Forecasting Demand of Potential Factors in Data Centers

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1 Iformaica Ecoomică vol. 3, o. /29 9 Forcasig Dmad of Poial Facors i Daa rs Alxadr PINNOW, Sfa OSTERBURG, Lars HANISH Oo-vo-Guric-Uivrsiy, Magdburg, Grmay {alxadr.piow sfa.osrburg lars.haisch}@ii.cs.ui-magdburg.d This papr dals wih forcasig dmad of poial facors i daa crs. Firsly i will dfi facors hmslvs ad hir imporac i h procss of daa crs. Th i will b show how hr sadard forcasig mhods ca b applid for prdicig capaciy ds i daa crs. Kywords: daa cr, forcas, capaciy plaig. Moivaio Nowadays, daa crs ar big ru icid-driv. Qui of furhr hardwar sysms ar isalld as a racio o w cusomr ds. Dspi acquisiio coss for furhr hardwar sysms big cosidrd ucriical, h xsio of h iformaio ifrasrucur lads o highr admiisraio, maiac, ad fially prsol coss. For a ffici usag of h xisig iformaio ifrasrucur, hr ar cocps such as Virual ad Adapiv ompuig o logically spara hard ad sofwar. Ralizig hs cocps allows abadoig iciddriv busiss srucurs. Thrfor, h adapio of suiabl procsss of opraiv producio plaig ad corol sms o b mos usful. Th plaig of uilizaio coms alog wih capaciy ad im maagm. Fudam for h capaciy ad im maagm is h producio plaig, which ca b coducd wih opimizaio modls ad forcasig procsss. Facors of a daa cr ar idifid i h followig chapr. Nx, forcasig procsss of producio program plaig ar applid i ordr o drmi h amou of cssary poial facors. 2. Facors Th daa cr as a producio sysm producs IT-srvics as oupu, which ar mad availabl o h cusomrs as IT-producs [8]. Such a producio sysm ca b dscribd by is producios facors. Facors which fulfill plaig, corollig, ad orgaizaioal aciviis ar labld as maagrial facors. Thy corol h combiaio of all producio facors. Producio facors ar dividd io raw marials ad supplis ad poial facors. Raw marials ad supplis ar cosumd durig h producio procss by bcomig par of h oupu or bcaus i is hir limiaio which abls h producio i h firs plac. Th capaciis of poial facors ar pu a h producio procss disposal wihou ay loss of hir produciv ffcivss [9]. Prsol, applicaio sysms, ad fudamal sysms ar major pars of h iformaio ifrasrucur i daa crs [2]. Applicaio sysms, fudamal sysms, as wll as h prsol chargd wih opraig h daa cr ca b cosidrd poial facors. Poial facors ca b ophysical ad physical. Applicaio sofwar ad fudamal sysms such as dvlopm virom, daa bas sysms, or opraioal sysms ar o-physical poial facors. Hardwar as a fudamal sysm ad h prsol, which is chargd wih opraig h ifrasrucur, is physical poial facors. Th maximum oupu of a poial facor is dscribd as capaciy [5]. Wh dscribig compur sysms as hardwar uis, hy ca b cosidrd as a s cosisig of procssor, sorag ad ipu/oupu dvics. Ipu/oupu dvics ar usd for h commuicaio wih h compur sysm. Th procssor rrivs isrucios from h sorag, dcods hs isrucios, ad fially xcus hm. Th hardwar compo sorag is dividd io primary ad scodary sorag. Primary

