Time Delay Oriented Reliability Analysis of Avionics Full Duplex Switched Ethernet

Transcription

1 me elay Orened elably Analyss of Avoncs Full uplex Swched Eherne Shaopng ang School of Auomaon Scence and Elecrcal Engneerng, Behang Unversy, Bejng, 9, Chna engfeng Sun School of Aeronaucs and Asronaucs Engneerng, Purdue Unversy, I 4797, US dsun@purdue.edu Jan Sh School of Auomaon Scence and Elecrcal Engneerng, Behang Unversy, Bejng, 9, Chna shjan23@sna.com Mlea omovc eparmen of Engneerng echnology, Old omnon Unversy, Vrgna 23529, US momovc@odu.edu Absrac Besdes he hardware/sofware falure of swched Eherne, he capably of daa ransmsson affecs s performance and relably. Afer summarzng he nfluence facors of Eherne servce capably, hs paper focuses on he me delay orened relably model and analyss mehod. Based on he operaonal mechansm analyss of Avoncs Full uplex Swched Eherne (AFX, hs paper emphaszes on he man facors ha affec he daa ransmsson capably, vz. he raffc shapng delay and schedulng delay. h he oken bucke prncple, hs paper carres ou he raffc shapng o decrease he sudden raffc dsurbance. Based on Frs Come Frs Servce (FCFS sraegy, hs paper provdes he approprae servce and conrols he mulple vrual lnks n real me. Combnng he raffc shapng delay and adjusmen delay o radonal relably model, hs paper esablshes he negraed relably model o evaluae he relably of AFX. Keywords raffc shapng; raffc adjusmen; me delay orened relably; negraed relably evaluaon I. IOUCIO In order o keep he relable communcaon among he avonc sub-sysems and realze he real me conrol, Avoncs Full uplex Swched Eherne (AFX s wdely used o guaranee he relable operaon even n some falure occurrng. h he redundan swchboards, buses and ermnals, he avonc sysem could carry ou daa ransmsson relable even n some falure happenng hrough deecng he falures, carryng ou he acve swchng and adjusng he nformaon resources. recng o he absoluely relable daa ransmsson requremen, he mos mporan ssue s he daa ransmsson relably when hardware and sofware are relable enough. he earles researcher on nework relably s based on opology srucure [], n whch only he hardware and sofware falures could affec he relably. h he ncreasng of componen relably, Beaudry [2] and Meyer [3] dscovered ha he communcaon capably also nfluences he performance-relaed nework relably wh daa negry and real-me funcon. In 982, he classcal Posson model was used o descrbe he nework raffc and capure s shor range dependen [4]-[6] whle was no easy o depc sysem acual raffc characersc accuraely. In 993, S. Para and P. B. Msra ulzed he mum raffc and mnmum cu heory o calculae he raffc relably of nework [7]. Over pas decades, he Posson dsrbuon s a popular raffc dsrbuon whle Leland dscovered ha he raffc dsrbuon submed o he self smlary, whch leads o he more heavy me delay of daa ransmsson [8]. Alhough ncreasng he bandwdh and cache sze could mprove he daa ransmsson performance, also can accumulae he mum cluser. h he nework calculus, we could ge he exac he daa ransmsson requremen and servce regulaon wh me delay parameers. In order o keep hgh qualy of servce, Ashok Erramll dscovered he nework raffc s varable n 27 [9] and he performance-relaed relably model s no suable o he relably evaluaon for AFX. In he desgn of AFX, he enough bandwdh and scale buffer ensure never lose he daa packe, bu he servce wang due o daa ransmsson delay also can nfluence he nework capably. recng o he bolenecks of me delay of AFX, hs paper analyzes he nfluence facors ha cause me delay from node o node under lmed bandwdh and specal dspachng sraegy. hen esablsh s relably model and realze he relably evaluaon for AFX. he res of hs paper s organzed as follows. he me delay analyss s llusraed n secon II. he relably model s esablshed n secon III. Secon V gves he negraed relably evaluaon consderng he componen falures and daa ransmsson me delay. he applcaon ndcaes ha he proposed model and mehod s conen /3/$3. c 23 IEEE 982

