Redundant Virtual Machine Placement for Fault-tolerant Consolidated Server Clusters

Transcription

1 Redudt Vrtul Mche Plceet for Fult-tolert Cosoldted Server Clusters Fuo Mchd, Mshro Kwto d Yoshhru Meo Servce Pltfors Reserch Lbortores, NEC Cororto 753, Shoube, Nkhr-ku, Kwsk, Kgw , J {h-chd@b, -kwto@, d y-eo@j}.j.ec.co Abstrct Cosoldted server systes usg server vrtulzto volves serous rsks of host server flures tht duce uexected dows of ll hosted vrtul ches d lctos. To rotect lctos requrg hgh-vlblty fro uredctble host server flures, redudt cofgurto usg vrtul ches c be effectve couteresure. Ths er resets vrtul che lceet ethod for estblshg redudt cofgurto gst host server flures wth less host servers. The roosed ethod esttes the requste u uber of vrtul ches ccordg to the erforce requreets of lcto servces d decdes otu vrtul che lceet so tht u cofgurtos survve t y k host server flures. The evluto results clrfy tht the roosed ethod cheves requested fult-tolerce level wth less uber of hostg servers cored to the covetol N+M redudt cofgurto roch. Idex Ters Vrtul Mche, Fult-tolert, Redudt Cofgurto, Plceet Algorth I. INTRODUCTION ever vrtulzto hs eerged s owerful techque for Scosoldtg servers dt ceters. Vrtulzto ltfors such s VMwre Ifrstructure [] d Ctrx XeServer [2] vrtulze hrdwre resources d geerte ultle vrtul executo evroets clled vrtul ches. Ech vrtul che c behve s deedet hyscl server, d hece ultle OS stces c ru cocurretly o hostg server. Dt ceters d lrge-dstrbuted eterrse systes hve y teorl uutlzed servers. By covertg these servers to vrtul ches d rug the o the fewer hostg servers, resource utlztos of the whole dt ceters roves [3]. The reducto of the uber of hostg servers lso cotrbutes to cuttg bck the ower cosutos the dt ceters [4][5]. A flure of hostg server becoes serous roble cosoldted server systes usg vrtulzto. Vrtul ches deed o hyscl devces d vrtulzto ltfor o the hostg server. Whe the hostg server goes dow due to y flures of ther cooets, ll vrtul ches o ths server re uble to esce fro servce dow. The ore vrtul ches the hostg server hosts, the ore serous dge flure of ths hostg server cuses. Ay couteresures gst ultle server dows cused by host server flures re requred. Ths er resets ethod to ke redudt cofgurto of vrtul ches tcto of host server flures cosoldted server systes hostg vrous ole lctos. The roosed ethod esttes the requste u uber of vrtul ches ccordg to erforce requreets of lcto servces d decdes otu vrtul che lceet so tht u cofgurtos survve t y k host server flures. I ters of the cost reducto by server cosoldto, the uber of hostg server should be zed. A otu vrtul che lceet for zg the uber of requred hostg server deeds o severl fctors such s the requred fult-tolerce level k, the ccty of hostg server, the uber of lctos d ther erforce requreets. The er defes ths roble s cobtorl otzto roble d resets lgorth for deterg otu vrtul che lceet uder gve codtos. Fro soe evluto results, we hve observed the roosed ethod cheves requested fult-tolerce level k wth less uber of hostg servers cored to the covetol N+M redudt cofgurto roch. N+M redudt cofgurto reres M redudt cooets so s to kee N cooets t y M cooet flures. The rest of the er s orgzed s follows. Secto II descrbes cofgurto d requreets for cosoldted server systes usg vrtulzto. Secto III rovdes roble defto for deterg redudt vrtul che cofgurtos whle zg the uber of requred hostg servers. Secto IV dscusses erforce odel for esttg requred resources to eet erforce requreets for lctos. I Secto V, ethod for deterg redudt cofgurto uder the gve costrts s roosed. Exerets d evlutos re show Secto VI, relted work s reseted Secto VII, d flly the sury of ths er s gve Secto VIII. II. REQUIREMENTS FOR HOSTING SERVER CLUSTER Ths secto descrbes the cofgurto of hostg server cluster tht hosts vrous ole lctos, d ther erforce requreets d level of fult-tolerce /0/$26.00 c 200 IEEE 32

