS 3 at t 22 MAC external event: MAC interval event: 0 1 2 3 Pkt 0,1 Pkt 3,4 RTS 3,4 (b). Sequence of MAC events (a). MAC scenario M 4 CTS 1,0 Data 0,1 RTS 2,1 4 RTS 0,1 Pkt 2,1 CTS 4,3 (c). MAC cycles from scenario M 4 Node 0: Failed, destination = 1, time length = a r + a c + b + BO Node 2: Failed, destination = 1, time length = a r + BO Node 3: Failed, destination = 4, time length = a r + a c + BO Node 1, 4: Null _ ø8Œ< =>¥ƒ>P§ TID? S0¿ E–A X 5 YzS ? ¤ E V TA8? V E V NFD-? 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N?›EGK0A ¿R ¤ E "V`¿ E ¥ N V EGA)?7A)K\E¢? ¤ D O D-? ¤ D? V ?FA ¤ D 2~„ „!’&’‡·C…%$J„%¶.‡‚=·¶”‡£$J‡ƒ•Z‚’„C<!;”ƒ$(”%.ƒ‡»o‡L.‡l·„.ƒ‡=•Z‚(‡6ƒ„-p…%ƒ,#‹„‚(‰l&F .ƒ7·7‚(‘…·7‡.L„‡‚·¶”‡Y$(”•·7„»„&’„¿`4;·¶”‡Y⁄…‰<‘‡‚|„# $J‡ƒ•Z‚(’„•Z‚¶‡Q”ƒ’¿2”co·¶”ƒnM$•7‡c %7·7‡ˆ•.„#1$J„2‰»¢•Z‚(¿•&&M$J‡ƒ•Z‚(’„w!¨‡.‡⁄·¶,#W´·¶”‡»‚¶„»‡‚¶·¶’‡Q„#•[$J‡ƒ•Z‚’„›’¶·7‡ˆ•. 7·¶•Z·7‡x·¶”ƒ•Z·M!¨‡‡fi»‡$J·T·7„3&F‡ˆ•.·7„·¶”‡<!¨„‚ ¶·M$•7‡j•‰˘„¿•&& $J‡ƒ•Z‚(’„Tn·¶”ƒ£$"&F• "¨C’¿2…‚(‡ ¸ (a) Number of competitors of nodes 0 1 2 3 4 5 6 7 8 9 C 0 = 2 C 1 = 3 C 2 = 4 C 3 = 4 C 4 = 4 C 5 = 4 C 2 = 4 C 7 = 3 C 8 = 2 0 1 2 3 4 5 6 7 8 9 C 0 = 2 C 1 = 3 C 2 = 4 C 3 = 4 C 4 = 4 C 5 = 4 C 2 = 4 C 7 = 3 C 8 = 2 (b) Selecting node 7 as next independent node * * * * =F¿2…‚¶‡w¸-= <UGS TD R D-? V A)KEG? ¤ D O D-? ¤ D-? V ?A ¤ D EG? 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Sƒº EGAeLD-?FD ºXSWV EGA)?+K º A R ¥r>@§ TD-? Sº EGA C’¿2…‚¶‡zˆ˜ni-•I_;»‚¶‡7‡⁄·;•„·¶”ƒ‡‚ ` ˝ $J‡ƒ•Z‚(F„dim _…%¶n¿l!|”ƒn$(”x!‡z(”„!t•„·¶”‡‚ ‡fi•‰»)&’‡„#¿‡‡‚•Z·¶¿˘”ƒ’¿2”^&F‡"‡&$J‡ƒ•Z‚(F„•&’¿„‚(’·¶”ƒ‰$•&&’#C’¿2…‚¶‡tˆ˜niG‘8_»ƒ‚¶‡7‡⁄··¶”‡ ‚¶‡7»‡$J·¶,‡ƒ’·¶A•& ` ˝ $J$"&F‡" „ „·7‡·¶”ƒ•Z·t.‡»‡%.ƒ‡%$J•‰„¿ ` ˝ $J-$"&’‡•Z‚¶‡»„¶‘L&’‡ '·¶”ƒ$•7‡•‡ˆ•$(”e„-.‡$•Z»•‘)&’‡„#¿‡‡‚(•Z·¶¿ ` ˝ $J$"&’‡'·¶”ƒ$”ƒ•—i‹‡W$J‡»ƒ· ·¶”‡‚(F¿2”l·¶‰„¶·b„-.‡_{…ƒ‰‡‚(•Z·¶’„´„#T•&&¨»„¶,‘L&F‡l.‡»‡%.‡%$’‡j•&&’„!Mj…Lx·7„¿‡‡‚(•Z·7‡ ”ƒ’¿2”&’‡"‡&£$J‡ƒ•Z‚’„Y#W‚(„2‰ ›'C’¿2…‚¶‡xˆ˜ni¢$_˘»ƒ‚¶‡7‡⁄··¶”‡^$J„‚¶‚¶‡7»„%.¿‹.‡»‡%.‡%$J ‰˘•Z·7‚(#`+„W‚‡‚¶„˘‡⁄·7‚¶„#=·¶”‡‰˘•Z·7‚•Z·T‚(„!v”o•%.x$J„&F…ƒ‰wjK‚¶‡»ƒ‚(‡7‡l·|•.‡»‡%.‡%$J ‘o‡·Q!¨‡‡L·¶”ƒ‡„-.‡”•%.K\n·¶”ƒ‡’·¶F•& ` ˝ $J-$"&’‡"?C’¿2…‚¶‡1ˆ˜ni¢.)_6(”„!M·¶”‡»„¶‘L&’‡ •¶’¿ƒ‰˘‡l·:„#y7„2…‚{$J‡<i-%.‡»‡%.ƒ‡l·6„-.‡{_•%.^.‡¶·¶ƒ•Z·¶’„%:„#›æƒ„!M‡…ƒ‰‡‚(•Z·7‡.g#W‚¶„2‰ ·¶”‡‰˘•Z·7‚( C’¿2…‚¶‡z»ƒ‚(‡7‡l·|·¶”‡7‡b#W„2…ƒ‚;”ƒ’¿2”&’‡"‡&F $J‡ƒ•Z‚(’„•%.·¶”ƒ‡ˆ’‚4$J„‚¶‚(‡7»„%.ƒ¿l.ƒ‡»o‡W .‡%$J›c¿‡‡‚•Z·¶’„'„# ` ˝ $J$"&F‡"›˙c·¶”‡7‡x$J‡ƒ•Z‚’„"c\•‹$’‚ $"&F‡.7ƒ„.‡‚¶‡»ƒ‚(‡7‡l·• %.‡»‡%.‡⁄·1„-.‡•%.c•g„-.‡l!;’·¶”„2…·x•$’‚ $"&’‡‚¶‡»ƒ‚¶‡7‡⁄·•g.‡»‡%.‡⁄·<„-.‡`—·¶”ƒn$( ¸ 0 1 2 3 (a) MAC scenarios M 1 . MC 2,3 (D i ) (b) Initial MAC cycles MC 0,1 (D i ) MC 1,2 (D i ) 0 0 0 0 1 0 0 0 2 1 0 0 3 2 1 0 (c) 4x4 Dependency matrix Enumeration of non zero entries of matrix (0,1) (0,2) (0,3) (0,1),(1,2) (0,1),(1,3) (0,1),(1,2),(2,3) (0,2),(2,3) (d) Enumeration of high level scenarios 3 2 1 0 3 2 1 0 =F¿2…‚¶‡lˆ˜= SLR5OU D –9~fl EG +U DIC8D U TD-? Sƒº EGAeLD-?FD ºXSWV EGA)?+K º A R ¥r>@§ TD-? Sº EGA › ¸ MC 2,3 (D i ) MC 0,1 (D i ) MC 1,2 (D i ) (a) Scenario 1 0 1 2 3 MC 1,2 (D i ) MC 0,1 (D i ) MC 2,3 (D i ) 0 1 2 3 0 1 2 3 MC 2,3 (D i ) MC 0,1 (D i ) MC 1,2 (D i ) (b) Scenario 2 (c) Scenario 3 MC 2,3 (D i ) MC 0,1 (D i ) MC 1,2 (D i ) 0 1 2 3 (d) Scenario 4 C’¿2…ƒ‚¶‡t= fl E– U DC)D U\ TD-? Sƒº EGA])D?D ºSWV D ¤ K º A R ¥ƒ>P§ TD-? Sƒº EGA7´ •Z‚¶‚¶„!n‚¶‡»ƒ‚¶‡7‡⁄·|•”ƒ’¿2”x&’‡"‡&æƒ„!tC’¿2…‚¶‡zni-•I_|»ƒ‚(‡7‡l·T·¶”‡x”ƒ’¿2”g&’‡"‡&$J‡ƒ•Z‚’„x¶)˜‡‰ »)•‡”¢…3†;nw!|”$(”‡ˆ•$(”^„-.‡;n%7‡‚¶·•<æ„!N˘·¶”ƒ‡‡·Q!¨„‚ (%.ƒ‡»o‡L.‡l·&FC’¿2…‚¶‡sniG‘8_ »ƒ‚¶‡7‡⁄·1¶)˜‡‰»)•‡”m…z!|’·¶”L·Q!¨„3æƒ„!M=?wt-yzT ł •L.wt-yz ł ¨=F¿2…‚¶‡<ni¢$_T»ƒ‚¶‡7‡⁄·1¶)˜‡‰ »)•‡”¢…@·z!|’·¶”·Q!¨„Pæƒ„!M"=:wt-yzT ł •%.wt-yz ł =F¿2…‚¶‡zni¢.)_|»ƒ‚(‡7‡l·<¶)˜{‰"»)•‡”¢…l·¶”ƒ•Z· ¶”„!4¨[|”ƒ„»P$J‡•Z‚(’„Ql!|”$(”3æƒ„!4#‹‚¶„2‰„‡|‡L.n#‹„‚!•Z‚{.‡.w‘˘·¶”‡⁄·7‡‚(‰‡.ƒA•Z·7‡ „.ƒ‡Q·7„ˇ·¶”‡„·¶”‡‚‡L.'„#;·¶”‡x$”ƒ• „ „·7‡·¶”ƒ•Z·˘·¶”ƒ‡7‡•Z‚¶‡·¶”‡g $J‡ƒ•Z‚(’„Q·¶”ƒ•Z·w!¨‡x$• ¿‡‡‚(•Z·7‡x…%L.‡‚·¶”‡x•(…ƒ‰»ƒ·¶’„L!‡<.ƒn$…%7‡.n « ‡$J·¶’„g æ ^ıołøœQßQ—´(œQø øQ 9ıø ı¢Qß c #c´ æ! #" $ø%& ˙ ˝ ”ƒ•Z»ƒ·7‡‚:˜c!‡;»‚¶‡7‡⁄·¨•<$•¶‡7·¶…L.Q„#,„2…‚ ` ˝ $J‡ƒ•Z‚(F„x¿‡‡‚(•Z·¶F„w#‹‚(•‰‡"!„‚(˘…%¶n¿ ˙¨\ : ¸2˜ ı˝ ^»ƒ‚(„·7„$J„&ml*,‡ˇ•^ƒ‡·0!„‚(·7„»„&’„¿•%.ˇ•L»‡‚#‹„‚(‰˘•%$J‡‰‡·7‚$c!¨‡ ”ƒ•‡…%7‡.c„2…‚ ` ˝ $J‡ƒ•Z‚’„¿‡‡‚(•Z·¶’„•&’¿„‚’·¶”ƒ‰l•%.'¿‡‡‚(•Z·7‡.•h&A,‘ƒ‚(•Z‚¶„# ` ˝ $J‡ƒ•Z‚(’„%$"&A…%.ƒ¿·¶”ƒ‡ ` ˝ $J‡ƒ•Z‚(F„j·¶”ƒ•Z·£&’‡ˆ•.L¨·7„Q·¶”‡!„‚ 7·»o‡‚ #W„‚(‰•%$J‡;„·¶”‡¿2,‡ ·7„»o„&F„¿˙·¶”ƒM¶‡$J·¶’„cL!‡x»‚¶‡7‡⁄·;•w$•¶‡b7·¶…L.L„##„2…‚;”ƒF¿2”x&’‡"‡&›$J‡ƒ•Z‚(’„¿‡‡‚(•Z·¶’„ #W‚(•‰˘‡"!¨„‚(…%¶ƒ¿·¶”‡»ƒ‚(„·7„$J„&m*,‡·¶”‡¶‡ ` ˝ $J‡•Z‚(’„•%.·¶”‡‡·Q!¨„‚ (·7„»„&’„¿c !¨‡”ƒ•‡…%7‡.„2…‚:”ƒ’¿2”P&’‡"‡&8$J‡ƒ•Z‚(’„¿‡‡‚(•Z·¶F„•&F¿„‚(’·¶”ƒ‰l\·7„Q¿‡‡‚(•Z·7‡•z&A,‘ƒ‚(•Z‚¶„#4”ƒF¿2” &’‡"‡&%$J‡ƒ•Z‚’„"C˛ˇ‡|”ƒ•‡;…%7‡.”‡ˆ…‚(¶·¶$"C»ƒ‚¶‡7‡⁄·7‡.˘ « ‡$J·¶’„3 ; ·7„¿‡‡‚(•Z·7‡”ƒ’¿2”&’‡"‡& $J‡ƒ•Z‚(’„˘·¶”ƒ•Z·•Z‚¶‡‡fi»‡$J·7‡.