2 Iformaica Ecoomică vol. 3, o. /29 sorag holds h daa durig h immdia opraio of applicaio ad fudamal sysms [5]. Scodary sorag is o-volail sorag, usually dis sorag. Th capaciy of h scodary sorag ormally xcds h primary sorag svral ims [3]. Evry hardwar compo has a capaciy ha is dscribabl by a suiabl masur. A masur o xplai h procssors capaciy is h maximum umbr of opraios pr scod ha h procssor ca xcu [8]. Th valuaio of capaciy is coducd i millios of isrucios pr scod (MIPS). Th commuicaio of ipu/oupu dvics as plac via chals. A chal is h cocio bw h sdr of iformaio ad h rcivr. Th rasfr spd is drmid hrough badwidh [6], which is giv i bis/s [6]. Th sorag capaciy drmis how may sorag clls, which ca sor biary digis, hr ar o a mdium. Th capaciy valuaio is coducd i bi or by [4]. Th commuicaio wih xral sorag sysms as plac via ipu/oupu dvics. hal badwidh ds rcogiio alog wih sorag capaciy. Th dvlopm of h hardwar compo capaciy ca b dscribd hrough Moor s Law, which xplais ha h umbr of rasisors i a igrad circui doubls approximaly vry 8 mohs [5]. Th hardwar compos capaciy grows xpoially dpdig o im. Th facor dscribs h iiial capaciy. Th xpo is h growh ra. () = (2.) Th followig is valid for h - muliplicaio of capaciy wihi h im T : = ( T ), = T l =, l = T, = T (2.2) Th growh ra for doublig h capaciy vry.5 priods is: l 2 = (2.3) If all q hardwar uis of h arlis graio wr subsiud by q rc hardwar uis i his modl, h h ovrall capaciy of h hardwar compos i h daa cr icrass: h daa cr s ovrall capaciy Hardwar i h mom is h sum of oal capaciis of ach hardwar graio i h daa cr. From formula (2.) follows: Hardwar () = q * = (2.4) A daa cr cosiss of graios wih q hardwar uis. Th capaciy of h arlis hardwar graio is dscribd by formula 2.5: = ( ) (2.5) Th rsulig capaciy for h daa cr (2.4) is: ( ) () = q Hardwar = = q = (2.6) This is a gomric sris ad hus, ca b rasformd: ( ) Hardwar () = q = q ( ) = q (2.7) ( ) = q ( ) = q ( ) Hc, h ovrall capaciy of h daa cr s hardwar compos grows xpoially T as wll, y i grows slowr ha h capaciy of hardwar compos i avrag. This ffc is du o h usag of hardwar compos from oldr graios. Th followig is valid for h avrag capaciy φ of a daa cr wih hardwar graios, ach quippd wih q hardwar Hardwar uis:

3 Iformaica Ecoomică vol. 3, o. /29 () Hardwar q q = = φ (2.8) If a daa cr mploys mor ha o hardwar graio, h avrag capaciy φ Hardwar of h daa cr will grow slowr ha h commo capaciy. Th avrag capaciy is qual o h commo capaciy i h spcial cas of h daa cr cosisig of oly o curr hardwar graio: () () Hardwar δ δ δ δ φ for N R, > (2.9) R, > Th rsul of h firs drivaiv is: (2.) I is prov by mahmaical iducio, ha: (2.) Iquaio 2. holds for = : (2.2) Th iduciv sp for iquaio 2. rsuls o: (2.3) Th xpoial fucio is > udr h codiio of >, hc i mus b ru ha: q..d. (2.4) Fig.. Dvlopm of procssor capaciy Fig. shows h dvlopm of procssor capaciy i a daa cr udr h assumpios ha h capaciy doubls vry wo priods, a hardwar graio is xchagd afr fiv priods, ad h iiial capaciy is 8 MIPS. Th xpoially icrasig capaciy of hardwar compos ar also dmadd by h cusomrs. Th compsaio of chological progrss hrough highr cosumpio of rsourcs is ow as h Rboud-ffc []. Th icras i cosumpio of rsourcs is calld primary Rboud-ffc [7]. Th capaciy of poial facors hld availabl dos o rprs h acual dmad. A dmad progosis is cssary, i ordr o rval h acual dmad of poial facors, which will b discussd i h followig chapr.