2 A. Hostg Server Cluster Dt ceter rovders recetly rovde vrtul che hostg servce by troducg server vrtulzto to ow hyscl server clusters. Alcto rovders, who wt to luch lcto servces the dt ceter, c ret vrtul ches d strt servces quckly by sgg cotrct wth the dt ceter rovder. The lcto servces troduced by the lcto rovders ofte tke redudt server cofgurtos for ssurg sclblty d vlblty. There re y redudt cofgurto ethods for ole lctos such s web servers, l servers d dt bse servers. Web servers dstrbute ther worklods to ultle servers usg lod blcg odule [6]. Ml servers c rove ther erforce d fult-tolerce by dstrbutg rocesses to relcto servers usg DNS roud rob. Dt bse servers ofte use clusterg ethod for sclblty d hgh-vlblty [7]. Ths er ssues tht ech hosted lcto hs ow redudt cofgurto ethod d focuses o the vrtul che lceet ssue dt ceter rovders to rovde fult-tolert hosg server cluster. B. Perforce Requreets A dt ceter rovder d lcto rovder ke greeet for erforce of lctos the servce level greeet (SLA). Perforce requreets of ole lctos such s web lctos re usully secfed verge resose te of lcto servce. The resose te deeds o the vrous fctors lke resource cctes, utlzto lttos d etwork cogestos. The dt ceter rovder hs to llocte suffcet resources to the lctos to kee the requested verge resose te. Perforce requreets for lcto restrct the u resource cofgurtos cludg the uber of vrtul ches or CPUs for the lcto. By lloctg ore coutg resources, ost of CPU-tesve ole lctos lke web lctos rove ther rocessg ower d verge resose te. Sce the relto betwee verge resose te d the CPU llocto c be odeled usg queug theory, the requste uber of vrtul ches or CPUs c be estted fro the requested verge resose te. The detl of the erforce odel s descrbed the Secto IV. C. Fult-tolerce of Hostg Servers A host server flure s serous ssue the cosoldted server systes becuse t cuses the dows of ultle vrtul ches o the hostg server. Host server flures re duced by vrous cuses lke OS hg u, devce flures d uexected ower dow. To rotect lcto servces fro y host server flures, dt ceter rovder should cofgure the hostg server cluster wth redudt lcto stces. The fult-tolerce level of the dt ceter servce gst host server flure c be esured by the ccetble uber of sulteous host server flures. The etrc dctes cblty of keeg lcto servces survve t server flures the dt ceter. I the re of the dstrbuted coutg systes, syste tht c cotue servces cse of y k cooets flures s clled k-fult-tolerce [8]. I order to ke syste k-fult-tolerce wthout vrtulzto, the dt ceter rovder should rere k ddtol servers for ech lcto. For the dt ceter usg vrtulzto, lceet of vrtul ches s ortt s well s the rerto of redudt lcto stces to cheve k-fult tolerce. The fult-tolerce level c be chged by vrtul che lceets. Let us cosder exle of redudt cofgurto of four lctos {, 2, 3, 4 } usg three hostg servers {s, s 2, }. Ech hyscl server c ru three vrtul ches d ech lcto requres t lest oe vrtul che for u cofgurto. Fg. llustrtes two dfferet tters of vrtul che lceets. Fg. () dctes tht two vrtul ches for lcto d oe vrtul che for lcto 4 re lced o the hostg server s. The descrtos re se for s 2 d. 4 s s lcto vrtul che hostg server () o-fult-tolerce lceet (b) -fult-tolerce lceet Fg.. Redudt cofgurto of vrtul ches usg three hostg servers The dfferece betwee two lceets ers t host server flure. Whe y oe of hostg servers fls, the lceet () voltes the u cofgurto of y oe of lctos (, 2 or 3 ). O the other hd, the lceet (b) kees the u cofgurto of ll lctos d hece cheves -fult-tolerce. The lceet () becoes -fult-tolerce by ddg hostg server d lloctg ore vrtul ches for lcto stces s show Fg. 2 (c). The ore uber of hostg servers geerlly creses the uber of redudt lcto stces d roves the fult-tolerce level. However, the uber of hostg servers the dt ceter should be reduced ters of the totl cost. Dt ceter rovders eed to fd vrtul che lceet tht stsfes the requred fult-tolerce level, whle zg the uber of hostg servers s 4 s s 4 (c) -fult-tolerce lceet wth 4servers s 3 4 s 2 lcto vrtul che hostg server Fg. 2. Redudt cofgurto of vrtul ches usg four hostg servers III. PROBLEM DEFINITION The roble of vrtul che lceet for zg the uber of hostg server uder the secfed erforce requreets d fult-tolerce level s defed s cobtorl otzto roble. The ssutos de IEEE/IFIP Network Oertos d Mgeet Syosu - NOMS 200: M-Coferece 33