2 II. IME ELAY AALYSIS OF AFX A. Srucure of AFX Fg. shows he srucure of AFX, n whch sub-sysem falure, swchboard falure, lnk falure and servce performance degradaon (hroughpu, me delay ec. could lead o he AFX unsafe. I s necessary o analyze he falure mechansm and s sensve facors ha nfluence he relably and safey. he me delay beween nodes o nodes plays an mporan role n AFX, whch nfluence he real-me performance drecly. Alhough AFX adops full duplex and vrual lnk echnology can mprove he Eherne performance wh good real me, s swched sraegy of sngle node ransmsson whle oher nodes wang wll make me delay. here are many facors ha lead o me delay. efne he me delay beween nodes o nodes as delay = des ( src here s he me of sendng daa a source node; src des s he me of recevng daa a desnaon node. Accordng o he daa ransmsson process, here are hree knds of me delay shown n Fg.2, vz. channel delay, raffc shapng delay and raffc adjusmen delay. raffc channel delay unadjused shapng delay adjusmen delay adjused VL shapng raffc resource node unadjused VL shapng adjused adjuser desnaon node raffc unadjused VL shapng adjused Fg. 2. me delay composon of mulple vrual lnk Fg.. he ypcal srucure of AFX Fg. shows he srong regon managemen and hgh faul oleran capably wh redundan swch boards and subsysems n AFX. For example, he engne conrol command could be ransmed o engne hrough swch board 3 o swch board 9 when engne conroller fals. Once one swcher fals, he oher swchers wll ake charge of hs subsysem s daa ransmsson requremen by AFX faul reconsrucon sraegy. Meanwhle, he proocol can perform frame flerng, raffc conrol and daa roung. In order o conrol he daa ransmsson delay, AFX adops he cred oken bucke conrol mehod n every vrual lnk o assure skew me of he daa conrolled n specal range. So AFX can realze he real-me falure olerance and reconfguraon managemen. B. me elay Analyss of AFX he emplae s used o forma your paper and syle he ex. All margns, column wdhs, lne spaces, and ex fons are prescrbed; please do no aler hem. You may noe peculares. For example, he head margn n hs emplae measures proporonaely more han s cusomary. hs measuremen and ohers are delberae, usng specfcaons ha ancpae your paper as one par of he enre proceedngs, and no as an ndependen documen. Please do no revse any of he curren desgnaons. In Fg.2, he channel delay ncludes he frame ransmsson delay and lnk ransmsson delay. he frame ransmsson delay expresses he me from he frs ype o he las ype. he lnk ransmsson delay means he me form resource node o swcher lnk or form swcher o desnaon node, whch depends on he lnk lengh and daa ransmsson rae. he delay of swchboard ransmng daa frame consss of exchangng delay, ransmng delay, raffc shapng delay and raffc adjusmen delay, n whch he frs wo delays depend on he nework composon. ue o access raffc of swchboard s full of sudden raffc, how o shape he sudden raffc and sable raffc appropraely could nfluence he me delay of nework. he oken bucke prncple s a popular mehod o shape he raffc, whch can be consdered as a G/M/ queung model. h queung model, we could calculae he raffc shapng delay. he raffc adjusmen delay s he mum delay n realme conrol. hen he daa flow afer shapng s enered no he adjuser, no servce requremen lnes up and s wang for servce when mulple daa packe vs same por. he nework calculus wll be used o calculae he mum raffc adjusmen delay. Compare wh he oher facors, he raffc shapng delay s relaed o he swchboard characerscs and raffc shapng sraegy, whle he real me adjusmen depends on he access raffc, servce capably and raffc conrol mehod, so he and are he man facors ha can be modfed hrough approprae desgn and compensaon. Base on he fxed AFX, he me delay from node o node can be descrbed as 23 IEEE 8h Conference on Indusral Elecroncs and Applcaons (ICIEA 983