4 2 Iformaica Ecoomică vol. 3, o. /29 3. Dmad Forcas omig alog wih h producio plaig, forcasig procdurs ar usd wih h goal o prdic h fuur dmad of raw marials ad supplis basd o hir hisoric dmad [6]. I cas of rgular d o disiguishs bw forcasig procdurs for cosaly, rdily, ad sasoally flucuaig dmad. Procdurs for rdy dmad ca always b usd isad of forcasig mhods for cosa dmad. I h spcial cas of cosa dmad h rd coms o zro []. Forcasig mhods for sasoally flucuaig dmad ar mos ssibly usd i sasoal cycls. Liar rgrssio is h bs-ow dmad forcasig mhod for a rdy dmad [], ad so is Brow s Liar Expoial Smoohig [2] as wll as Hol s mhod [4]. Th miod forcasig modls rly o h assumpio ha h lvl of dmad liar rd ovr im. This mas ha [6]: y b b ε = (3.) Th variabl b rfrs o h axis scio of h rd li. Facor b dscribs h slop of h rd li. Th idpd variabl rprss h chroological cours. Radom flucuaios ar displayd via є. I formula 3. є is ormal-sadard disribud wih a aicipaio rm of E є = [9]. Furhr forcasig procdurs xis for rd-li courss of highr ordr. Liarizaio is cssary i advac if hs masurs ar mployd []. Th followig liar rasformaio rsuls i cas of xpoial dmad fucios [7]: y l y l y = b ε = lb = b b b lε b b = lb (3.2) Producio plaig should adap forcasig procdurs as a mhod o drmi h dmad of poial facors. Th avrag capaciy dmad of hardwar uis shall b simad usig of his mhod. Th applicaio of forcasig procdurs is usful bcaus h pas dmad of capaciis ca b ascraid wih rspciv ools. Usually, oly o hird or lss of h hardwar capaciis ar mployd. If a poial facor is o fully uilizd, h is dgr of uilizaio rflcs is acual dmad. Hc, h dvlopm of avrag uilizaio of capaciy ca srv as daa bas for forcasig procdurs. Th progosis for ach hardwar ui is coducd sparaly. Th avrag uilizaio of capaciy of ach hardwar compo pr hardwar ui is drmid via h rspciv masurig ools. Th avrag capaciy dmad c is drmid by h avrag uilizaio of capaciy of hardwar compos ŋ pr hardwar ui i: ci = ηi i (3.3) Th avrag capaciy dmad of a hardwar compo c rsuls from h sum of h sigl dmad of capaciy: c = c i i= (3.4) Th avrag procssor capaciis displayd i abl srv as daa sampl. Th capaciy dmad for poial facors is o fr from sasoal flucuaios. Thus, h progosis priod is dimsiod so ha i compasss a compl sasoal cycl bcaus hardwar uis cao b isalld ad d-isalld wih sasoal dpdcy. Th show forcasig procdurs ar applicabl bcaus h growh of capaciy dmad follows a xpoial rd ad sasoal flucuaios mus o b cosidrd. Tabl. Masurd avrag procssor capaciy dmad Priod apaciy c i MIPS l c I ordr o prdic h avrag procssor capaciy dmad, a liar rgrssio, Brow s Liar Expoial Smoohig, ad h Hol s mhod ar coducd. Th dvlopm of dmad follows a xpoial

5 Iformaica Ecoomică vol. 3, o. /29 3 rd. Liarizig h xpoial valus accordig o formula 3.2 is compulsory wih h iio of applyig h dscribd forcasig procdurs. Th liarizaio rsuls show i abl as wll. Fig. 2 shows h dvlopm of h avrag dmad of procssor capaciy for daa crs ad h liarizaio rsuls. Suiabl valus for paramr α hav o b simad wih h goal of achivig saisfyig forcas rsuls wih h Brow s Liar Expoial Smoohig. For h simaio of h smoohig cosa of firs ordr, havig sampls, h followig rul is suggsd [3]: 2 α = (3.5) Fig. 2. Masurd valus of procssor capaciy Th smoohig cosa of m-h ordr is rlad o h smoohig cosa of firs ordr [2]: α = ( α ) m m (3.6) Smoohig cosa α is simad o α =.8 for h igh prs sampls. α is rusd for h Hol s mhod. Du o simplificaio rasos, smoohig paramr β is cosidrd as a paramr of h x highr ordr ad simad a β =.84. Th progosicad valus of h las four priods of h rspciv forcasig procdur ar compard o h rlva sampl valus wih h aim of valuaig h forcasig procdur s rsuls. Th sampl valus of h firs four priods oly srv as a daa bas. Th prdicio of h valus for o priod is oly coducd a had of h prcdig priod s sampl valus. I abl 2 o ca s h forcasig rsuls ŷ as wll as h rsidual valus ε of h forcasig procdurs ou of h las four priods. Tabl also shows h sadard dviaio valus of h rsidu σ ε, which wr calculad i a x-posaalysis. Hol s mhod has h smalls sadard dviaio valu of h rsidu. Hc, h procdur dlivrs h bs rsuls for h prs sampl valus i coopraio wih h giv smoohig paramr.