3 here re tht ll hostg servers hve the se ccty d ll vrtul ches re equl ters of the requred ccty. The ssutos re relstc eseclly for the sle hostg servces chrgg by the out of used vrtul ches d rovdg the coo qulty of the hostg servce. For rovdg the bss of the roble defto, the erforce requreets re ssued to secfy by the verge resose te. A. Redudt Vrtul Mche Plceet Let the set of lctos hosted the dt ceter be A= {, 2,.., }, d the set of equed hostg servers be S={s, s 2,.., s }. The x uber of vrtul ches s deoted s tht equls to the uber of vrtul CPUs o the server f ech vrtul che uses oe vrtul CPU. Vrtul ches o the server s j re deoted s {v j, v j2,..,v j }. The vrtul che lceet s exressed by the rojecto fucto φ ( v xy ) tht dctes the lcto rug o the vrtul che v xy. The gol of the otzto roble s to ze the uber of hostg servers, whle stsfyg the fult-tolerce level k d ll erforce requreets tht re secfed by the verge resose te r for ech lcto. Redudt vrtul che lceet roble: Solve vrtul che lceet φ so s to ze the uber of hostg servers uder the gve vlues of,, k d ( ). r The roble s cobtorl otzto roble tht hs objectve fucto. TABLE I NOTATION USED IN THE REDUNDANT VIRTUAL MACHINE PLACEMENT PROBLEM Sybol s j k r v xy φ( v xy ) Descrto Alcto clss ( ) Hostg server ( j ) Nuber of lcto clsses Nuber of hostg servers Mx uber of vrtul ches o hostg server Requred fult-tolerce level Requred verge resose te for lcto A vrtul che o the hostg server s x ( x, y ) Vrtul che lceet tht dctes the lcto clss tht rus o the v xy B. Lower Boud The uber of vrtul ches llocted to lcto s lted by the erforce requreets r. Let the u uber of vrtul ches for lcto be c. The lower boud of the uber of hostg server the redudt vrtul che lceet roble c be derved theoretclly fro the cosderto of the uber of vrtul ches survvg fter k host server flures. The uber of survvg vrtul ches t k host server flures out of host servers s gve by ( k). Sce these vrtul ches ust cot the u uber of vrtul ches c for ll, the followg codto s obted. c = ( k) () Becuse s teger vlue, the lower boud of s gve s follows. c + k (2) = IV. PERFORMANCE MODEL Ths secto descrbes the erforce odel for deterg the requste u uber of vrtul ches to stsfy the gve erforce requreets. The erforce of ole lcto such s web lcto servce s ofte lyzed usg queug odels. A sle erforce odel for sgle web server whch ssues Posso rrvl, geerl servce te d bouded cceted request uber of K hs bee odeled s M/G//K queue odel [9]. To cororte the burst request rrvl, the exteded odel MMPP/G//K hs bee reseted [0]. For ult-ter lcto systes, the request rrvl rte for ech server deeds o the lod blcg/schedulg lgorths. Severl studes used G/G/ to odel the erforce of ult-ter web lctos [][2]. Sce there s o geerl erforce odel tht c ly vrous ole lctos, ths er troduce M/M/ queue odel s bsc exle whch ssues Posso request rrvl d exoetl servce te. These ssutos re ot relstc soe ole lctos systes. The rorte erforce odel for ech lcto should be detered through soe exerets or observtos of rel worklod. Accordg to M/M/ odel, the verge resose te r of lcto wth servce rte μ d request rrvl rte λ s odeled s follows [3]. r = (3) μ λ Whe the lcto gets c tes lrger coutto ower by usg ore vrtul ches or vrtul CPUs, the verge resose te s roxted s follows. (4) r = λ μ c Cosequetly, gve the requested verge resose te r, the requste u uber of vrtul ches c s bouded by followg exresso. λ (5) c c = μ r Although the vlue of μ deeds o the lcto d vlble resources, t c be estted by observg the vlues of λ d r fro soe erforce exerets. Exresso (5) llows us to detere the requste u uber of vrtul ches c for stsfyg the requested verge resose te r. The estted u cofgurto s used to detere the vrtul che lceet ethod descrbed the ext secto IEEE/IFIP Network Oertos d Mgeet Syosu - NOMS 200: M-Coferece