3 = = + (2 delay des src C. Influence facor Analyss of me elay Because he me delay of AFX consss of and, s necessary o analyze her nfluence facors shown n Fg.3. shapng delay adjusmen delay Besdes he above facors, he average lengh of daa frame, he number of worksaon, he bandwdh of Eherne and opology srucure of AFX. III. QUEUIG MOEL OF BASE O G/M/ wang oken mulple oken move oken arrval γ ( nework calculus arrval d ω servce A. me elay Mechansm Based on G/M/ From he pon of queung heory, daa ransmsson process can be descrbed as a cusomer-servce model wh fxed capacy shown n Fg.4. Fg. 3. he nfluence facors of me delay for AFX he nfluence of fferen daa raffc characersc causes dfferen me delay. Suppose he access raffc of swchboard ncludes sudden raffc s u and sable raffc s s, he raffc model can descrbed as -b a e + c,< M (3 f( = γ, M 2 2 > π ( + γ where sudden raffc s u subm o he modfed exponenal dsrbuon, n whch abc,, are parameers; sable raffc ss obey o he Cauchy dsrbuon, n whch s he locaon parameer, γ s he scale parameers; M s nework raffc; s opmal hreshold ha can separae he sudden raffc s u and sable raffcs s.he selecon of abc,,, γ, can nfluence he. he nfluence of In AFX, he mulple daa packes vs same por a he same me, so s dffcul o avod he queung afer he daa flow shapng. In order o guaranee he real me capably, s necessary o adjus he daa n lm buffer. he nfluence facors of raffc adjusmen nclude: Arrval curve fferen daa ransmsson requremen arrval nfluence servce response, so he arrval curve leads o he me delay. 2 Servce curve he servce curve affecs he nework npu and oupu, he mum servce delay s relaed o he dsance beween npu and oupu. 3 Adjusmen sraegy o he swchboard, here are hree knds of ypes: Frs Come Frs Servce (FCFS, General mulplexer and Local Frs Come Frs Servce. fferen sraegy has dfferen me delay. Fg. 4. Queung model of nework he nework raffc arrves servce saon wh ransmsson rae f, hen was for ransmsson. Suppose he average ransmsson me s S and he capacy s, he daa wll say a buffer wang for ransmsson when he servce un s no enough. he laer daa wll be hrown away when he number s larger han fxed capably. A hs me, he nework congeson happens. hs process can be descrbed wh four facors as follows: ework servce applcaon arrval Generally, he servce applcaon arrves one by one or group by group, whose arrval dsrbuon subms o he Posson dsrbuon and s arrval me nerval obeys o he exponenal dsrbuon. 2 Servce rules of queung he common servce rules of queung conss of Frs Come Frs Served (FCFS, Las Come Frs Served (LCFS and andom Selecng Servce (SS. If we don consder he Qualy of Servce (QoS, he normal servce regulaon acly agrees o FCFS. 3 Servce law he node provdes he servce one by one. Snce he servce me s oally dfferen wh he dfferen servce requremen. efne he servce me as a random varable, he servce law ofen subm o he exponenal dsrbuon. 4 Queung lengh he buffer of node s lm, so he daa ransmsson congeson wll occur when he queung s oo long. B. Calculaon Based on oken Bucke Algorhm Suppose he arrval me nerval subm o he normal dsrbuon P (,( : p ( = ps ( u p ( su + ps ( s p ( ss (4 where P( s he probably dsrbuon when he average arrval me nerval s less han, whch consders he sudden raffc su and sable raffc s s. p( su expresses he condonal probably under sudden raffc s u, whch leads o IEEE 8h Conference on Indusral Elecroncs and Applcaons (ICIEA