6 4 Iformaica Ecoomică vol. 3, o. /29 Tabl 2. Rsidu valus of h forcasig procdurs Brow s Liar Expoial Liar rgrssio Smooh- ig Hol s mhod α β ε ε ε Th avrag procssor capaciy dmadd ĉ i priod 9 is: yˆ cˆ = = 269MIPS (3.7) 9 4. oclusios Th capaciy of mos hardwar compos pr daa cr grows xpoially. Th Rboud-ffc dscribs h circumsac ha h xra capaciis ar cosumd by h cusomr as wll. Liar rgrssio, Brow s Liar Expoial Smoohig, ad Hol s mhod ca b mployd i ordr o prdic h avrag capaciy dmad of hardwar compos i daa crs. Th sampl daa of avrag uilizaio of capaciy of prcdig priods srvs as daa bas. Th hardwar compos capaciis ar usually dimsiod so ha hir uilizaio of capaciy is lowr ha o-hird. Thus, h uilizaio of capaciy of hardwar compos is suiabl as daa bas. Th daa collcio is coducd wih h cssary masurig ools. Th rsul of h forcas is h xpcd avrag dmad of capaciy for h succdig priod. Th dmad of capaciy is o cosa ovr h priod bu is xplaid via a disribuio fucio. apaciy shorags ca b prvd bcaus o ca cofigur h capaciy of hardwar compos wih h hlp of saisical procdurs ha ar basd o h avrag uilizaio of capaciy. Hc, h show forcasig procdurs ar a corrso for h acual capaciy plaig. Rfrcs [] R. G. Brow. Marials maagm sysms: a modular library. Malabar, Fla.: Krigr, 984, pp [2] R. G. Brow ad R. F. Myr. Th fudamal Thorm of Expoial Smoohig. Opraios Rsarch: h joural of h Opraios Rsarch Sociy of Amrica, Vol. 9, No. 5, 96, pp [3] S. A. DLurgio. Forcasig pricipls ad applicaios. Boso, Mass. a.o: McGraw-Hill, 988, p. 56. [4].. Hol. Forcasig sasoals ad rds by xpoially wighd movig avrags. I: Iraioal joural of forcasig, vol. 2, 27, pp. 5-. [5] W. Kr, W. Idusrill Produioswirschaf. Poschl: Sugar, 992, pp. 2. [6] H. Klima, R. Piorasch ad D. SchöfldIformaios- ud Kodirugshori. Sugar: Tubr, 26, pp. 75, 86. [7] R. Kuhl. Wisssöologi, i: Kuhl, R./Sgr, T./Srauch, D. : Grudlag dr praisch Iformaio ud Doumaio. Müch: Saur, 24, pp. 8. [8] H. Lagdörfr, H, Lisugsaalys vo Rchsysm: Mss, Modllir, Simulaio. Müch: Hasr, 992, pp. [9] S. Maridais, S.. Whlwrigh ad V. E. McG. Forcasig: mhods ad applicaios. a.o. Nw Yor : Wily, 983, p. 22. [] J. Nr al. Applid liar saisical modls. a.o. Boso, Mass.: McGraw- Hill, pp [] F. J. Radmachr. Buildig h Ifor-