·7„»ƒ‚(„fi.‡·¶”‡^!„‚ 7·w$•¶‡‡%.'»‡‚#‹„‚(‰˘•%$J‡•‰˘„¿·¶”‡7‡ ”ƒ’¿2”^&’‡"‡& $J‡ƒ•Z‚(’„"Cƒ•&&’c-!‡z¶A‰j…%&A•Z·7‡·¶”‡7‡x”ƒF¿2”^&’‡"‡&F$J‡•Z‚(’„·7„‡"•&F…•Z·7‡·¶”‡‡%. »o‡‚ #W„‚(‰•%$J‡…L¶¿P%*˜ ¶F‰…%&F•Z·¶’„‚t9T”‡¶F‰…%&F•Z·¶’„Z•&F.ƒ•Z·7‡!|”‡·¶”ƒ‡‚·¶”ƒ‡l$J‡ƒ•Z‚(’„ !¨‡¿‡‡‚•Z·7‡z$•…%7‡x·¶”‡t!„‚ 7·o$•7‡j»o‡‚ #W„‚(‰•%$J‡•‰„¿˘•&&F$J‡ƒ•Z‚(’„T·¶”ƒ•Z·o!‡<¶F‰…%&F•Z·7‡ « ‡$J·¶’„gWj»ƒ‚¶‡¶‡l·;”ƒ’¿2”^&’‡"‡&$J‡ƒ•Z‚(’„|·¶”ƒ•Z·o!‡x¿‡‡‚•Z·7‡j…%¶n¿„2…‚|•&’¿„‚’·¶”ƒ‰lTn •Z‚(F„2…%:·7„»„&’„¿2’‡" « ‡$J·¶F„W/˜»‚¶‡7‡⁄·„2…‚M¶A‰j…%&A•Z·¶’„‚¶‡¶…%&’· ˆ˜ Scenario M 1 Scenario M 2 Scenario M 3 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 1 2 3 4 5 6 Scenario M 4 0 1 2 3 4 5 6 Scenario M 5 0 1 2 3 4 5 6 Scenario M 6 0 1 2 3 4 5 6 Scenario M 7 0 1 2 3 4 5 6 C’¿2…‚¶‡<W=(’\E ¥=ºSº' A)K4¥ƒ>P§ TID? Sƒº E–A E¢? S[ DC)D-??A ¤ DdT FS E¢? V A O A U AL '% UCVFb?V0| mhL}%lk¢_2‘Q}?dp´‘pd4etfoWF¢hiy~-L}?kl‘paF ˛ˇ‡•Z»»L&’„2…‚•&’¿„‚(F·¶”ƒ‰l:·¶”‚¶‡‡·p»‡¨„#·7„»„&’„¿2’‡"=Mi_$(”•ci ˜_\$J‚¶„"c•%.him_\¿‚(. ˙‡ˆ•$”„#·¶”‡¶‡T·7„»„&’„¿2’‡"c!¨‡|…L7‡T·¶”‡T‚(‡7»‡$J·¶,‡ ` ˝ $J‡ƒ•Z‚’„?•\•»…ƒ· $J‡ƒ•Z‚(’„·7„ „2…‚;”ƒF¿2”x&’‡"‡&F $J‡ƒ•Z‚(’„¿‡‡‚(•Z·¶’„•&’¿„‚(’·¶”‰l"69T”‡x•&’¿„‚’·¶”ƒ‰l|„2…·7»…·|•3&F,‘ƒ‚•Z‚¶„#?”ƒF¿2” &’‡"‡& $J‡ƒ•Z‚(’„s#‹„‚·¶”‡j¿2‡·7„»„&’„¿j=nƒ•&&’c)!¨‡$J„2‰»•Z‚(‡Y $J‡ƒ•Z‚(’„·7„.‡⁄·¶,#‹^!|”ƒ$” $J‡ƒ•Z‚(’„l&F‡ˆ•.·7„˘·¶”‡1!„‚ 7·M$•¶‡»‡‚#W„‚‰˘•%$J‡ § S E¢? V A O A U A))EGD ~ ‡·…%·¶•(‡•5$”ƒ•„#17‡"‡e„-.‡gi „ S ⁄ _{=F¿2…‚¶‡ »ƒ‚¶‡7‡⁄·•^&F,‘‚(•Z‚¶„# ` ˝ $J‡ƒ•Z‚’„¿‡‡‚(•Z·7‡.5‘⁄„2…‚ ` ˝ $J‡ƒ•Z‚(’„¿‡‡‚•Z·¶’„›•&’¿„ ‚(’·¶”ƒ‰l\˙·¶”‡tj¿2…‚¶‡cL!‡z(”„!g•w¶…W‘)7‡·T„#C·¶”‡z $J‡ƒ•Z‚(’„|·¶”ƒ•Z·|„2…‚4#W‚•‰‡"!¨„‚ (¿‡‡‚(•Z·7‡"c ƒ•‰‡&’w ·¶”‚…3*)X?=F¿2…‚¶‡ ; »ƒ‚(‡7‡l·:•b7‡·„#4”ƒ’¿2”P&’‡"‡&8$J‡ƒ•Z‚(’„¿‡‡‚•Z·7‡.3‘˘„2…‚ #W‚(•‰˘‡"!¨„‚(819T”‡7‡Y$J‡ƒ•Z‚’„‚¶‡»ƒ‚¶‡¶‡l·•L”ƒ•&,#&’„2•.‡.‹‡·Q!¨„‚ (!|”ƒ$””•&,#?„#?·¶”‡Q·7„·¶•& „.ƒ‡x•Z‚¶‡·7‚(•%¶‰˘F·7·¶¿W „ „·7‡·¶”ƒ•Z·‡ˆ•$(”$J‡•Z‚(’„nx¿2,‡c•g…ƒ‰z‘‡‚<#‹„‚j‚¶‡"#‹‡‚¶‡%$J‡`4 !¨‡˘¿‡ƒ‡‚(•Z·7‡3$J‡•Z‚(’„xnh$(”ƒ•·7„»o„&F„¿2’‡x…»·7„˜Z¸x„-.‡"c!¨‡w.ƒ‡„·7‡•x7‡·j„#£$J‡ƒ•Z‚(’„ 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 1 2 3 4 5 6 Scenario 1 (Sys 1): Scenario 2 (Sys 2): Scenario 3 (Sys 3): Scenario 4 (Sys 4): Scenario 5 (Sys 5): Scenario 6 (Sys 6): C’¿2…‚¶‡< ; = fl EG eU DIC8D U\ TID? Sƒº E–A E¢? S5FS)U K U A S%¤ D ¤e DC)D-??A ¤ DT FS EG? !|’·¶”l¶A‰˘&F•Z‚\• ¶’¿ƒ‰‡⁄·?„#æ„!M¨•M‡flX‡˘0‰˝l•˘¢”m˜6$J‡ƒ•Z‚’„\„#9·¶”ƒ‡4¶•‰‡$"&F•"?ƒ„‚¨‡•‰»L&’‡c ¶)˜{‰"»)•‡”¢…l†;\‚¶‡"#W‡‚(‚¶‡.˘·7„•M¶%flX1†|•<#‹„‚(‰¿‡ƒ‡‚(•&F,‡.w#W„‚6$(”ƒ•n˘·7„»„&’„¿2’‡¨„#¶,‡#W‚¶„2‰ #W„2…‚\·7„˜Z¸-#˙^¶%flXs†c#W„‚¨‡ˆ•$(”„#9·¶”‡7‡M$”ƒ•·7„»o„&F„¿2’‡"cl‡"‡‚(‡"‡3…ƒ‰z‘o‡‚(‡.l„-.‡o7‡%.% æƒ„!M¨·7„’·\‡ˆ’¿2”‘o„‚¨·7„j·¶”ƒ‡;‚(F¿2”l·"#˛ˇ‡•¶F¿…%u⁄…ƒ‡˙.%¨·7„Q·¶”‡7‡s7-7·7‡ˆ‰˘•Z·¶$$J‡ƒ•Z‚(F„¨·7„ ‚¶‡"#W‡‚|·7„˘·¶”‡7‡< $J‡ƒ•Z‚(’„Tn^‡·0!„‚(-T„#.ƒrq‡‚¶‡l·o(,‡" 9•‘)&’‡d»ƒ‚¶‡¶‡l·•]¶‡·„#x”’¿2”B&’‡"‡&s$J‡•Z‚(’„’#-…%&&’/&’„2•.ƒ‡.7‡"‡p„-.‡d$(”ƒ• ·7„»o„&F„¿2’‡" „ „·7‡j·¶”ƒ•Z·•‰„¿·¶”‡7‡b$J‡ƒ•Z‚(F„"c¶LflY†,+Pi „ ”„»8_{c›¶%flXb†·^i-”„»S_{c›¶%flX ††i-”„»St˜_{cƒ•%.‹¶%flX-‚¶‡»ƒ‚(‡7‡l·£$J‡•Z‚(’„P!|”ƒn$(”P7„2…‚ $J‡„#·¶”‡sæƒ„!4•Z‚¶‡…%ƒ,#‹„‚(‰l&’ .ƒ7·7‚(‘…·7‡.„‡‚·¶”‡$(”ƒ•niG!;’·¶”…ƒ‰z‘‡‚;„#\„.ƒ‡;‚•¿2¿P#W‚(„2‰#‹„2…‚·7„˜Z¸I_{x„&&F„!|ƒ¿ ¨•Y&Fn7·?„#F!„‚ 7·£$•7‡1$J‡•Z‚(’„¿2,‡@‡·0!„‚(·¶”‚¶„2…¿2”»¢…·"c#-•’‚ ƒ‡¨•L.P.ƒ‡&F,‡‚¶‚(•Z·¶F„• ·¶”‡»‡‚#W„‚‰˘•%$J‡‰‡·7‚(n$ t¶)˜‡‰»)•‡”m…x˛‰•”–»¿˘‚…x˘GˇW‰…{‡˘˜ •X‰w‰˛Æ”–‰‡fl^•˘¢”m…/. `$"$J„‚ .ƒ¿L·7„O;‡ˆ…‚(7·¶n$wcy¶%flX -Q;‡»‡$J·7‡.·7„P&F‡ˆ•.·7„L·¶”‡b!¨„‚{7·$•¶‡Y.ƒ‡&F,‡‚¶L‚(•Z·¶’„Wb¶%flXY†0+T‡fi»‡$J·7‡.·7„^&’‡ˆ•. ·7„˘·¶”‡1‘‡7·o$•¶‡z.‡&F‡‚¶‚(•Z·¶F„W ˜t¶)˜‡‰»)•‡”m…^˛‰•”G»¿˘‚…x˘Gˇ-‰…{‡˘M˜{•X"‰l»8‰"˘¢… ^˘GˇI…˙¿ˇ"¨)˙W˘M”–»hˇ-•˛ Y˛,…•I‰ ‹˜ˇ•”G».˛ˇ‡ $J„2‰»•Z‚(‡$J‡ƒ•Z‚’„˘»ƒ‚(‡7‡l·7‡.^C’¿2…ƒ‚¶‡ ; ·7„´.ƒ‡l·¶,#‹7!|”ƒ$”„#·¶”‡7‡‹$J‡ƒ•Z‚(F„ 9=•‘L&’‡<= fl E– pU DC)D U\ TD-? 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‡‚„Zys„Sm‡nTs ·¶”‡r(”ƒ•|s·7„»„ l „¿•Zsomq—p•:|n:‚¶‡»ƒ‚(‡n7‡sl·jn:·7„·¶• l sƒ‡·tp„‚ju·¶”ƒ‚¶„2…¿2”»…ƒ·¨|sLP »ngv&|„·7‡·¶”ƒ•Z· yW„‚|• ll s‡·tp„‚jurJ„/somƒ’·¶F„/songo:H%n¶”ƒ„6pn·¶”ƒ‡%p¨„‚n7··¶”‚¶„2…¿2”ƒ»…·•Znp‡‡‚fi»o‡rJ·7‡mv Z (a) CBR rates = 0.2 Mbps 0 500 1000 1500 2000 2500 0 5 10 15 20 25 Number of nodes Network throughput (Kbps) Sys 1 Sys 2 Sys 3 Sys 4 Sys 5 Sys 6 (b) CBR rates = 0.42 Mbps 0 500 1000 1500 2000 2500 3000 3500 4000 4500 0 5 10 15 20 25 Number of nodes Network throughput (Kbps) Sys 1 Sys 2 Sys 3 Sys 4 Sys 5 Sys 6 (c) CBR rates = 1 Mbps 0 1000 2000 3000 4000 5000 6000 7000 8000 0 5 10 15 20 25 Number of nodes Network throughput (Kbps) Sys 1 Sys 2 Sys 3 Sys 4 Sys 5 Sys 6 (d) CBR rates = 2 Mbps 0 1000 2000 3000 4000 5000 6000 7000 8000 0 5 10 15 20 25 Number of nodes Network throughput (Kbps) Sys 1 Sys 2 Sys 3 Sys 4 Sys 5 Sys 6 (e) CBR rates = 2.4 Mbps 0 1000 2000 3000 4000 5000 6000 7000 8000 0 5 10 15 20 25 Number of nodes Network throughput (Kbps) Sys 1 Sys 2 Sys 3 Sys 4 Sys 5 Sys 6 =F¿2…‚¶‡V8v|8 ¤ “0⁄¨¥ º: ⁄ ˜º ¥M¯ ˜ §M⁄¥` «´ “SƒM¢ º £¥ « ƒ ˜ ¢¡`¡£¥z¢zˆ]“8ˆ ´:˜ ¢zƒ*⁄6¥§¥¡£¥z¯£“ « ˆ˜Z¸ Scen Id (Sys Id) Description CBR-0.2Mbps CBR-0.4Mbps CBR-1Mbps CBR-2Mbps CBR-2.4Mbps 1 (Sys 10)(0,12) 1813.68 2884.8 2367.12 2515.68 2521.44 2(0,11),(11,12) 1781.82 2721.1 2118.64 1853.4 1830.54 3(0,10),(10,12) 1850.52 2759.96 1829.84 1856.04 1832.2 4 (Sys 20)(0,10),(10,11),(11,12) 1806 2561.12 1735.28 1765.66 1786.16 5(0,9),(9,12) 1971.06 2685.54 2141.16 2161.8 2221.68 6(0,9),(9,10),(10,12) 1951.28 2403.2 2382.4 2429.02 2445.78 7(0,9),(9,11),(11,12) 1852.9 2486.34 2593.96 2787.6 2881.74 8(0,9),(9,10)(10,11),(11,12) 1903.14 2410.9 2522.54 2597.42 2601.52 9(0,8),(8,12) 2046.8 2644.08 2058.96 2179.6 2144.4 10(0,8),(8,10),(10,12) 1947.4 2394.92 2510.84 2549.04 2545.4 11(0,8),(8,10),(10,11),(11,12) 1996.4 2444.84 2417.14 2467.48 2440.9 12(0,8),(8,9),(9,10),(10,12) 1982.84 2440.08 2683.54 2772.32 2736.62 13(0,8),(8,9),(9,12) 2041.84 2337.14 2128.6 2192.58 2170.58 14(0,8),(8,11),(11,12) 2049.76 2758.7 1848.96 2040.42 1985.34 15(0,8),(8,9),(9,10),(10,11),(11,12) 1979.26 2452.02 2722.78 2890.34 2850.18 16(0,7),(7,12) 2099.88 2625.3 2265.64 2268.3 2372.98 17(0,7),(7,11),(11,12) 2155.24 2540.98 2106.36 2254.64 2197.78 18(0,7),(7,10),(10,12) 2146.14 2436.34 2187.24 2183.66 2265.52 19(0,7),(7,10),(10,11),(11,12) 2096.76 2466 2159.52 2294.46 2249.68 20(0,7),(7,9),(9,12) 1993.18 2658.82 2447.1 2491.62 2524.62 21(0,7),(7,9),(9,11),(11,12) 1929.98 2654 2916.3 3347.46 3242.08 22(0,7),(7,9),(9,10),(10,12) 2074.94 2599.86 2368.56 2388.62 2372.22 23(0,7),(7,9),(9,10),(10,11),(11,12) 2005.28 2622.22 2479.52 2518.84 2540.44 24(0,7),(7,8),(8,12) 2062.76 2416.86 2335.74 2357.98 2374.34 25(0,7),(7,8),(8,10),(10,12) 2067.88 2607.96 2956.24 2969.7 3062.1 26(0,7),(7,8),(8,9),(9,10)(10,11)(11,12) 2016.12 2721.62 2987.2 3064.16 3142.86 27(0,6),(6,12) 2107.68 2635.44 2415.84 2691.48 2596.8 28(0,6),(6,9),(9,12) 2183.52 2577.54 2366.88 2438.16 2386.92 29 (0,5),(5,10),(10,12) 2205.18 2627.36 2529.46 2552.44 2607.22 30 (Sys 13)(0,3),(3,6),(6,9),(9,12) 2158.32 3012.3 2029.38 1971.78 2084.82 31 (Sys 11)(0,2),(2,4),(4,6),(6,8),(8,10),(10,12) 1855.6 3446.48 3799.32 3990 3995.68 32 (Sys 8)(0,1),(1,2),(2,3)…..,(11,12) 2160.95 3814.06 4493.31 4660.42 4744.4 Worst case 1781.82 2337.14 1735.28 1765.66 1786.16 Best case 2205.18 3814.06 4493.31 4660.42 4744.4 %Reduction-wrt -Scen1 (S1-worst)/S1*100 1.76 18.99 26.7 29.82 29.17 %Reduction-wrt- Best (best-worst)/best*100 19.2 38.73 61.39 62.12 62.36 C’¿2…ƒ‚¶‡8v| ¤ “,⁄4¨w¥ ºG ⁄ ˜4º ¥]¯ ˜ §'M⁄¥` «´ “Sƒ]¢ º £¥ « ƒ$`A]¡¡ ¡£¥z¢oˆ'“8ˆ “† ƒ]¥ˆ]“ ´:˜ ¢zƒ Œ /¸ ¥ º:« ⁄ ´ ¢ « “Hƒ]“,⁄4¨¥ º: ⁄ ˜º ¥]¯ ˜ §'M⁄ƒ`'¡¡ ¡£¥z¢zˆ]“8ˆ ´T˜ ¢zƒ⁄6¥z§¥¡£¥z¯£“ «Z˛ C’¿2…‚(‡ 8v| »ƒ‚¶‡n7‡s⁄·jns‡·p¨„‚ju·¶”‚(„2…¿2”»…·•Zr(”’‡g}‡m njrJ‡s•Z‚(’„/n|ss„Sm‡y-… l|l l „2•Zmƒ‡mr(”ƒ•|s ·7„»o„ l „¿2’‡ngvT”‡rJ„ l …‰sm‡s„·7‡m [)˜4ª‚ºzGVJ;»ƒ‚¶‡n¶‡sl·jn:˙EmL„Zy4·¶”‡%n<rJ‡sƒ•Z‚(’„•ZsomL·¶”‡ …osƒ|Ø…‡fi8n˙Em'„Zy|·¶”‡·¶”‡njrJ‡s•Z‚(’„YvT”‡rJ„ l 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yn(•Z·¶…‚(•Z·7‡ms‡·tp„‚juoo:VZJn¶”„Gpn\·¶”ƒ‡p„‚<n7·xsƒ‡·tp„‚ju˘·¶”‚¶„2…ƒ¿2”»…·\s yW‡gp˝r•Zn7‡ngv¨`:· ˝£ ‚•Z·7‡n:„Zy=˜ »n•ZszmL˜8v »zngo:%Z%n¶”„Gpn·¶”‡Vp¨„‚<n¶·»‡‚jy‹„‚(‰˘•ZszrJ‡ |s‰„/n7·r•Zn7‡nv ˆ˜˜ (a) CBR rate = 0.2 Mbps 0 500 1000 1500 2000 2500 3000 3500 4000 0 5 10 15 20 25 Number of nodes Network throughput (Kbps) Sys 8 Sys 9 Sys 10 Sys 11 Sys 12 Sys 13 Sys 14 Sys 15 Sys 16 Sys 17 Sys 18 (b) CBR rate = 0.42 Mbps 0 1000 2000 3000 4000 5000 6000 7000 0 5 10 15 20 25 Number of nodes Network throughput (Kbps) Sys 8 Sys 9 Sys 10 Sys 11 Sys 12 Sys 13 Sys 14 Sys 15 Sys 16 Sys 17 Sys 18 (c) CBR rate = 1 Mbps 0 1000 2000 3000 4000 5000 6000 7000 8000 0 5 10 15 20 25 Number of nodes Network throughput (Kbps) Sys 8 Sys 9 Sys 10 Sys 11 Sys 12 Sys 13 Sys 14 Sys 15 Sys 16 Sys 17 Sys 18 (d) CBR rate = 2 Mbps 0 1000 2000 3000 4000 5000 6000 7000 8000 0 5 10 15 20 25 Number of nodes Network throughput (Kbps) Sys 8 Sys 9 Sys 10 Sys 11 Sys 12 Sys 13 Sys 14 Sys 15 Sys 16 Sys 17 Sys 18 (e) CBR rate = 2.4 Mbps 0 1000 2000 3000 4000 5000 6000 7000 8000 0 5 10 15 20 25 Number of nodes Network throughput (Kbps) Sys 8 Sys 9 Sys 10 Sys 11 Sys 12 Sys 13 Sys 14 Sys 15 Sys 16 Sys 17 Sys 18 =F¿2…‚¶‡w8v/˜Z¸S ¤ “0⁄¨¥ º: ⁄ ˜º ¥]¯ ˜ §'M⁄¥z` «´ “SƒM¢ º £¥ « ƒ#`A]¡¡ ¡£¥¢oˆ]“8ˆ ´T˜ ¢zƒ<]ƒ'£`t¥ º ˆ' « ⁄ º ¥ M⁄G£¥ƒ¥z`'¥8¨ « ˆ˜Z Data Rate N Sys 10 Sys 13 Reduction % 1 Mbps 4 1308.9 1308.9 0 7 1372.44 1447.02 -5.44 10 1897.56 1777.44 6.34 13 2367.12 2029.38 14.27 16 2896.8 2565.3 11.45 19 3355.2 2728.08 18.7 2 Mbps 4 1338.6 1338.6 0 7 1465.32 1518.78 -3.65 10 1944.36 1742.46 10.39 13 2515.68 1971.78 21.63 16 3018.3 2156.4 28.56 19 3760.2 2464.2 34.47 2.4 Mbps 4 1346.88 1346.88 0 7 1480.8 1521.66 -2.76 10 1948.14 