4 Sybol λ μ c TABLE II NOTATION USED IN THE M/M/ PERFORMANCE MODELS Descrto Request rrvl rte of lcto Servce rte of lcto Requste u uber of vrtul ches for lcto V. VIRTUAL MACHINE PLACEMENT Ths secto troduces k-redudcy ethod d ultle k-redudcy ethod for deterg redudt vrtul che lceet. The ultle k-redudcy ethod cheves theoretclly u uber of hostg servers. A. Aroch r Perforce exerets λ μ Perforce Model c k Estto of redudt resources ' c Plceet Algorth Fg. 3. Procedure to solve the redudt vrtul che lceet roble A overvew of the roosed rocedure to solve the redudt vrtul che lceet roble s dected Fg. 3. Frst, erforce odel for ech lcto s geerted through exeretl erforce evlutos. Usg the geerted odel, the requste u uber of vrtul ches c s estted for stsfyg the requred verge resose te r. Next, to cheve the requred fult-tolerce level k, the uber of redudt vrtul ches c ' s estted cosderto wth c d. The uber of requred hostg servers s solved t the se te. Flly, lgorth for vrtul che lceet deteres lceet φ by c d. The detl of the lgorth s show the followg secto. Clerly, the estto ste dotes the decso of the requred uber of hostg servers tht s the objectve fucto of the redudt vrtul che lceet roble. As the estto ethods, the k-redudcy ethod s descrbed Secto C d the ultle k-redudcy ethod s descrbed Secto D. B. Plceet Algorth We defe lgorth for vrtul che lceet so s to cheve k fult-tolerce uder the gve c d. The redudt vrtul ches tht rovde the se lcto servce should be dstrbuted to the dfferet hostg servers order to dversfy the rsks of servce dow or erforce degrdto due to the hostg server flures. Therefore, the lceet lgorth for vrtul che lceet s desged wth the heurstc of dstrbutg the se lcto stces to dfferet hostg servers. The lceet lgorth s show Fg. 4. The fucto h-v-lceet returs vrtul che lceet lceet[] wth ut reters of c[] d. Ths fucto φ sorts ll of the vrtul ches by the lcto clsses, d ths order, lloctes the to the dfferet hostg servers uber order. Algorth :# c[] : requred VMs for ech lcto 2:# : uber of the hostg servers 3: 4: h-v-lceet(c[], ) { 5: cs[] = sort(c[]); # sort by lcto tye 6: totl = cs[].legth; # totl u of VMs 7: =0, y=; 8: whle (=<totl) { 9: for (x=; x++; x=<) { 0: lceet[x, y] = cs[]; # llocte : ++; 2: } 3: y++; 4: } 5: retur lceet[]; 6:} C. K-redudcy Method K-redudcy ethod lloctes k redudt vrtul ches to ech lcto. To ccolsh the k-fult-tolerce of the hostg server clusters, t lest k redudt vrtul ches for ech lcto re eeded besdes the u cofgurtos estted s c. I the covetol server clusters wthout vrtulzto, k-fult-tolerce s ccolshed by rerg k redudt hyscl servers. The k-redudcy ethod s estblshed o ths covetol roch. The totl uber of redudt vrtul ches for ech lcto, c s exressed s follows. ' c ' = c + k (6) Wth the k-redudcy ethod, vrtul ches tht host the se lcto stces ust ot ru o the se hostg server. Otherwse flure of sgle hostg server cuses ultle dows of the se lcto stces d leds to SLA voltos. Sce the lceet lgorth lloctes vrtul ches to the dfferet hostg servers the order of s j, ths restrcto s secfed s the followg costrt for. x c ' = x c + k (7) Aother costrt for s derved fro the fct tht the totl uber of requred vrtul ches c ' s ot over the totl = vlble vrtul ches o the hostg servers. Ths restrcto s exressed s follows d leds to other costrt codto for. = Fg. 4. Algorth for vrtul che lceet c ' (8) c ' = c + k (9) = = Fro the costrts (7) d (9), the u uber of hostg servers KR by k-redudcy ethod s exressed s follows. KR = x{x c + k, c + k } (0) = 200 IEEE/IFIP Network Oertos d Mgeet Syosu - NOMS 200: M-Coferece 35