4 he s u a nex me nerval or he s s a nex me nerval. p( s s s smlar. Suppose he s u subms Cauchy dsrbuon and raffc ss obeys o he exponenal dsrbuon, he raffc dsrbuon of nework can be descrbed as -b x a b ( a pss = a e + cdx= e + c+ (5 b b γ psu = ( dx arcan( 2 2 = + π ( x + γ π γ 2 If he average servce rae of lnk subms o he exponenal dsrbuon wh parameer μ as follows: μ G ( = e, (7 o G/M/ queung, he cusomer wang me dsrbuon when he sysem acheve balance can be descrbed as: where:, < F ( = P( < = σ μ( σ e, ( μ σμ ( μ σμ e dp( e p( d σ = = Combne above equaon, he dsrbuon of nework can be descrbed as a a p = e + c+ b b 2 π γ b ( ( ( arcan( a b a + ( arcan( + ( + e c π γ 2 b b a a a a = e + c+ e + c+ 2 b b π γ b b b b ( arcan( ( a a a a + + e c + + e c π γ b b 2 b b b b arcan( ( ( arcan( 2a = b 2a (+ e 2 c + π γ b b 2 So he σ can be descrbed as ( μ σμ ( μ σμ e dp( e p( d σ = = ( μ σμ 2a b 2a e ( arcan( ( e 2 c d (6 (8 (9 ( ( = + + π γ b b 2 Based on he colleced daa, we can ge he parameers of Cauchy dsrbuon wh he leas squares mehod, vz. =.2γ =.3, a =.772b =.2852 c =.496. Accordng o he confguraon of AFX, he average servce rae s μ = ω /8, n whch ω s he bandwdh of lnk and s he servce requremen lengh. If AFX consss of vrual lnks, he servce rae of he h lnk can be descrbed as μ ω μ = = (2 8 Selec =52byeω = Mbps and =3, hen we could ge σ =.735, hen, < F ( = P( < C = ( 8 σ e σ, C. Calculaon Based on ework Calculus (3 In AFX, an mporan ssue s how o calculae he nework me delay. Cruz presened a nework calculus algorhm based on Mn-Plus Algebra o analyze he me delay []. he raffc access curve α ( efne he access curve as { } x( x( s α( s (4 where α s he access curve when me s, x( s he npu of daa raffc. Generally, he AFX ulzes he vrual lnk o mark he daa flow, n whch he bandwdh BAG and he mum frame lengh L can descrbe he arrval curve as he servce curve β ( L α ( = + BAG L (5 efne he servce curve as y ( x ( β( (6 here y ( s he oupu of daa raffc, x( s he npu of daa raffc a me. Suppose he oal servce capably s, he oal servce curve provded for he daa flow s where: + β ( = ( (7, ( + = >, Amoun of hyseress ω (8 he backlog of daa raffc s deermned by he vercal dsance beween arrval cure and servce curve. he mum me delay d he mum me delay can be calculaed by he horzonal dsance beween arrval curve and servce curve. Suppose here are ( daa raffc no he adjuser ha are VL, VL 2 VL he oal arrval curve can be descrbed as L A a L ( = ( = ( = = BAG + (9 23 IEEE 8h Conference on Indusral Elecroncs and Applcaons (ICIEA 985

5 he nework me delay under he - daa raffc can be descrbed as A( a( = a( a( = L L = + ( ( L L = BAG BAG = (2 h Frs-In-Frs-Ou (FIFO ransmsson sraegy, he servce curve can be descrbed as ( L L L L = β ( = L L = BAG BAG = ( L L = L L = = BAG BAG + (2 he servce rae and servce delay ha he swchboard provde he h daa raffc can be shown as IV. L L = = BAG BAG = ( L = L ELIABILIY EVALUAIO OF AFX (22 (23 A. elably Modelng of Apparaus h he radonal relably heory, he relably model of swchboard and subsysem can be expressed as ( P = e λ (24 where λ s he falure rae of ndvdual apparaus. efne he random varable ( = {,,2,, } s he number of worksaons, hen n n ( ( n P ( = n = C P( P (, n=,,2,, (25 where s he number of normal worksaons, whose mahemacal expecaon can be descrbed as Le n = k, hen n= ( ( = np ( = n n n ( = P ( C P ( P ( n= = P( C P ( P( ( k k k = ( ( ( ( ] = P P + P = P( = e λ ( n k (26 (27 I s obvous ha he probably of nework apparaus Pλ ( = f( λw, ( = f( λw, s relaed o he average falure rae λ of worksaon and he number of normal worksaons under nal sae. B. elably Modelng of Servce Performance h he raffc shapng and real me