1790.4 8.1 13 2521.44 2084.82 17.32 16 3582.9 2278.14 36.42 19 3916.44 2666.22 31.93 =F¿2…‚¶‡8v/˜ST“0ˆ ´ ⁄G£¥ƒı¥z`wƒM“0⁄¨¥ º: ⁄ ˜º ¥M¯ ˜ §M⁄[¢ ´T˜ £“0¿“8ˆ ¥ zGZ ´ ¥§'¢ º “8ˆ ⁄6¥o:H,+ ˆ˜X |„Gp l ‡·…znxrJ„2‰»¢•Z‚¶‡Vn<rJ‡sƒ•Z‚(’„o:J,+p;’·¶”˘·¶”‡Vp„‚<n7·~r•Zn7‡njrJ‡sƒ•Z‚(’„·7„n¶”„6p·¶”‡‚¶‡mƒ…zr4— 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‡Jq‡rJ·¶{}‡Hs‡·p¨„‚<u·¶”ƒ‚¶„2…¿2”»…ƒ·:•Zr”ƒ’‡g}‡m n¶|sƒ¿ l ‡”„»ƒ”„»S˜8¢”„»S 8”„»SrY —<;”„»•Zszm—x”„»njrJ‡sƒ•Z‚(F„/ngv,‡·:…onƒ‚n7·rJ„/son¶m‡‚¨…os{yW„‚‰ mƒ|n7·7‚( …·¶’„/sQ„Zyn7„2…ƒ‚<rJ‡ngvC˙As n¶…or(”•r•Zn¶‡Zp¨‡wrJ„2‰»•Z‚¶‡Q• l|l njrJ‡sƒ•Z‚(’„/n;‡‚YrJ‡»ƒ·;·¶”ƒ‡w—”ƒ„»njrJ‡s•Z‚(’„YvT˛ˇ‡”ƒ•6}‡|mƒ‡sl·¶{‡m ·¶”ƒ•Z·L»o‡‚’„8m|r •Zr<u l „¿/n•Z·m‡»‡somƒ‡sl·s„Sm‡ns^”ƒ„»NS*njrJ‡sƒ•Z‚’„*r•…zn7‡nL·¶”‡njrJ‡sƒ•Z‚(F„ ·7„›•Zr(”ƒF‡g}‡·¶”‡p¨„‚<n¶·r•Zn7‡·¶”ƒ‚¶„2…¿2”»…ƒ·gv$|„·7‡·¶”ƒ•Z·s=F¿2…‚¶‡8v/˜˜8v |·¶”‚¶„2…¿2”»¢…·jnQ„Zy ˆ˜Z C 0 = 2 C 1 = 3 C 2 = 4 C 3 = 4 C 4 = 4 C 5 = 4 C 6 = 4 C 7 = 4 C 8 = 4 C 9 = 4 C 10 = 3 C 11 = 2 0 1 2 3 4 5 6 7 8 9 10 11 12 (a) 13 node chain topology (11, 12) (10, 11) (0, 10) Flow N-3 hop scenario 1786.2 831.5 616.0 33.8 Thpt 2521.4 2688.3 2084.8 3995.7 4744.4 Network throughput 865.5 (11, 12) 587.5 (10, 11) 25.8 (9, 10) 227.8 (8, 9) 531.6 (7, 8) 272.5 (6, 7) 708.5 (10, 12) 220.5 (5, 6) 38.8 (8, 10) 403.0 (4, 5) 415.7 (9, 12) 347.5 (6, 8) 431.3 (3, 4) 319.9 (8, 12) 85.6 (6, 9) 260.7 (4, 6) 189.0 (2, 3) 175.0 (4, 8) 99.3 (3, 6) 230.4 (2, 4) 265.4 (1, 2) 210.1 (0, 12) 177.0 (0, 4) 94.4 (0, 3) 411.9 (0, 2) 724.1 (0, 1) Thpt Flow Thpt Flow Thpt Flow Thpt Flow Thpt Flow N-1 hop scenario Hop = 4 scenario Hop = 3 scenario Hop = 2 scenario Hop = 1 scenario (b) Flow throughput and network throughput of some scenarios =F¿2…‚¶‡8v/˜˜8¡£¥8¨ ⁄ ˜º ¥M¯ ˜ §M⁄[¢zƒ]ˆıƒ]“,⁄4¨¥ º: ⁄ ˜4º ¥]¯ ˜ §⁄[¥` « ¥“ «´ “Sƒ]¢ º £¥ « ƒ “⁄† ƒ]¥ˆ'“ ´T˜ ¢£ƒ$⁄6¥§¥¡£¥z¯ % ˆ˜Z‰ Data rate Scenario Flow 1 Flow 2 Total Index of fairness 0.2 Mbps Sys 1 130.76 214.56 345.32 1.65 Sys 2 192 192 384 1 Sys 3 186.72 186.72 373.44 1 Sys 5 213.12 213.12 426.24 1 Sys 6 213.6 213.28 426.88 1.01 0.42 Mbps Sys 1 255.14 423.6 678.74 1.67 Sys 2 368.32 369.34 737.66 1.01 Sys 3 367.02 366.14 733.16 1.01 Sys 5 421.04 421.92 842.96 1.01 Sys 6 421.2 420.64 841.84 1.01 1 Mbps Sys 1 231.96 1025.82 1257.78 4.43 Sys 2 639.16 585.22 1224.38 1.1 Sys 3 665.12 628.72 1293.84 1.06 Sys 5 702.32 696.5 1398.82 1.01 Sys 6 729.46 687.52 1416.98 1.07 2 Mbps Sys 1 94.08 1363.82 1457.9 14.5 Sys 2 657.68 611.48 1269.16 1.08 Sys 3 653.02 732.9 1385.92 1.13 Sys 5 735.32 711.02 1446.34 1.04 Sys 6 738.58 727.92 1466.5 1.02 2.4 Mbps Sys 1 81.44 1397.28 1478.72 17.16 Sys 2 654.08 627.12 1281.2 1.05 Sys 3 713.34 689.32 1402.66 1.04 Sys 5 733.94 720.32 1454.26 1.02 Sys 6 753.82 719.82 1473.64 1.05 =F¿2…‚¶‡w8v/˜Z8¡£¥0¨⁄ ˜º ¥M¯ ˜ §M⁄¥`V¿S¢ º £¥ ««´ “Sƒ]¢ º £¥ « `¥ º´ ¥§]¢ º « ¥ƒ¥z`J`t¢z º ƒM“ «« £ƒ$`t¥ º ƒ]¥ˆ]“ ´:˜ ¢zƒ l „6p| ł l „Gp ł •Zsom´ l „6p ‡ł |sˇ”ƒ„»cSn<rJ‡sƒ•Z‚(’„•Z‚(‡ l ‡njn·¶”•Zs”ƒ• l y„Zy:·¶”‚¶„2…¿2”»¢…·jn„Zy æƒ„6pnQ|sc”„» S“ˇ•Zsom—<”ƒ„»n<rJ‡sƒ•Z‚(’„/ngv l „Gp˚·¶”‚¶„2…¿2”ƒ»…·x„Zy”„»¡SnjrJ‡sƒ•Z‚(’„/nQ•Z‚¶‡ ‡g}‡s l „6p‡‚~rJ„2‰˘»•Z‚¶‡m·7„wn(|s¿ l ‡”„»•Zszm”„»S˜Hn<rJ‡sƒ•Z‚(’„/ngv&;„6p l ‡·…on(rJ„2‰»•Z‚¶‡”„»S njrJ‡sƒ•Z‚(’„p|F·¶”—”„»n<rJ‡sƒ•Z‚(’„Q·7„|szr l …om‡VnjrJ‡sƒ•Z‚(’„/nsp|”ƒ|r”n¶„2…‚<rJ‡nT•Z‚¶‡%sƒ„/sS—p…osƒ{y‹„‚(‰ l mƒ|n7·7‚( …·7‡mv&;„·7‡x·¶”ƒ•Z·;·¶”‚¶„2…¿2”»¢…·:„ZyC l „Gp ł p |n|• 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‡n<nwsƒ‡·tp„‚jup|’·¶”ƒ|s´·¶”‡[rJ„/s⁄·7‡‚fi·˘„Zy ` ˝ l •ˆ‡‚p‡mƒ‡gzs‡·¶”‡jł¥ø •Zn7‡m¡„/s·¶”‡•Zsƒ• l Sn¶|nQ»ƒ‚¶‡n¶‡sl·7‡m^|s ‰ v˙·”ƒ•Zn ‡‡s |m‡s⁄·¶{ƒ‡m|s ‰ ·¶”ƒ•Z· l ‡¿2•ZrJZ¸2˜8v|Z‹˙\¨#Z¸2˜8v|Z mƒ„⁄‡nVs„·;”•}‡Q•Zsl[n(…»ƒ»„‚¶·y‹„‚qæ„0 ‡r•…zn7‡T·¶”‡‚¶‡|nsƒ„j‰‡r”ƒ•Zsƒ|n¶‰ ·7„wmrqo‡‚(‡sl·¶F•Z·7‡ ‡·p¨‡‡sn7·¶•Z·¶F„/son¨•Zszm˘·¶”‡ˆ’‚¨·7‚(•?„rTvGo:•Zn7‡m „/s·¶”ƒ‡•Zsƒ• l 8n¶n|»ƒ‚(‡n7‡sl·7‡m|s ‰ p‡yW„‚(‰• l|l m‡gzs‡†æ„0•ZnVyW„ ll „6pnvA4‡·œ(g$œ&ŁTv{v{vhœ_ß ‡wº»ƒ‚(F„‚(’·p·7‚•?„rr l •Znjn7‡nsp|F‚¶‡ l ‡njn~s„Sm‡n„Zy•s‡·p¨„‚jup|”‡‚(‡œ mƒ‡s„·7‡n:·¶”‡”ƒ’¿2”‡n¶· »ƒ‚(’„‚(F·p·7‚(•?„qrr l •Znjn•Zszmœ_ßmƒ‡s„·7‡n·¶”‡ l „6p‡n7·»ƒ‚(F„‚(’·p·7‚(•?„rr l •Zn<ngv†,‡·\$,.\$GŁTv{v{v \$ ß mƒ‡s„·7‡˘·¶”‡˘·¶”ƒ‚¶„2…¿2”»…ƒ·•Zr(”ƒ’‡g}‡my‹„‚x·¶”‡˘‚(‡n7»‡rJ·¶{}‡˘»ƒ‚(F„‚(’·pr l •Znjn7‡nv`—»ƒ‚¶„·7„SrJ„ l |n n¶•|m·7„ ‡¿2…ƒ•Z‚(•Zs⁄·7‡‡ˆ|s¿4æ„0{yŒ.ut'Œ.zŁqt‚886tcŒ.ßv#˙Es„·¶”ƒ‡‚p¨„‚<mzng0y‹„‚:·tp„»ƒ‚(’„‚’·p r l •Znjn7‡neœ •Zsomœ ø n(…or(”›·¶”ƒ•Z·eœ nx•”’¿2”‡‚r l •Zn<nrJ„2‰»•Z‚(‡m›·7„:œ ø =·¶”‡æ„0¿2…ƒ•Z‚(•Zs⁄·7‡‡n ·¶”ƒ•Z·:Œ. t'ŒA ø v ˙AsP‡rJ·¶’„/sIYv…8v|Tp¨‡mƒ|njr…znjnQ·¶”‡‡‚fi·7‡son¶F„/son˘„Zy„2…‚r…‚¶‚¶‡s⁄·y‹‚(•‰‡gp„‚ju'‚¶‡Ø…ƒ’‚¶‡m·7„ |sorJ„‚¶»„‚(•Z·7‡·¶”‡n7·¶…om„Zyæ„0v‡rJ·¶’„/skIYv…8v/˜c»ƒ‚¶‡n7‡s⁄·jnL• ‚(’‡gy%m‡n<rJ‚(’»ƒ·¶’„/s¡„Zyx„2…‚r•Zn7‡ n7·¶…om„/s˙¨\PZ¸2˜8v|ZJ‡Hp|F·¶”n7„2‰‡x|s’·¶F• l ‚¶‡n¶… l ·jngv b?VWUCV C_?dW#‘%Z‘a$#&%a’x_e‘diG+2k9[d m a+Rn =F¿2…‚¶‡†IYv|»ƒ‚¶‡n¶‡sl·jnj·¶”‡L‰„8mƒ‡ l „Zy|•[p|’‚¶‡ l ‡n<ns„Sm‡s·¶”‡rJ„/sl·7‡‚fi·„Zyæ„0n¶…»ƒ»„‚¶·gv˛ˇ‡ »ƒ‚¶‡n7‡s⁄·;·¶”ƒ‡m‡njrJ‚(’»·¶’„/s•Zn<n¶…ƒ‰˘|sƒ¿ ˝ `q” ˝ ` ` ˝ »ƒ‚¶„·7„SrJ„ l n•Z‚¶‡…on7‡my‹„‚‰‡mƒF…‰ •Zr4— rJ‡njngv#C’¿2…‚¶‡IYv|Tv-•,\»ƒ‚(‡n7‡sl·jn¨·¶”‡|‰˘„8m‡ l „Zy,•%p|’‚(‡ l ‡njns„Sm‡p|”ƒ‡ss„^æ„0|nxn¶…»ƒ»„‚¶·7‡mv˙As ·¶”ƒ|nC‰„Sm‡ l •n¶|s¿ l ‡(Ø…‡ˆ…‡|n#•Z·7·¶•Zr”‡m˘·7„qª< 1 N&£QªXS{ª‚<ºæ0/0ª#|swp|”ƒr(”·7‚(•?