IJCSI Inrnaonal Journal of Compur Sn Iu Vol. No. 9 ISSN (Onln): 9-78 ISSN (rn): 9-8 g Aalably Clur Sym for Loal Dar Rory w Marko Modlng Approa..Lwn and.n Unry of Compur Sud Yangon Myanmar Abra nd for g aalably (A) and dar rory (DR) n I nronmn mor rngn an mo of or or of nrpr. Many bun rqur aalably of bun-ral applaon our a day n day a wk and an afford no daa lo n n of a dar. I al a I nfraruur rln w rgard o drupon n falur and a bun opraon an onnu wou gnfan mpa. A a rul DR a gand gra mporan n I. Clurng of mulpl ndur andard rr ogr o allow workload arng and fal-or apabl a low o approa. In papr w prn aalably modl roug Sm-Marko ro (SM) and alo analyz dffrn n downm of SM modl and approxma Connuou m Marko Can (CMC) modl. o aqur ym aalably w prform numral analy and SARE ool aluaon. Kyword: aalably lur ym loal dar rory marko modlng. Inroduon g aalably lur (alo known a A Clur or falor Clur) ar ompur lur mplmnd o prod g aalably of r. y opra by ang rdundan ompur or nod w ar ud o prod r wn a ym omponn fal. A lur a ollon of ompur nod -- ndpndn lf-onand ompur ym workng ogr o prod a mor rlabl and powrful ym an a ngl nod alon [8]. Clurng a pron o b a ry ff mod for alng o largr ym for addd prforman a wll a prodng gr ll of aalably and lowr managmn o. For raon ofwar pakag u a IBM RS/ Clur nology [8] (.. onx) and Mroof Clur Sr [] (.. Wolf pak) ar bng ud o buld g aalably ym. Dar rory oluon a gand populary n pa fw yar bau of r ably o olra dar and o a rlably and aalably.. Rlad Work unr [] drbd om ym arar a bnf from lurng and prnd a wo-nod Mroof Clur Sr (MSCS) lur onfguraon and alo prnd an aalably modl of a ym ung Marko modlng nqu. In [] y dud g aalably and dar rory oluon and drbd ow A and DR oluon dffr from on anor and ow y an b ombnd o prod g ll of rlny for I nfraruur. rd. al [] drbd an aalably modl for a g aalably plaform ung a mul-ll raral ompoon approa a mx rlably blok dagram and Marko an o a o allow dald baor o b apurd wl aodng a pa xploon. Song al [9] prodd nol oluon w r ky omponn aalably modlng modl aluaon and daa analy and xamnd numral oluon for Marko modl on unformzaon mod. papr alo prn a monorng and daa analy framwork w rponbl for falur analy and aalably ronfguraon. m-marko don modl a powrful ool n analyzng qunal don pro w random don po []. y prnd applaon of Marko don pro algorm a jon opmzaon of npon ra and orrpondng mannan poly ar alo prnd.. Sym Arur arur bad on an a-pa g aalably oluon. Ea r undr g aalably nd a la wo dnal rr: a prmary o on w r run on or mor ondary o abl o ror applaon. A a rul of falur don a-pa rol ar wd. A arba kp-
IJCSI Inrnaonal Journal of Compur Sn Iu Vol. No. 9 al ym ud o monor al of nod n lur. A dar rory oluon ypally ompod of wo nod on a and on pa. a nod uually alld mar or produon nod and pa nod alld ondary or andby nod. Durng normal opraon only workng nod mar nod; n n of a nod falor or wor andby nod ak or produon rol by akng I numbr and omplly rplang mar on. o manan andby nod for falor andby nod onan omognou nallaon and applaon: daa and onfguraon mu alo b onanly ynronzd w mar nod. Boo Dr Applaon Srr A W wdprad u of ompur daa bomng mor and mor mporan n uman lf. Bu all knd of adn and dar our frqunly. Daa orrupon and daa lo by arou dar a bom mor domnan aounng for or % [] of daa lo.rn g-profl daa lo a rad awarn of nd o plan for rory of onnuy. Many daa dar olran nolog a bn mployd o nra aalably of daa and o rdu daa damag aud by dar []. A ru dar rory oluon ably o ror full ym qukly on aalabl ompung rour w may b loal bu may alo b rmo f uaon da and mu allow rory from -wd dar. prmary may b omplly down a ondary load n a non-affd ara would b ud o ror r unl prmary om bak onln.. Modlng and Analy Daa A Daa B Boo Dr arba ra Applaon Srr B LAN/WAN W propo wo-omponn ym on omponn ondrd a a and or a a andby (par) un. falur ra of a un and andby un ar dffrn and alo ff of falur of andby un dffrn from a of a un. Aumng a m o roraon and rboo ar xponnally drbud w ra and rply. W ondr a roun dagno a run ry m un nndd o d lan faul of andby un. Wl un falur and roraon m ar xponnally drbud roun dagno m nral no a onnuou m Marko an. modl for ym w dagno roun alld a m- Marko an. o ol modl w ould rudly approxma m o nx dagno o b Fgur: Sym Framwork If a ra our and f daa no rord an a daang onqun for a bun. So mpra for ompan o ffly bakup and ror daa and pro m from ug lo n produy and downm. In way ardwar xpour mgad roug pyal ardwar rdundany. Clurng prod g aalably by prong agan a nod falur. owr do no prn agan orag falur. Gn z of ypal lur nronmn mulpl ard dk ar ud o buld larg orag array. In Nwork and Sym Admnraon wn larg numbr of any on d ar ud falur xpd. Wn a ard dk fal applaon drupon unaodabl a all nod n lur ould b ung a on parular dk a ard orag w onan all fl. xponnally drbud w man.drpon of a ar own n abl (). abl (): Sa Drpon for ranon modl Sa Drpon Bo a and par un ar workng roon w fal o or falur of a un Wn a un fal proon w ufully ror r by andby un falur of andby un wl a un ll workng dd mmdaly falur of andby un no dd ym n falur a