5 The lgorth geertes vrtul che lceet usg the reters c d KR tht re decded by the exresso ' (6) d (0). I ths vrtul che lceet, u cofgurtos gve s c ecessrly survve t y k hostg server flures. Sce the syste s dssble to k host server flures, k-fult-tolerce of hosg server cluster s cheved. A drwbck of the k-redudcy ethod s tht the uber of hostg server KR s ot lwys equl to the theoretcl u vlue. For exle, the k-redudcy ethod does ot cheve the theoretcl u uber of hostg server the syste =3, k=, =3, d (c, c 2, c 3 ) = (3,, ). s 2 s 2 3 s () 8 VMs o 4 hosts (b) 9 VMs o 3 hosts Fg. 5. Redudt vrtul che cofgurto by k-redudcy ethod () d ltertve (b) The uber of redudt vrtul ches (c ', c 2 ', c 3 ') re clculted s (4, 2, 2) by the exresso (6). The KR equls to 4 by the exresso (0) d the vrtul che lceet s decded s Fg. 5 () by the lgorth. However, the k-fult-tolerce c be cheved wth oly three hostg servers, f the lceet s rovded s Fg. 5 (b) wth ddtol vrtul che for. I ths exle, the k-redudcy ethod requres uecessry hostg server. As result the k-redudcy ethod zes the totl uber of requred vrtul ches for k-fult-tolerce, but does ot lwys ze the uber of hostg servers. D. Multle k-redudcy Method Multle k-redudcy ethod roves the k-redudcy ethod for zg the requred uber of hostg servers. There s rsk of ore th k flures t k hostg server flures, f c + k s greter th. I order to kee c vrtul ches t k hostg server flures, the ultle k-redudcy ethod reres the tegrl ultle (ultles of x, where x s teger) of k of redudt vrtul ches. More secfclly, the totl uber of redudt vrtul ches for ech lcto decded by the ultle k-redudcy ethod s exressed s follows. c c ' = c + k k () The u cofgurtos secfed by c c be susted cse of y k hostg server flures, f the vrtul che lceet s decded by lgorth wth c ' estted by exresso (). The roof s gve s below. c < k Fro the exresso (), the uber of redudt vrtul ches s gve by c ' = c k (2) + s s Sce c ' s true ths cse, the c of vrtul ches c survve t y k server flures. ( α ) ( k) c < α ( k) where α s y teger greter th. Fro the exresso (), the uber of redudt vrtul ches s gve by c ' = c + α k (3) Sce ( α ) + k c ' < α s true ths cse, k server flures does ot cuse to ore th α k flures of vrtul ches d hece the c of vrtul ches certly survve. Fro the cosderto of the bove two cses, t s roved tht for ll ( c ), c of vrtul ches certly survve t y k hostg server flures. I the ultle k-redudcy ethod, there s o restrcto tht rohbts the exstece of ultle lcto stces o the se hostg server. The uber of hostg servers s bouded by the costrt of the totl uber of requred vrtul ches. The totl uber of requred vrtul ches s ot over the totl vlble vrtul ches *. = c ' (4) By rewrtg the c ' wth the exresso (), the totl uber of requred vrtul ches re exressed s follows. c c ' = c + k = = k (5) c c + k = k = c k = The exresso (4) c be rewrtte usg the bove equlty. c (6) k = The the costrt codto for c be exressed s below. c + k (7) = Cosequetly, the u uber of hostg servers MKR by the ultle k-redudcy ethod s gve by = c + k (8) MKR = By substtutg MKR to the exresso (), the uber of redudt vrtul ches for lcto s exressed s c ' = c + c c k (9) = The reters for lgorth, c ' d MKR re decded by the exresso (8) d (9), d the lgorth geertes vrtul che lceet tht cheves k-fult-tolerce of hostg server clusters. Sce MKR s equl to the theoretcl u vlue descrbed Secto III-B, the ultle k-redudcy ethod c ze the requred hostg servers uder y gve codtos IEEE/IFIP Network Oertos d Mgeet Syosu - NOMS 200: M-Coferece

6 VI. EVALUATION I order to evlute the roosed redudt cofgurto ethod, we coducted erforce exerets d sultos studes. A. Perforce Proflg The roosed roch descrbed Secto 5 uses the erforce odel for esttg the requste u uber of vrtul ches fro the erforce requreets secfed s r. A reter of the M/M/ odel μ whch vres deedg o lctos d vlble resources eeds to be estted by soe erforce exerets. Here, exle of erforce odel for web server s cosdered. The M/M/ odel for the web server s geerted fro the exeretl observto of the reltoshs og the uber of llocted CPUs, request rtes d verge resose tes. Clet Clet Clet CGI Ache HTTP requests Fedor Core 8 hostg server vrtul che CPU Core 2 Duo.8GHz x 2 Xe 3..2 RAM 0GB Fedor Core 8 Fg. 6. Cofgurto of testg evroet Fg. 6 llustrtes the cofgurtos of erforce test evroet. A Xe-bsed vrtul che rus o the hostg server tht hs 2 Dul Core Itel Xeo.8 GHz