„r:„Zy• l|l »ƒ‚(’„‚’·p r l •Znjn7‡n•Z‚¶‡Hn¶‡‚j}rJ‡mp|’·¶”ƒ„2…·|•Zs⁄[mƒrq‡‚¶‡s⁄·¶F•Z·¶’„/svC’¿2…‚¶‡IYv|Tv |»ƒ‚¶‡n7‡s⁄·jn|·¶”ƒ‡j‰„Sm‡ l „Zy?• p|’‚¶‡ l ‡n<ns„Sm‡p|”ƒ‡sæ„0|nxn¶…»ƒ»„‚¶·7‡mvT”ƒn\‰„Sm‡ l n(…»ƒ»„‚¶·jn\•‰˘•:F‰…ƒ‰„Zyy‹„2…‚»ƒ‚(’„‚’·p r l •Znjn7‡ngv\Jsƒ‡Ø⁄…ƒ‡ˆ…‡;|n\•Z·7·¶•Zr(”‡mL·7„ªj 1 qO4æT4ƒ2 1 S{:<}fiF•p|”|r(”·7‚•?„r|„Zy·¶”‡VrJ„‚¶‚¶‡n7»„/somY— |s¿Hr l •Znjn:|n~n7‡‚j}fi|rJ‡mvC˛^”ƒ‡s·7‚•?„rVyW‚¶„2‰—‰„‚(‡;·¶”ƒ•ZsL„/sƒ‡;»ƒ‚’„‚(’·*r l •Znjn:•Z‚¶‚({}‡•Z·•wp|’‚¶‡ l ‡n<n JI, 0 1 2 3 0 1 2 3 (a) Model of wireless nodes with no support for QoS. (b) Model of wireless nodes with QoS support for 4 traffic classes. 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Number of priority classes attached ³ ³ ³ ³ 1. Active priority class is in bold. P 4 j (c) Assignment of priority classes to gainer node j. Number of priority classes attached = 1. 0 1 2 3 4 5 6 7 8 9 (d) Worst QoS scenario. Lowest priority class P 4 at gainer nodes (0,1,3,5,7,9) transmit while highest priority class P 1 active at victim nodes (2,4,6,8) defer access to the channel. P 4 P 4 P 4 P 4 P 4 P 4 P 1 P 1 P 1 P 1 ACK 3,7 ACK 0,1 ACK 5,9 Defer Defer Defer Defer C’¿2…‚¶‡AIYv/˜8 ˚ ¨¥ º:« ⁄ ´ ¢ « “ł¥ø «6´ “8ƒ]¢ º £¥*ƒ { r –f} ““ “ } rJ„/sl·7‡s⁄·¶’„/sp|som„6pt„Zy·tp„„‚x‰„‚¶‡ •Zr<u„Zq‡sl·¶F·¶’‡n|s·¶”‡n¶•‰‡s„Sm‡• l|l „Gp¯·¶”‡ •Zr<u„Zq ‡sl·¶’·¶F‡n\·7„Q•ZrgrJ‡njnr(”•Zsos‡ l •Z·¨·¶”‡Jn¶•‰‡·¶F‰‡Zfi•H}’‚(·¶…ƒ• l rJ„ l|l |n¶’„/s„Srgr…‚<nv?`:·¨·¶”ƒn\»„2|s⁄·gl·¶”‡ •Zrju„Zq‡sl·¶’·*p|’·¶”·¶”‡”ƒ’¿2”‡‚¨»ƒ‚(’„‚(F·pr l •Znjn¨·7‚(•Zson¶‰’·jng,p;”‡‚¶‡ˆ•Zn• l|l „·¶”ƒ‡‚ •Zr<u„Zq‡s⁄·¶’·¶’‡n •ZrJ·•Zn{y?•rJ„ ll |n¶’„/s”ƒ•Zn|„Srgr…‚¶‚(‡m„/s·¶”‡Hr”ƒ•Zsos‡ l vT”‡wr(”ƒ•Zsosƒ‡ l •ZrgrJ‡njn ‡·tp‡‡smƒrq‡‚¶‡s⁄· s„8mƒ‡n|„Zy?·¶”ƒ‡ws‡·p¨„‚<u|n;·¶”‡n¶•‰‡•Zn|s˙\¨˝Z¸2˜8v|Zn7·¶•Zsomƒ•Z‚<mv;˙Es·¶”ƒ|nn¶·¶…omZp¨‡Q‰˘•Tu‡ ·¶”‡%n¶•‰‡x•Zn<n¶…ƒ‰»ƒ·¶F„/son•ZnT|sL„2…‚n7·¶…om„Zy˙\¨Z¸2˜8v|Z »ƒ‚¶‡n7‡s⁄·7‡m|s ˝ ”ƒ•Z»ƒ·7‡‚IYv Tv £ “ « ⁄ º “ « ]¡⁄ «/˛ ˛ˇ‡'…on7‡´·¶”‡›‡‚fi·7‡som‡m˙yW‚•‰‡gp¨„‚<uN·7„¡»‡‚jy‹„‚(‰ •Zsƒ• l 8n¶n„Zy˙¨\ Z¸2˜8v|ZJ‡·7„´‡g}Z• l …ƒ•Z·7‡·¶”‡p¨„‚<n¶·qr•Zn7‡jæ„0v\C’¿2…ƒ‚¶‡·IYv/˜›»ƒ‚¶‡n7‡s⁄·jn˘·¶”ƒ‡‚¶‡n¶… l ·jn˘„Zy„2…‚ •Zsƒ• l Sn¶|nvC’¿2…‚¶‡PIYv/˜8v-•,»ƒ‚(‡n7‡sl·jn·¶”‡·7„»„ l „¿Zvˇ˛ˇ‡…on7‡”‡ˆ…‚(n7·¶|r ·7„ˇ•Znjn¶’¿/s »ƒ‚(F„‚(’·pr l •Znjn¶‡n\·7„w}rJ·¶F‰ •Zsom¿2•|s‡‚~s„Sm‡n\|s·¶”‡sƒ‡·tp„‚juv?C’¿2…ƒ‚¶‡uIYv/˜8v \»ƒ‚(‡n7‡sl·jn JI0˘ 0 1 2 3 (a). Topology I 0 1 2 3 4 5 (b). Topology II 0 1 2 3 4 5 6 7 8 9 P low P high P high P high P high P low P low P low P low P low P high P high P low P low P high P high P low P low P high P high (d). Topology IV 10 12 11 13 P high P high 0 1 2 3 4 5 6 7 8 9 P low P high P high P high P high P low P low P low P low P low (c). 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…osor(”•Zs¿‡mˇ|s·¶”‡‡‚fi·7‡som‡myW‚(•‰˘‡gp¨„‚juvT”‡n¶•‰˘‡•Z‚¶¿2…ƒ‰‡s⁄·x•Z»ƒ» l ’‡n·7„·¶”‡rJ„/sorJ‡»·„Zy F‰» l r•Z·¶’„/sv]|”‡»ƒ‚¶„2”ƒ ’·7‡m l |n7·|n •Zn¶‡mL„/s·¶”‡F‰» l |r•Z·¶’„/s‚(… l ‡n…zn¶|s¿p|”ƒr(”p¨‡Hr(”‡r<u ·¶”‡}Z• l |mƒF·p„Zy,•njrJ‡sƒ•Z‚’„Yv&T”‡r”ƒ•Zs¿‡|s·¶”‡Vs‡ˆ’¿2” „‚(”„„8mQ·7„Q‰‡njn¶•Z¿‡ l ‡g}‡ l r(”ƒ•Zs¿‡n·¶”‡ ‚(… l ‡n:»ƒ‚(‡n7‡sl·7‡m|s ˝ ”ƒ•Z»·7‡‚˜•Zn;• l|l „ZyC·¶”‡n7‡‚… l ‡nT|s0}„ l }‡·¶”ƒ‡‚¶‡rJ‡»ƒ·¶’„/s„Zy#•Zs‡g}‡sl·gv:˛ˇ‡ „/s l qm|njr…onjn:·¶”ƒ‡%r(”ƒ•Zs¿‡n;|sn¶…zrgrJ‡njnQy-… l ‚¶‡rJ‡»ƒ·¶’„/s‚(… l ‡Zv&T”‡„·¶”ƒ‡‚r(”•Zs¿‡n|•Z‚¶‡Hn¶F‰˘ l •Z‚v p £ ¥z§¥¡£¥z¯ 5 ¥ˆ]“S¡ ˛ ˙Es“ ˝ •Zn¶‡mqnjr”‡ˆ‰‡n¨·¶”‡;•‰˘„2…osl·„Zy9»„6p‡‚…zn7‡m˘·7„j·7‚(•Zson¶‰˘F· •|‰˘‡njn¶•Z¿‡xmƒ‡»o‡szmon9„/s·¶”ƒ‡\·p»‡\„Zyfi·¶”‡‰‡njn¶•Z¿‡Zv#„‚=‡‚fi•‰˘» l ‡ZB•Zsom ˝ »¢•Zrju‡·jn •Z‚¶‡n7‡s⁄·#•Z·&C"DFEVp|”ƒ l ‡ fl •Z·¶••ZsomQ` ˝ P^»•Zrju‡·jn¨•Z‚¶‡n7‡s⁄·C•Z·HGFI 7J I GTv'T”ƒ‡¨»„6p‡‚?…on7‡m y‹„‚T·7‚(•Zson¶‰|njn¶’„/sm‡·7‡‚‰˘|s‡n·¶”ƒ‡·7‚(•Zson¶‰˘njn¶’„/sL‚(•Zsƒ¿‡Zv ˝ „/son¶m‡‚·¶”‡s‡·p¨„‚<un(”„6ps |sC’¿2…ƒ‚¶‡4IYvIYv·4‡·Hs„Sm‡˜|sƒ’·¶A•Z·7‡•[mƒ•Z·¶•·7‚(•Zson¶‰|njn¶’„/s·7„s„Sm‡q n7‡szmƒ|s¿•Zs BvYT”‡ØŒ§ Ł ł N nn7‡sl·T•Z· C"DFE p|”ƒr(”L|n”‡ˆ•Z‚<m • l|l s„Sm‡n|sL·¶”‡·7‚(•Zszn¶‰˘|njn(’„/s ‚(•Zs¿‡x„Zy=·¶”ƒ‡hBv˛ˇ‡Q‰„Sm‡ l n¶…or”•‰˘‡njn¶•Z¿‡Hn¶»o‡r|zr·7„»„ l „¿…on¶|s¿·¶”ƒ‡s„·¶•Z·¶’„/s K C 6 vƒ„‚x‡‚•‰» l ‡Z·¶”‡˘·7‚(•Zson(‰˘|njn¶F„/s‚•Zs¿‡n„Zy~s„Sm‡]y‹„‚B ˝ fl •Z·¶••Zsom ` ˝ P—‰‡njn(•Z¿‡n•Z‚¶‡‰˘„8m‡ l ‡m•Zn9KOQPSR T UKVWPSR T K9X D D T •ZszmMKZY[V\ T ‚¶‡n7»‡rJ·¶{}‡ l Zv˙As C’¿2…‚¶‡IYvIY8y‹„‚?