adjusmen, he nework can realze he relable ransmsson a lm me delay. So he raffc shapng and adjusmen are key facors ha nfluence he me delay. Afer effecve raffc shapng wh oken bucke, he arrval cusomer wang dsrbuon a he h lnk can be descrbed as h F L h swchboard s, τ < ( τ = P( < τ = ( e μ σ σ τ, τ (28 L BAG + as adjuser, he servce me delay a he = ( L = L (29 where s he number of normal operaon worksaons a me C. Inegraed elably Modelng of AFX Afer esablshng he relably model of apparaus and servce performance, s necessary o combne hem o oban he negraed relably model as ( = P( delay < τ M > P( M > (3 where P( M > = e λ s he relably of apparaus and P( delay < τ M > expresses he probably of me delay delay s less han fxed delay upper lm τ under normal apparaus. hen he negraed relably can be descrbed as ( = P( < τ M > P( M > delay τ τ μ( σ( τ ( σ = P( + < M > P( M > = P( < ( M > P( M > = e λw e ( L L = μ( σ( τ = ( σ e e ue o ( = e λ, hen ( = P ( < τ M> PM ( > delay ( L L = μ( σ( τ = ( σe e ( L L = μ( σ( τ = ( σe e e λw λw λw λw (3 ( IEEE 8h Conference on Indusral Elecroncs and Applcaons (ICIEA

6 Suppose =Mbps, = 3, L =58bye/s μ =8.3/s τ =.5s, we can ge he relably under dfferen falure rae shown n Fg.5 and upper lm of me delay shown n Fg.6. he wo key facors, ha s he raffc shapng delay and raffc adjusmen delay. In order o decrease he sudden raffc, he oken bucke heory and he queung heory G/M/ are used o realze he raffc shapng and FCFS s ulzed o adjus he mum me delay. ( 3 λ = λ = λ = 3.47 h he number of normal operaonal worksaon (, we can combne he nheren relably of apparaus and servce performance o realze he negraed relably evaluaon. Applcaon ndcaes ha opmal parameers n relably model could mprove he nework relably effecvely. 4 Fg. 5. Inegraed relably under dfferen I s obvous ha he negraed relably ( decreases wh he falure rae λ ncreases under same me. ( 4 λ Fg. 6. Inegraed relably under dfferen τ τ =.5 τ =.9 τ = 2 Fg.6 shows ha he negraed relably ( ncreases wh he upper lm of me delay τ ncreases under same me. V. COCLUSIOS hs paper focuses on he falure mechansm of AFX and analyzes he nfluence facors of me delay, hen summarzes ACKOLEGME he auhors would lke o apprecae he suppors of he aonal Hgh echnology esearch and evelopmen Program of Chna (863 Program, Gran o. 29AA442 and he Program of Chna and aural Scence Foundaon (Gran o EFEECES [] hou Qang, Xong Huagang, esearch on he relably model wh AFX nerconnecon of cvl avoncs sysem, Journal of elemery,rackng and Command, 29 (4, 28: [2] M.. Beaudry, Performance-relaed relably measures for compung sysems, IEEE ransacons on Compuers. 6(27, 978: [3] J. F. Meyer, On evaluang he performably of degradable compung sysems, Proc. 8h In l Symp. On Faul-oleran Compung, 978: [4].Anck,e al., Sachasc heory of a daa-handlng sysem wh mulple sources, Bell Sysem eehneal Journal, 6, 982: [5].Jan and S.ouher, Packe rans: measuremens and a new model for compuer nework raffe, IEEE Journal on Seleeed Areas n Communeaons, 4(6: 986: [6] H.Heffes, H. Heffes and. M. Lueanon, A markov modulaed characerzaon of packezed voce and daa raffc and relaed sascal mulplexer performance, IEEE Journal on Seleeed Areas n Communcaons, 4(6, 986: [7] S. Para,. B. Msra, elably evaluaon of flow decomposon barrer, Assoc Compuer, 5(45, 998: [8]. Leland, Murad S. aqqu and aier llnger e al. On he selfsmlar naure of Eherne raffe(exended verson, IEEE/ACM rans.on eworkng, 2(l, 994: -5. [9] Ashok Erramll, Self-smlar raffc and nework dynamcs, Proceedngs of he IEEE, 9(5, 22:8-89. [] Cruz L, A calculus for nework delay, par I:nework elemens n solaon, IEEE ransacons on nformaon heory, 37(, 99: IEEE 8h Conference on Indusral Elecroncs and Applcaons (ICIEA 987