rocessors d 0GB of RAM wth Fedor Core 8 d Xe 3..2 hyervsor. A Ache web server rus o to of the test server. The erforce exerets re coducted by test CGI scrt tht receves web requests fro other clet host. Resose te (sec) Arrvl rte Fg. 7. Observtos d odel for request resose tes cu 2 cu 3 cu 4 cu Fg. 7 shows the chge of reltos betwee the request rtes d the verge resose tes by vryg the uber of vrtul CPU llocto fro to 4. The verge resose te s lwys uder 00 sec, uless the request rte over cert ot. Whe the request rte exceeds the ot the verge resose te creses steely. The vlue of the flecto ot of request rte s roortol to the uber of llocted vrtul CPUs. The roxto curves by M/M/ queue odel wth μ =0.6 re lso fgured s dotted les the Fg. 7. Although the she of the curve does ot coletely ft to the observed vlues, the odel gves good dcto for the boudry vlue of the request rte corresodg to the uber of llocted vrtul CPUs. By coductg slr erforce exerets, erforce odel for ech lcto c be geerted. The requste u uber of vrtul ches or vrtul CPUs s estted fro the geerted erforce odel secfed s exresso (5) d requred verge resose te r. For exle, to kee the verge resose te of ths lcto below 500 sec uder the codto λ = 25, the erforce odel revels tht t requres ore th 3 vrtul CPUs. B. Allocto Methods As descrbed Secto II, the uber of requred hostg servers for chevg the k-fult-tolerce uder y gve codtos chges deedg o the vrtul che lceet. I ths secto covetol roches for vrtul che lceet re descrbed for corso. The roble of vrtul che lceet for zg the uber of requred hostg server s forulzed s b ckg roble [4][5]. The b ckg roble s kow to NP-hrd roble whch s dffcult to solve coletely the relstc te, thus soe heurstc lgorths re used to coe wth ths roble. Frst-Ft decrese (FFD) s well kow owerful heurstc roch to the b ckg roble [6]. The FFD s effectve soluto to vrtul che lceet where ech lcto stce o the vrtul che requres dfferet sze of resources (e.g. the uber of CPUs). However, sce the cluster cofgured usg FFD does ot hve redudcy, ddtol k clusters tht hs the se cofgurto re requred to ccolsh the k-fult-tolerce. The requred uber of the hostg servers s show s below. FFD The FFD decdes vrtul che lceet of u cluster tht stsfes ll erforce requreets of hosted lctos, whle zg the uber of requred hostg servers s uch s ossble. By rerg k bcku clusters of ths u cluster, the syste c cheve k-fult-tolerce. Let the requred uber of hostg servers for the u cofgurto by the FFD be FFD. The vlue of FDD s bouded s follows. c (20) FFD = I ddto, uer boud of FFD s gve by FFD OPT c (2) = where OPT s otu soluto of the b ckg roble [6] d the vlue of OPT s ore th c. = The the best d worst of the requred uber of hostg servers by FFD re gve s follows. FFD -best = c ( k + ) (22) = FFD -worst = c = ( k ) (23) 200 IEEE/IFIP Network Oertos d Mgeet Syosu - NOMS 200: M-Coferece 37

7 Nuber of hostg servers MKR KR-best KR-worst FFD-best FFD-worst Nuber of lctos () (b) (c) Nuber of hostg servers MKR KR-best KR-worst FFD-best FFD-worst Fult-tolerce level k Nuber of hostg servers Ccty Fg. 8. Corso results by vryg () the uber of lctos, (b) the requred fult-tolert level k, d (c) the ccty of hostg server. MKR KR-best KR-worst FFD-best FFD-worst k-redudcy ethod The syste wthout vrtulzto hs to rere k redudt servers to cheve k-fult-tolerce. Ths kd of redudt cofgurto techque s clled s N+M redudt cofgurto. The k-redudcy ethod les ths roch to the vrtul che cofgurtos. The requred uber of the hostg servers by the k-redudcy ethod s rovded s KR s show Secto V-C. The vlue of KR deeds o the xu vlue of c whch vres wth the followg rge. c x c c + (24) = = The the best d worst of the requred uber of hostg servers by k-redudcy ethod re gve s follows. KR -best = x{ c + k, c + k } (25) = = KR -worst = x{ c + + k, c + k } (26) = = Multle k-redudcy ethod The ultle k-redudcy ethod roves the k-redudcy ethod to cheve k-fult-tolerce wth lower uber of the hostg servers. Ths ethod reres the tegrl ultle of k of redudt vrtul