‡‚fi•‰˘» l ‡Z]K OQPSR ^ S‘_«¸S|T…8Iba/WK VWPSR N c _,T/˜8IY…da/WK X DfegD ^ c _,T…da/•Zsom KZY[V\ N c _˜]hIba/v p ø ´/´ “ «« `'¡ º “ ´ “0§]⁄G£¥ƒ º ]¡£“ ˛ {}‡s•n¶…orgrJ‡njnjy‹… l ‚(‡rJ‡»ƒ·¶’„/sL„ZyC•‰‡njn¶•Z¿‡†T-–v1‡Zv{ƒ• ‰‡njn(•Z¿‡x„ZyC·p»‡†Tzm‡s„·7‡m•Zn|‰—B; T h iZ•Z·;·¶F‰‡·kjj•Z·Vs„Sm‡e§•Zsom[rJ„‚¶‚¶‡n7»„/somƒs¿ ‰—BJ T h i•Z··¶F‰‡T·klQ|s˘•j·7‚¶‡‡sƒ„8m‡TŒSm0⁄·¶”on‚fn;‰…on7·xsƒ„· n|•Zs⁄ng}+nsl·~sS—BJqp]h •qr<rFsF‰n r : „‚sY—B|&pbh •qrrFsF‰tntrkEus|sŒ[mqn¶…zr(”Mr¶”ƒ•qrºvs|n•‰tnnjn¶•Z¿+n„Zy<r¶”on»‚¶„+r7„8rJ„ l §ws|n•Zs n l nˆ‰tnsdrT„ZyHr¶”onnknxrjnZK C T •ZszmvK ß p ¢•Zsomyrkl r : rkjj•Zsomv”„‚zrkl rkE rkj0v Z 0 1 2 3 4 G i RTS G i CTS G i Data G i ACK 5 Transmission ranges: RTS : CTS : Data: ACK: G 2 RTS = {0,1,3,4}, G 3 CTS = {1,2,4,5}, G 2 Data = {1,3}, G 3 ACK = {2,4} s’¿2…‚FnqIYvIY{x¥§¥¡£¥¯ ¥ˆ]“S¡(£ƒ}|'¢ « ´ {h{ Œ «´T˜ “S“ «} ˚ } Œ ¢ « “jø⁄G]ˆ &˛9~ ¢ « ´ {{ Œ { º ¥z⁄6¥ ´ ¥¡ «/˛ ˛n›…onkn2…Q»QF»[/nknmn‚brknsonFsg/sZyrFQny5‰tngp<+<urk¡»Snx<y5+(‰Zss|sQsrFsg l ZsQ l 8nFsn Zyp<+nkrrxZnknL»[nxjy5+‰ZsornyZy Znfs|rqu“ ˝ njrfQnˆ‰tnngvVnFs|sooyf+tngp"+jup"ny+nsonxfqrkn njrnsQqfs/nVps|rfnFoGprFqrZ l rFoorFon ZnFs|rw“ ˝ njrontnnsgQF6}+nwnsonxF+vnX„rxsnsorZ rFonxmQnx+fZmon9rFofooorZsomy+ssonnjn~y+zrFonp"+<nkrrxZnknHnjrnsQqfs/nv Tv{(“ « ⁄ º “ « ]¡⁄ «/˛ nFssooyf+tngp"+jup"n+nsQnxfqrknnjrnsQqfsg/nps|rf*nFoGprFqrw l — rFoorFon ZnFs|rx“ ˝ njrfonnnHstQFG}+nnsonxF+LnX„rxsnsorZ+rFonx%mQnx+fZmon"rFoFooWor Zsomy+s<sonnjny+rFonHp"+<nkrrxZnknn<rnsQqfs/ngv9sQFnhIYv…FnnknsdrjnZsvG}+nxj}bsngpZyrFon p"+<nkrqn<rnsQqfsp<nQ}+n+nsonxfqrknmv‘HsgoFn·IYv…8v,Qfnnkns¡rjnn<rnsQqfspons$sQ [6p"nxr/s¡rkF l njrontnts|n¢onknmpQs l nLsoFn^IYv…8v QFnnFns¡rjnZnjrnsQqfsgqpQnxFnLrFon ZnFsr“£PnjrfQntn9s|nonknmv&nxrso8mQn¢⁄ts|ssrFsgqrknZrkZsonFs|n<nFs/srkso8mQnZs|sysofn IYv…8v,Zsom!sofn&IYv…8v v@¥EsnjrfQntnnpsrFoQr$[6p"nx&r/s¡rkf l ¡ l|l tnnjnFq+nnqFnnkns¡r qr¢rFonwnf+tn[Gp<nx l ng}+n l vVzonwso8mQnn¢ƒZsomIZsomsoSmonnJ‰Zsomqmongy5nxZ/sonqfs|sQ rFon˘ØŒZ§¤“'‹«ZZsom›ZfiZ§$«k' ¤:UFnnFSnrrFs|}+n l ZUZnnFQ6pss|sMsofn^IYv…8v,vflQns“"£s|n onknm rkfZsonfsrkrFs|sorFonBvZsom£~vqr:osg–[Gp<nx l ng}+n l sQ8monnƒ8]8fIY Zsom[mongy5nx/srFonhB'VyZsomurFonHso8mQnn‰8˘08Zsom·mongy5nx/srFonw£QZnnfo6ps s|ssQFnIYv…8v vzs|nnnjnknsdrFsg l|l yFnmornnzrFonHrfQZsornnZyr l|l snFs/sv†6p"ng}+nxs|s zI 0 1 3 2 4 5 7 6 9 8 (a) CSMA/CA (without TPC) scenario. Nodes 2, 4 defer on RTS and 6, 8 defer on CTS. Defer (RTS 0,1 ) Defer (RTS 0.1 ) Defer (CTS 1,0 ) Defer (CTS 1,0 ) Defer (RTS 0,1 ) Defer (RTS 0.1 ) Defer (CTS 1,0 ) Defer (CTS 1,0 ) Defer (RTS 0,1 ) Defer (RTS 0,1 ) Defer (CTS 1,0 ) Defer (CTS 1,0 ) (b) CSMA/CA (with TPC) scenario. Nodes 2, 3, 4, 5 defer on RTS and 6, 7, 8, 9 defer on CTS. 0 1 3 2 4 5 7 6 9 8 soFnqIYv…8 ¸ ¥W‡ « ⁄ ´ ¢ « “ «´ “Sƒ]¢Q‡:£¥ƒ «´T˜ “8“ « ¨q⁄ ˜ ¥⁄¢ƒMˆ¨q⁄ ˜ {h{ Œ } Qs l r/sosonrrknmsQnxrtp"+juZns|srFQs|nZn‚o+t l nZUsrmonrfnZnknny+s<sonnjnZZnp"n l|l ZnZrFon rFoFQoor@ZyrFonVpo l nsonxrtp"+juv@¥yrFQnmQqrFLrkfZsonFsnjnFs/s nxrp<nxnssoSmonn⁄wZsom[ r/sdrFs|sdQnn&y5+< l /sorFsgtnZd l|l +rFonxsoSmonnss!rFonsonxrtp"+jumongynxy+@rFonznsdrFsFn[nxfsSm Zy[rkfZsonFs|njnFs/spons“£·s|nonknmv¥EsrxZnkn¢ZyrkfZsonFsnjnFs/spsgrFoor@[6p"nx(r/sdrkF l rFonwnFsgw l rFZsonxonrkfZsonFs|njnFs/s nxrp<nxnssoSmonn¢⁄Zsom*TsQ8monnVZszm˘0Zsom[sQ8monn tZsomtqFn9[/njnFs zl nVpQs|rus|sorFnZnknnzrFon%y+s<sonnjnZnp<n ll ZnrFon9rFQFooQrZy$rFon sonxrp<+juv bs/ss{zrxZsdr+tosdrZyQs+FnnknqrfQZnsmons¡rFs|Qnm}qqfsonqnFo+Frjrsso/nZyrFon ZnFsrH“£QF+rkSr l ngvL]rknsonfs/son¢ZyrFon Znfs|rHu“"£˙njrfQntnnQ}+n nxnsQf+S/nFnm rkFnnk l }+nrFonnknus|njnfonngv†6p"ng}+nxrkrFon nnkrZyoHuSsoGp l nmo+nZ@rFonFnnF l rjnLZsom s|njnfonn9FnxqmQs|sovrFonqy+s<sQnnjn9ZyzrFQn“£F+rk8r l nrFqrHp"n}+nus|monsdrFs{Qnm%Q}+n so+r nxns%s|monsdrFs{Qnm Zs¡Fng}]sgon%p"+juv Bznxq<mQssorFonrFoFooWor9s|njnFQnng¶‚• QZn"s|monsdrFs{QnmrFQqr<rFQnrFoFQoor<ZyrFon ZnFs|ru“"£„F+rk8r l n(mQnx+fZmonn(rtqFnm rktrFonw£o”»q”+£»‘…F‰fonn9srFoQr"[‚<nx‰¿drkF´`<†‚<ng}+nxWrFon9tbˆon[+˜HsFnn…f… ‰f+¿Q¿onS+…F…FQtnˆysg¿M¶/•sg…"ˆQs7¯[nxFn¿¡rx`˘on¢‰Q+¿Q¿onStbˆon[sg¿v¶q•‰¿…Fsgˆonxf…<rFon 1 T44–ªg Z gªgºY£ºV7„˙æTºªuorF…fsgˆonM+˜rFQnrkf+¿Q…Fsg…F…Fs¿}f+¿o+n+`–˘zon¿obˆon…usg¿‰xqFfsgnx…kn¿Q…Fs¿o x¿onu‰x+¿„…kn¿Q…knrFonu…Fs¿+ Qr‰x+¿Q¿o+rtˆon‰bˆonrFon¨‰+FFn‰rF%QsggnrFony¿o]ˆQn…ws¿ rkf+¿Q…fsg…F…Fsg¿„f+¿o+nM…kn¿Q…kn+…"ng+…ˆon‰bˆonrFQn…Fsg¿Q+z‰+FFn‰rFg+`‘˘zonxfnx˜5+FnZ¿ …kn¿Q…fsg¿o!rFonL‰Q+¿Q¿on Q…k¿B˘”+£˘W+‰F+nxrF…gSrFonL¿obˆon…sg¿‰xqFfsnxz…kn¿…Fsg¿ox¿on ˆonx˜nx˜+t[nxfsg]ˆy+˜¥ sg‰fs…wQ‰fv…F+gnx‰tqFnˆrkrFonrFsgtnLn¿Q+rFu+˜ n¿drFsFnˆQqrFZ+¿Qˆ»£˚}rk+¿Q…Fsg…f…Fs¿`&˘dQ…$rFon¿obˆon…sg¿9rFQs…Mx¿onn‚osrHrFon"ˆQnx˜5nx@…krFqrkn nqfgsgnx"rF+¿yrFon¿o]ˆQn…sg¿rFonZrkf+¿Q…Fs…F…Fs¿f+¿o+n+¿Qˆu‰x+¿u‰gsgˆon¢srFrFonZ¿o+sg¿o rkf+¿Q…fsg…F…Fsg¿¸+…rFonsBH˘Vb…qFnM+g…k„…kn¿drqry C<DFE `‘oggsg¿QrFQsg… …knxF˝qqrFs¿ ¶‚•z‰¿Q‰xgQˆQn…rFQnyˆQnx+f+ˆQqrFs¿„+˜rFoFooWorsg¿˛rFon +…fsg‰˘u“"£ˇ…F‰fonnuQsg‰%sg… ˆQs7¯[nxFn¿dr˜F—oyFn…FQgrF…x`‘fln+g…F˛‰¿Q‰xQˆonrFQqrrFQnrFQFooQrˆonx+f+ˆon…us¿ rFon +…Fsg‰˘u“"£…f‰fontn…‰tqfnˆrk˛rFonv…f‰fontn…srFQor˘“£¢`†"nx˝+nxo ‰¿Q‰xg…Fs¿sg… +…knˆy¿rFon…Fsgtgn…kr<‰Q+¿Q¿on[tbˆonS‰¿Q…Fsg…krFs¿oL¿Qg+˜&rkf+¿…Fsg…F…fs¿ f+¿o+n+` ƒ]`u{9‡:¥o⁄6¥ ´ ¥¡J¢zƒ]¢z¡ « «Z˛ o9+¿+]…fsg…¢QF˝bsgˆon……srFsg¿…FsdrF…˜+9Qf+rk]‰]ˆQs|Y— ‰xqrFs¿Q…`%fln˝+n[nxF˜+ftnˆ„+¿·sg¿QsgrFsg+<+¿+]…fsg…w+˜¿on…fQ‰f·tbˆQs{W‰xqrFs¿˛Qsg‰ …Fo‚…![nxF˜+f+¿Q‰nysgtQf˝+ntn¿drF…t˜+…ktn…F‰n¿Qqs…x`flnvqFnu‰xoFFn¿drF˜oFrFQnx sg¿d˝+n…krFsqrFsg¿QtrFonLtbˆQs{Qnˆ˝+nxf…fs¿u+˜HrFon9QF+rkb‰´` g w dW#‘%q$#&% @ˇ_!dGdkd6% m BÆ +3dW! 2$#ªz:# d6#&#f% ¥ ¿yoW+…Fsg‰¢˜5+tnx<+fWQ"n9‰¿Q…FsˆonxrFon9‰xg+…F…+˜HQF+rkb‰g…rFqrzQ…kn¿QsˆQsFn‰rFs¿+W+¿S— rkn¿Q¿Q+…xs`‹n+`rFon+¿drkn¿Q¿Q+…tsrF·Z‰q⁄ˆonx+Fnxn…tWqrkrknxf¿„Fn…FQgrFsg¿oMsg¿„‰xsf‰xQgq!rkf+¿…Fsg…F…fs¿ f+¿o+n…x`%¥ ¿„…F‰ontn…tsgrF%ˆQsgFn‰rFs¿Q++¿drkn¿Q¿Q+…x<rFonyrkf+¿Q…FsgrkrFsg¿oM¿o]ˆQn…[n+t˜+f…!srF… +¿¡rkn¿Q¿!rkqfˆQ…rFon9s¿¡rkn¿QˆQnˆyFn‰ns˝+nx+¿Qˆyrk+¿Q…Fsrsg¿yrFqrzˆQsFn‰rFs¿U`H¥¿u‰x+…kn9+˜HFn‰nxY— rFs¿orFonFn‰nsg˝]sg¿Q¿o]ˆQnZy[n+t˜5+ŁsrF…Fn‰nsg˝]sg¿Q!+¿drkn¿Q¿QrkqfˆQ…zrFQn9rkf+¿Q…Fsrkrknx` …fsg¿orFQn…f+tnQFnqbˆo¿w+˜W+…Fsg‰"tbˆong…+¿Qˆ!‰¿Q‰nxQrFQ+b‰t[¿on¿drF…+˜QH˜f+tn‚— <+FFn…kn¿drknˆsg¿]n‰rFs¿hIo`Io`gØq+<n‰x+¿w…Fo˛rFQqrH<n¿onxnˆLrk¢‰Q+¿o+nrFonrk+[++9]ˆon` ØŒZ‰ (a) Omni-directional antenna. Nodes 2,3,5,6 in the direction of omni-antenna defer on RTS while 0 º 1 transmission is in progress. G 0 (b) Directional antenna. Node 0 can beamform its antenna towards node 1 using angle f f f f1 or f f f f2. Node 2,3 in the direction of f f f f1 (G 0,f f f f1 ) and node 2,6 in the direction of f f f f2 (G 0,f f f f2 ) defer on RTS while 0 º 1 transmission is in progress. G 0,f1 0 1 3 2 4 5 6 f1 f2 0 1 3 2 4 5 6 G 0,f2 HsgoFnAIo`] 5$æb"$ædı! ‡/ ıłSøQœß/$æbæ]tß5ı‚·ß ‡ æ]+ı‚ßSSı‚æ]H} †‚<nx˝+nxosg¿rFQsg…‰x+…Fn+drFon¢‰fQ+¿Q+n…<sg¿rFonzrk+[++tbˆonQs¿¡rkFbˆQQ‰n…<L¿onx}˝/qsgqnrFQqr Q…FrSnZrF+‰f]nˆv]‰Q+¿osg¿otQ…knqf‰+++fsgrFQu` p { łSøQœ5‘Hæb sQFnGIo`Fn…kn¿drF…&rFon<‰fQ+¿o+n…sg¿9o$¿onxr3<+frk+Sg++9t]ˆQn on¿yˆQsgFn‰rFs¿Q+S+¿¡rkn¿¿Q+…qFnQ…knˆ`sQFnIo`]`QFn…kn¿drF…"rFon¿onxr2"+Frk+[++ tbˆonHsg¿Q+…fsg‰L˜f+tnx"+FsrF¿QsgˆQsfn‰rFs¿Q+U+¿drkn¿Q¿Qb`¥¿rFQnoFn+[¿o]ˆQn ⁄¿QsgˆQsfn‰rFs¿Q+grkf+¿Q…FsrF…z+¿BH˘urk¿o]ˆQnØ9Qsg‰fvsg…Qnqfˆ]¿obˆon…ƒ]][Œ] +¿Qˆy]`˘zon…knZ¿obˆon…"ˆonx˜5nx"rFons"rkf+¿Q…fsg…F…Fsg¿t¿rFon.B˘˜+<rFon¢n¿drFsFnZˆQofqrFs¿+˜ rkf+¿Q…fsg…F…Fsg¿˜F‘⁄rkØq`soFnGIo`]`[QFn…Fn¿¡rF…&rFon…F+tn"¿onxr2"+FZsrFLˆQsFn‰rFs¿+ +¿drkn¿Q¿Q+…x`]ˆon⁄·‰x+¿Sn+˜5+f>srF…u+¿drkn¿Q¿Q¸rkqfˆQ…¿obˆon·Øqr+¿d+¿Qn [nxr2"nxn¿vFnx˜nxFn¿Q‰nwgsg¿on9+¿QˆvrFonw+¿¡rkn¿Q¿b`zflnw+…f…FQtnL˝+nxFrFsg‰x+$Fnx˜nxFn¿Q‰nwgsg¿on9+… …Fo‚¿s¿urFonQQFn+`+rknwrFQqrrFonw‰¿Q…krkf+s¿¡rF…+˜@rFonL+¿on+˜rFon+¿drkn¿Q¿Qsg…z⁄ 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Qs‰fs…rFonZˆong+˜.˜FˇrFQnrkf+¿…FsrFs¿rFQqr‰Fnqrkn…(.b+¿Qˆ:7FnxFn…kn¿drF…<rFQn¢…knxr +˜¿obˆon…/¯[n‰rknˆtd;.`<+rknrFQqrsgrFˆQsgFn‰rFs¿Q+]+¿¡rkn¿¿Q+…x¡Ztn…F…fq+n"rk+¿Q…Fsrkrknˆ ˜F ¿o]ˆQn=&rk‚"qˆQ…¿obˆon%ˆonx[n¿QˆQ…z¿MrFQnwˆQsgFn‰rFs¿v+˜<+¿drkn¿Q¿Qb`9˘zon!…kn+¿drFsg‰x… +˜U+¿nx˝+n¿¡r.]rFonxFnx˜+Fn+bsg¿rFonn"!]rkn¿ˆonˆ˜f+tnx"+Fsg…</ T h i@h 032+4"5>798@onxFnFnxQfn", …kn¿drF…rFQn+¿on+˜rFon+¿drkn¿Q¿Qqr<sg‰ftrFQn¿obˆono[n+t˜+f…@rkwrkf+¿Q…fsrrkw¿o]ˆQn %“`@¥ ¿+n¿onxf+´brFon‰¿Q…Frkf+sg¿Q…<¿rFon+¿onZsg…fnxQFn…kn¿drknˆds¿on*?d+gsrFsn…xdn+`‹o`+$Ø Sƒ]`@+rknrFqr<˜+"˘+¿Qˆ˘z„nx˝+n¿drF…rkf+¿Q…Fsr<…krFqfr"+¿Qˆn¿QˆAB7vFnxQFn…Fn¿¡rF…5 +¿QˆeBL+¿QˆeBMnx˝+n¿drF…x7FnxFn…kn¿drF…@K T ' `˘Qsg…&‰Q+¿o+nzsg¿rFon…kn+¿drFsg‰x…+˜QQf+rk]‰ nx˝+n¿drF…w‰Q+¿o+n…wrFon…kn+¿drFsg‰x…w+˜rFonrkf+¿…FsrFs¿rFqWn+`˘zon+sg¿‰¿‰nxQr[nQs¿Qˆ rFonw‰fQ+¿o+n…Zsg…+…˜g‚…x`¥ ¿…krkn+ˆ+˜tn…F…Fq+nwrkf+¿Q…fsg…F…Fsg¿u˜5f ¿obˆonCrk¿o]ˆQn %“SrFQnn"!brkn¿Qˆonˆ˜f+tnx"+Fv‰¿Q…fsgˆonxf…rFon!tn…F…Fq+ntrky[nLrkf+¿…FsrkrknˆMˆQsfn‰rFs¿Q+g ˜F ¿o]ˆQnDqr+¿u+¿ogn+˜’y˜F fnx˜5nxFn¿‰nZsg¿on+bQ¿Qˆonx"rFonZ‰¿Q…krkf+sg¿…)$Ø Sƒ]QsrFu¿Q]ˆon)%+…zrFQn9sg¿¡rkn¿ˆonˆyFn‰xssgn¿¡rx` pFE $æbGæbH ‡ ß ˘on‰t[¿on¿drF…+˜U…F‰n¿Qqfssg¿to<+…Fsg‰˜f+tnx"+FqFn+ Qsg…Frk+FLn¿drkfsn… JI I +¿Qˆ§ K ¡+¿QˆrFonQFQsgsrknˆwn¿¡rksn… I d I +¿Qˆt RLNM onxfny§ K +¿Qˆ% RLNM FnxQfn…kn¿¡rwrFony…kb…krkn +˜zrFsgtnysg¿on*?]Q+gsrFsgn…9sg¿rFQnQs…krk+F +¿QˆvrFonwQFQsWsrknˆugsg…krF…Fn…k[n‰rFs˝+ng+`˘zon!sg¿drkFbˆQQ‰rFs¿u+˜<¿onx˝qqfsgqnO+ˆQˆQ… sg¿on*?]Q+gsgrFsn…&fnxQFn…kn¿drFsg¿oZrFon‰¿Q…krk+sg¿¡rF…¿!rFonz+¿on+˜[+¿¡rkn¿¿QˆQsFn‰rFsg¿Q…HS+rFts¿ rFonQsg…Frk+F+¿QˆyrFonZQfQssrknˆgsg…krx`’P&nxrzQ…ˆon¿o+rknZrFon9sg¿Qn*?dQ+srFsn…+˜$rFon9+¿on…s¿ ØŒRQ rFon9Qs…krk+Fy+¿QˆurFonQfQssrknˆygs…krd§ K +¿Qˆ `˘z]Q…rFon‰t[¿on¿¡rF…z+˜ …F‰n¿Qqstsg¿yrFonn"!brkn¿Qˆonˆy˜f+tnx"+Fqfn+ =I I W§ K W§ K Q GI W I Q RLNM +¿Qˆ ` pTS H$øæ]ßı‚ß%æ ‡VU;W 5æ]R ˘zont‰Q+¿o+nsg¿MrFont‰¿Q‰nxr9+˜<+¿nx˝+n¿drL‰Q+¿o+n…rFon fQgn…rFQqrsg¿d˝+˝+nrFon9Fn‰nxQrFsg¿+˜@+¿nx˝+n¿drO…Fnxn!£Qqrknx¢ƒ`"fln¿QgˆQs…F‰xQ…F…rFon 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Abstract (if available)