7 Iformaica Ecoomică vol. 3, o. /29 5 maio Sociy: Labour Mar Prssurs, Globalisaio, ad h Poliical Goal of Susaiabiliy as hallgs o h Rgios i Europ. I: Surm, R., Wima, G.: Th iformaio sociy ad h rgios i Europ: a Briish- Grma compariso. Bad-Bad: Nomos-Vrl.-Gs, 2, p. 232 [2]. Rausrauch. Effizir Eisaz vo Arbisplazsysm -- Kozp ud Mhod ds Prsölich Iformaiosmaagms. a.o. Bo: Addiso-Wsly Logma, 997, pp. 3. [3] A. Hur ad G. Saa, Daba: Implmirugschi. Bo: MITP, 999, pp. 44. [4] H. J. Schidr. Lxio Iformai ud Davrarbiug. a.o. Müch: Oldbourg, 998, p. 82. [5] A. S. TabaumSrucurd compur orgaizaio. a.o. Eglwood liffs: Pric-Hall Ira, 999, p 25, 3. [6] H. Tmplmir. Marial-Logisi: Modll ud Algorihm für di Produiosplaug ud -surug i Advacd-Plaig-Sysm. a.o. Brli: Sprigr, 26, pp. 36, 5 [7] K. Wbr. Wirschafsprogosi. Müch: Vahl, 99, p. 7. [8] R. Zarow, W. Brr, U. Pilgram. Igrad Iformaio Maagm: Applyig Succssful Idusrial ocps, i IT. Brli, Hidlbrg: Sprigr, 26, p. 6. [9] G. Zäpfl, Grudzüg ds Produiosud Logisimaagms. Müch, Wi: Oldbourg, 2, pp 6. Alxadr PINNOW sudid Busiss ad ompur Scic uil 23. Th h word as sofwar gir spcializd i fiacial mars. Sic 26 h is sciific assisa a h Vry Larg Busiss Applicaios Lab of h Oovo-Guric-Uivrsiy i Magdburg, Grmay. His ara of rsarch is h daa cr as a producio faciliy for IT-srvics wih focus o capaciy maagm i adapiv ad virualizd daa crs. H publishd svral paprs i his fild of sudy. Th rsarch i his ara is a coopraio of h VLBA-Lab ad h Grmay basd IT-srvic providr T-Sysms. Sfa OSTERBURG sudid ompur Scic uil 2 ad passd his diploma wih disicio. H had word as a sofwar gir ad cosula for Microsof ERP sofwar (Dyamics AX) for svral yars, bfor i 26 h bcam sciific assisa a h Vry Larg Busiss Applicaios (VLBA) Lab of h Oo-vo-Guric-Uivrsiy i Magdburg. His ara of rsarch is h daa cr as a producio faciliy for IT-srvics wih focus o availabiliy maagm i adapiv ad virualizd daa crs. Th rsarch i his ara is a coopraio of h VLBA-Lab ad h Grmay basd IT-srvic providr T-Sysms. Lars HANISH has b sudyig Iraioal Maagm a h Oo-vo- Guric Uivrsiy Magdburg sic 23. Durig his sudis h word for Volswag i Grmay ad hia cosulig h maagm of h Tchical Dvlopm dparm. Furhrmor, h assisd h rsarch of h Oovo-Guric-Uivrsiy i Magdburg, focusig o Erpris Rsourc Plaig Sysms for IT srvic providrs. His ara of rsarch irss ar iraioal coopraio ad iraioal supply chai maagm.