ches. The requred uber of hostg servers by ultle k-redudcy ethod s rovded s MKR s show Secto V-D. A. Sulto Studes The requred uber of hostg servers by the ultle k-redudcy ethod s evluted uder vrous ut reters wth corso to the FFD bsed roch d k-redudcy ethod. Frst, order to observe the effects of the chge of the uber of lctos, the requred uber of hostg servers re evluted wth the gve reters =4,k=, d c = c = 3 (the verge uber of c ). Corso = results show Fg. 8 () dcte the roosed ultle k-redudcy ethod s ror to y other ethods deedet to the vlue of. The greter, the ore dvtge the ultle k-redudcy ethod hs. The drwbck of the k-redudcy ethod s the vrto of the results deedg o the cobto of the uber of lcto stces for ech lcto clss. The result rglly worse th the ultle k-redudcy ethod the best cse, however, the worst cse, the k-redudcy ethod requres ore th twce uber of the hostg servers cored wth the ultle k-redudcy ethod. Next, order to observe the effects of the chge of the requred fult-tolerce level k, the requred uber of hostg servers re evluted wth the gve reters =4, =5, d c = 3. Corso results show Fg. 8 (b) dcte the ultle k-redudcy ethod cheves best erforce the gve requreets k cored to other ethods. Furtherore, order to observe the effects of the chge of the ccty of ech hostg server, the requred uber of hostg servers re evluted wth the gve reters k=, =20, d c = 3. Corso results show Fg. 8 (c) dcte the ultle k-redudcy ethod s ror to y other ethods deedet to the vlue of. Accordg to the crese of the ccty, the dfferece betwee the ultle k-redudcy ethod d the best cse of the k-redudcy ethod becoe sll. However, the worst cse of the k-redudcy ethod does ot rove eve f the ccty creses. VII. RELATED WORK Although there hs bee lot of works o hgh-vlblty techques for server clusters, the cobto of hgh-vlblty techques d vrtulzto s oe of the eergg ssues [7]. To ke lcto systes rug o vrtul ches hgh-vlble, VMwre rovdes VMwre HA (Hgh Avlblty) [8]. I the evet of host server flure, VMwre HA restrts vrtul ches utotclly o the other hostg server. Sce the VMwre HA s rectve roch, teorl servce dow or erforce degrdto s evtble. Cotrrly, roctve roch bsed o the flure erdto of the hostg server hs bee roosed for Xe vrtulzto ltfor [9]. The ethod redcts hostg server flure by resource otorg, d evcutes vrtul ches oto the dfferet hostg server before the occurrece of y flures. Soe flures re redctble by otorg the sttus of server resources lke CPU, eory, f d dsk logs. However, t s dffcult to redct ll flures by otorg dvce. The roosed ethod s ctegorzed s roctve roch d hs orgl dvtge tht kees the u IEEE/IFIP Network Oertos d Mgeet Syosu - NOMS 200: M-Coferece

8 cofgurto of lcto servce t y k hostg server flures. A sle redudt cofgurto ethod for vrtul ches o ultle hostg servers s reseted [7]. I cotrst, our study defes redudt vrtul che lceet roble s cobtorl otzto roble d rovdes otu soluto. Dyc resource llocto roble hs bee studed well the cluster systes, grd coutg d utlty coutg. Cluster Reserves reseted resource llocto echs for soltg the erforce of clustered web servces [20]. Cluster-O Ded resets utoted frework to ge resources shred hostg ltfor [2]. For the ult-ter web lcto systes, the dyc resource rovsog ethod bsed o G/G/ erforce odel hs bee roosed [22]. Sce the exstg resource llocto d rovsog ethods ly focus o the otzto of erforce d resource utlzto systes, they do ot tke to ccout the fult-tolerce crter. Few works cororte the requreets for relblty d vlblty of lcto systes the resource llocto lgorth [23][24]. However the vrtul che lceet roble corresodg to host server flures s ot forulted d otu soluto hs bee ot dscussed well. Ths er defes vrtul che lceet roble wth the codto of requred fult-tolerce level d shows lgorth to fd otu soluto. VIII. CONCLUSION Ths er resets ethod to ke redudt cofgurto of hostg server cluster for ultle lctos usg vrtul ches. Cosoldted server systes usg server vrtulzto volves serous rsks of host server flures tht cuses ultle dows of vrtul