Abstract We developed a new framework for worst case performance evaluation of MAC protocols for wireless adhoc network. Given a protocol with its performance metric and a topology, our framework first generates MAC scenarios leading to the worst case MAC performance. The framework first identifies protocol states that minimize a given performance metric. It then applies search techniques and implications to construct sequences of protocol events in the given topology that drive the protocol to these states and hence expose worst case MAC performance. The core of our search engine utilizes novel algorithms that use combinations of goal-oriented backward and forward search and implications as well as heuristics that enable the generation of worst case scenarios in manageable complexity for our practical purposes.

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Asset Metadata

Creator Begum, Shamim (author)

Core Title A framework for worst-case performance evaluation of MAC protocols for wireless adhoc networks

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Publication Date 03/11/2009

Defense Date 01/20/2009

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag FSM based models,IEEE 802.11 DCF,OAI-PMH Harvest,performance evaluation,protocol verification,search based methodology,wireless adhoc MAC,wireless MAC

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Gupta, Sandeep K. (committee chair), Govindan, Ramesh (committee member), Helmy, Ahmed (committee member)

Creator Email sbegum@usc.edu,shamim.begum3@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m2017

Unique identifier UC1471969

Identifier etd-Begum-2642 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-216990 (legacy record id),usctheses-m2017 (legacy record id)

Legacy Identifier etd-Begum-2642.pdf

Dmrecord 216990

Document Type Dissertation

Rights Begum, Shamim

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

Repository Email cisadmin@lib.usc.edu