IJCSI Inrnaonal Journal of Compur Sn Iu Vol. No. 9 7 Fgur : Sa ranon Modl falur ra of an a un falur ra of a andby un roraon ra of a fald un orag probably of an a un orag probably of a andby un m un o d lan faul of andby un W may ompu ady-a probabl by fr wrng down ady-a balan quaon of fgur ar a follow: () () () () () () onraon quaon of fgur oband by ummng probabl of all a n ym and um of quaon. n (7) Combnng abo-mnond balan quaon w onraon quaon and olng mulanou quaon w aqur lod-form oluon for ym. (8) (9)
IJCSI Inrnaonal Journal of Compur Sn Iu Vol. No. 9 8 () () () ().Sm-Marko Modl Analy A br approa would b o ak m nx dagno o b unformly drbud or [ ] rulng n a m-marko an. ndad n fg: ranon labld U ( ). A ourrng n wo ag of ranon SM drbd by a ranon probably marx and or of ojourn m drbuon (). () () () (7) (8) (9) L X~EX () and Y~U ( ) random arabl <
IJCSI Inrnaonal Journal of Compur Sn Iu Vol. No. 9 9 (X>Y) > Y d f X d () on-p ranon probably marx of DMC mbddd a m of ranon and a probabl of mbddd DMC ar gn by followng quaon rply. () [ ] D C () o oban ady a probabl ol quaon () yld () () () (7) (8)
IJCSI Inrnaonal Journal of Compur Sn Iu Vol. No. 9 man ojourn m n a () d (9) () () () () () () a probabl of m-marko an ar j j j () wr { } D C j... (7) (8) (9)
IJCSI Inrnaonal Journal of Compur Sn Iu Vol. No. 9 ( )( ) () ( ) ( ) () ( ) ( ) ( ) ( ) ( ) ( )( ). Exprmnal Rul () xa modl paramr alu for modl ar no known owr a good ma alu for a rang of modl paramr aumd. Fg: plo dffrn bwn downm (mnu pr yar) ma oband ung SM modl and a oband by approxmang U ( ) drbuon by an xponnal drbuon w man /. W ak alu.9.9 pr our pr our and /. W a gr / rao lowr downm ompud by wo modl. Aalably modl apur falur and rpar baor of ym and r omponn. Sa of undrlyng Marko an wll b lafd a up a or down a. ym no aalabl n a and a. ym aalably n ady-a dfnd a follow: Aalably-Unaalably -( ) () Downm..... D(m) D(mp) Fgur:Dffrn n downm of SM modl and approxma CMC modl. Valdaon of Clod-form Rul o rfy aldy of our formula draon w ompar rul oband from lod-form oluon and rul oband from numral oluon by SARE. W found a our rul ar am. D..... D(draon) D(SARE) Fgur: Downm of CMC modl........ D(SARE) D(draon) Fgur: Downm of SM modl
IJCSI Inrnaonal Journal of Compur Sn Iu Vol. No. 9. Conluon Organzaon oday fa a oug allng n oong an appropra g aalably oluon a m r bun rqurmn and I budg. o mplmn rqurmn organzaon mu g g aalably and dar rory. g aalably ym rqur fwr falur and far rpar. In papr w prnd g aalably lur and falor aalably for dar n.. W prn a Marko modl and xpr aalably and downm n rm of paramr n modl. W alua fably of our lurng modl ung SARE ool. and Engnrng Managmn Vol. (8) No. pp.-. Rfrn [] D. Clrow M. Brookbank N. Clayon and G. Spar Combnng g Aalably and Dar Rory Soluon for Cral I Enronmn IBM Sym Journal 7 No. 7 (8) [] D.Cn K.S.rd Opmzaon for ondon-bad mannan w m-marko don pro Aalabl onln a www.ndr.om [] R. Gama R Sor and Mk Maa "Wndow N Clurng Sr" IEEE Compur Oobr 998 pp.-. [] C.rl A. Robn Sanr X.Zang K.S.rd: Rlably and prformng modlng ung SARE. Compur rforman Ealuaon/OOLS. In Lur No n Compur Sn; Vol.78 Sprngr-Vrlag pp.-9. [] S. W. unr and W. E. Sm Aalably Modlng and Analy of a wo Nod Clur rodng of Inrnaonal Confrn on Informaon Sym Analy and Syn Orlando FL Oobr 999. []. Lumpp J. Sndr J. olz M. Mullr N. Lnz A. Baz and D. rn From g Aalably and Dar Rory o Bun Connuy Soluon IBM Sym Journal 7 No. 9 [7] M.Malora A.Rbman: Slng and Implmnng a Approxmaon for Sm-Marko Modl Volum 9 Iu 99 ag 7-. [8] G.F. fr In Sar of Clur: Comng Bal n Lowly aralll Compung rn all Englwood Clff NJ 998. [9].Song C.Langukun R.Naar Aalably Modlng and Ealuaon on g rforman Clur Compung Sym Journal of Rar and ra n Informaon nology Vol.8 No. Nombr. [] K. S. rd R. Varddy D. rndad S. Naan and R. Caro. Modlng g aalably ym. In ro. af Rm Dpndably Confrn. [] K.S.rd: robably and Sa w Rlably Quung and Compur Sn Applaon Jon Wly and Son. [] M.Wboonra ranformaon of Sym Falur Lf Cyl Inrnaonal Journal of Managmn Sn