ches. The roosed ultle k-redudcy ethod zes the uber of requred hostg servers to kee the u cofgurto for stsfyg the erforce requreets for ll lctos t y k host server flures. The ethod lloctes tegrl ultle of k of redudt vrtul ches to ech lcto d lces the to dfferet hostg server usg the sle lceet lgorth. The dvtge of the ultle k-redudcy ethod s show through the exeretl results of corso wth the covetol N+M redudt cofgurto roch d the FFD-bsed vrtul che lceet roch. Cosoldted server systes becoe ore relble wth low cost by usg the roosed ultle k-redudcy ethod. REFERENCES [] VMwre Ifrstrcture: htt:// [2] Ctrx XeServer: htt://ctrx.co/eglsh/s2/roducts/roduct.s?cotetid=68348 [3] G. Kh, K. Bety, G. Kr, d A. Kochut, Alcto Perforce Mgeet Vrtulzed Server Evroets, I Proceedgs of 0th IEEE/IFIP Network Oertos d Mgeet Syosu (NOMS2006), , [4] D. Kusc, J. Kehrt, J. Hso, N. Kdsy, d G. Jg, Power d Perforce Mgeet of Vrtulzed Coutg Evroets V Lookhed Cotrol, I Proceedgs of the 5th IEEE Itertol Coferece o Autooc Coutg (ICAC2008),. 3-2, [5] L. Hu, H. J, X. Lo, X. Xog, d H. Lu, Mget: A ovel schedulg olcy for ower reducto cluster wth vrtul ches, I Proceedgs of the 2008 IEEE Itertol Coferece o Cluster Coutg,. 3-22, [6] Ache Module od_roxy_blcer, htt://httd.che.org/docs/2.2/ od/od_roxy_blcer.htl [7] MySQL Cluster NDB 6.X/7.X Referece Gude, htt://dev.ysql.co/doc/#cluster [8] A. S. Tebu, d M. v Stee, Dstrbuted Systes Prcles d Prdgs, Pretce Hll Ic., , [9] J. Co, M. Adersso, C. Nyberg, d M. Khl, Web Server Perforce Modelg usg M/G//K*PS Queue, I Proceedgs of the 0th Itertol Coferece o Telecouctos (ICT 2003), [0] M. Adersso, J. Co, M. Khl, d C. Nyberg, Perforce Modelg of Ache Web Server wth Bursty Arrvl Trffc, I Proceedgs of the Itertol Coferece o Iteret Coutg (IC), [] Z. C, Y. Che, V. Kur, D. Mlojcc, d K. Schw, Autoted Avlblty Mgeet Drve by Busess Polces, I Proceedgs of the 0th IFIP/IEEE Itertol Syosu o Itegrted Mgeet (IM2007), , [2] B. Urgokr, P. Sheoy, A. Chdr, d P. Goyl, Dyc Provsog of Mult-ter Iteret Alctos, I Proceedgs of the 2d IEEE Itertol Coferece o Autooc Coutg (ICAC2005), , [3] G. Tesuro, N. Jog, R. Ds, d M. Be. A Hybrd Reforceet Lerg Aroch to Autooc Resource Allocto, I Proceedgs of the 3rd IEEE Itertol Coferece o Autooc Coutg (ICAC2006), , [4] G. Jugy, K. R. Joshz, M. A. Hltue, R. D. Schlchtg, d C. Pu, Geertg Adtto Polces for Mult-Ter Alctos Cosoldted Server Evroets, I Proceedgs of the 5th IEEE Itertol Coferece o Autooc Coutg (ICAC2008), , [5] N. Bobroff, A. Kochut, d K Bety, Dyc Plceet of Vrtul Mches for Mgg SLA Voltos, I Proceedgs of the 0th IFIP/IEEE Itertol Syosu o Itegrted Mgeet (IM2007),. 9-28, [6] B. Korte, J. Vyge, Cobtorl Otzto: Theory d Algorths, Jese Edto 2005, Srger, [7] S. Loveld, E. M. Dow, F. LeFevre, D. Beyer, d P. F. Ch, Levergg vrtulzto to otze hgh-vlblty syste cofgurtos, IBM Syste Jourl, Vol. 47, No. 4, [8] VMwre Hgh Avlblty: htt:// [9] A. B. Ngrj, F. Mueller, C. Egel, d S. L. Scott, Proctve fult tolerce for HPC wth Xe vrtulzto, I Proceedgs of the 2st ul tertol coferece o Suercoutg (ICS07), , [20] M. Aro, P. Druschel, d W. Zweeoel, Cluster Reserves: A Mechs for Resource Mgeet Cluster-bsed Network Servers, I Proceedgs of the ACM SIGMETRICS Coferece 2000,. 90-0, [2] J. S. Chse, D. E. Irw, L. E. Grt, J. D. Moore, d S. E. Srekle, Dyc vrtul clusters grd ste ger, I Proceedgs of the 2th IEEE Itertol Syosu o Hgh Perforce Dstrbuted Coutg (HPDC-2), , [22] B. Urgokr, P. Sheoy, A. Chdr, P. Goyl d T. Wood, Agle Dyc Provsog of Mult-ter Iteret Alctos, ACM Trsctos o Autooous d Adtve Systes (TAAS), Volue 3(), :-:39, Mrch [23] N. R. Gottuukkl, C. Legsuksu, R. Nssr, d S. L. Scott, Relblty-Awre Resource Allocto HPC Systes, I Proceedgs of the IEEE Itertol Coferece o Cluster Coutg 2007 (Cluster2007), , [24] F. Mchd, d Y. Meo, Avlblty-Costred Vrtul Mche Plceet for HA Clusters, I the Fst Abstrct of The 39th IEEE/IFIP Itertol Coferece o Deedble Systes d Networks (DSN2009), IEEE/IFIP Network Oertos d Mgeet Syosu - NOMS 200: M-Coferece 39