Preventive Maintenance for Cloud-Based Software Systems Subject to Non-Constant Failure Rates

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1 rvntiv Maintnanc for Cloud-Basd Softwar Systms Subjct to Non-Constant Failur Rats Jan Rahm and aiing Xu Comutr and Information Scinc Dartmnt Univrsity of Massachustts Dartmouth, Dartmouth, MA 0747, USA {jrahm, Abstract Onlin alications, such as -commrc, hav mad a hug imact in our daily lif. With th raid shift of onlin alications to cloud-basd latforms in rcnt yars, it bcoms vry imortant to maintain th high Quality of Srvic QoS for cloud-basd softwar systms in ordr to suort succssful businsss. Sinc hardwar rliability has bn wll undrstood and is tyically guarantd by th cloud rovidrs, softwar failurs hav now bcom th major factor of systm failurs in cloud-basd softwar systms. Corrctly masuring th rliability and availability of a cloud-basd softwar systm is critical for making rvntiv maintnanc schduls. In this ar, w addrss softwar-aging rlatd bugs or faults that may lad to rformanc dgradation or incrasd failur rats of systm comonnts. Basd on our rvious work, w study how to driv rvntiv maintnanc schduls for cloud-basd softwar systms subjct to non-constant failur rats. W adot th Wibull distribution to modl an incrasing failur rat for softwar comonnts with softwar-aging issus. Finally, w us a cas study to show that our analytical aroach can ffctivly suort dvlomnt of softwar rjuvnation schduls for rvntiv maintnanc of cloud-basd softwar systms. Kywords-Softwar rliability nginring; softwar aging; rliability analysis; rvntiv maintnanc; softwar rjuvnation schdul; non-constant failur rat I. INTRODUCTION Ovr th ast dcads, onlin alications hav mad a hug imact in our daily lif. Cloud comuting, th ida of using comuting rsourcs as a utility, has bcom an attractiv aradigm for dvlors to dloy thir srvics and gt thir srvics startd, without th nd to snd larg caital in hardwar rsourcs. As th shift to cloud comuting is raidly incrasing, thr is a rssing nd to maintain a high Quality of Srvic QoS for cloud-basd systms to suort succssful onlin businsss. As hardwar rliability is wll undrstood and is tyically guarantd by th cloud rovidrs [], softwar faults in cloud srvics hav bcom a major factor lading to systm failurs in cloud-basd systms. Various stratgis in Softwar Rliability Enginring SRE can b usd to combat against softwar faults to achiv highly rliabl softwar. Bfor th conct of softwar aging was introducd, SRE suortd analysis of softwar dfcts and rlatd to isnbugs or BohrBugs []. Bohrbugs ar asir to dal with sinc thy ar dtrministic, and can b liminatd at th dsign lvl by dbugging or adoting dsign divrsity. On th othr hand, isnbugs ar non-dtrministic rrors, which aar at th orational lvl, and can b dalt with by rtrying th oration or rstarting th associatd alication. owvr, nithr of ths two tys of bugs would lad to an incrasing failur rat; thrfor, w tyically assum constant failur rats for softwar comonnts that ar subjct to ths tys of bugs [, ]. Softwar-aging rlatd bugs ar non-dtrministic lik isnbugs, thus, both of thm ar classifid undr Mandlbugs []. owvr, softwar-aging rlatd bugs may rsult in an incrasd failur rat sinc th rror conditions, such as unrlasd mmory du to mmory laks, can accumulat in a running alication or within its nvironmnt.g., th orating systm. To dal with softwar aging and assur softwar fault tolranc, softwar rjuvnation rocss has bn introducd as a roactiv aroach to countracting softwar aging and maintaining a rliabl softwar systm [4]. In this work, w tak advantag of cloud-basd softwar dsign to rform rjuvnation in its siml form, namly to rstart th alication or its softwar comonnts subjct to softwar aging with incrasing failur rats that would lad to th dgradation of systm rformanc. Fault tolranc and fault or failur forcasting ar two major tchniqus that can b adotd sid by sid to imrov th systm rliability for an orational softwar systm [5]. Fault tolranc in this work is achivd by mloying standby ot Softwar Sars SS; whil failur forcasting is to stimat th failur-tim robability dnsity function df basd on mirical data collctd for th dsignd fault-tolrant systm. In th contxt of cloud comuting, SS is a Virtual Machin VM instanc that is availabl instantly whn a rimary comonnt fails. Th rliability of a cloud-basd systm can b comutd by lugging th dfs of its systm comonnts into a rviously roosd analytical aroach [6, 9], and thn driv a softwar rjuvnation schdul for rvntiv maintnanc. In this ar, w assum th tim-to-failur df follows th Wibull distribution. By slcting aroriat aramtrs, w can modl an incrasing failur rat function du to softwar-aging rlatd bugs. W show in a cas study th ability of our analytical tchniqu to valuat th rliability of cloud-basd systms with non-constant failur rats as wll as fault-tolrant dsigns suortd by ithr on SS or two SSs /7/$ IEEE 576

2 II. RELIABILITY MODELING AND ANALYSIS Dynamic Fault Tr DFT has modling caabilitis for dynamic faturs of a comutr-basd systm, such as sar comonnts, functional dndncy, and failur squnc dndncy. In this ar, w adot an xtndd DFT for modling softwar sar comonnts in cloud-basd softwar systms [6]. Th aroach suorts a two-hasd softwar rjuvnation rocss, whr has is a r-rjuvnation stag, and in has, systm comonnts in low rformanc ar rlacd by nwly dloyd ons. In articular, a Softwar Sar gat is usd to modl th fault-tolrant asct of a systm dsign that mloys on or multil SSs. It is imortant to mntion that a DFT can b dcomosd into indndnt sub-moduls sub-trs, so thir rliabilitis can b calculatd indndntly, and thn joind to driv th rliability of th whol systm [7]. In th following two subsctions, w show th modling and analysis aroach for sar comonnts with ithr -SS or -SSs that follow th Wibull distribution to simulat thir non-constant failur rats. A -aramtr Wibull distribution has th following two aramtrs: th sha aramtr and th scal aramtr λ [8], as givn in Eq. for its df: λt f t λ t Th rliability function Rt basd on ft can b drivd as in Eq.. Consquntly, w can driv th failur rat function ht as in Eq.. R t t λ t f t dt f t R t h t λ t Not that in a scial cas, whn, ht λ. This mans th robability dnsity function ft bcoms an xonntial distribution, whr λ is a constant failur rat. A. An Gat for Cloud-Basd Systms with -SS Following th sam modl construct dfind in rvious work [9], a gat with on rimary comonnt and on SS comonnt is illustratd in Fig.. A gat fails whn and all othr altrnat sars th only sar art in Fig. is fail. Whn fails, taks ovr s workload, and thn bhavs as * with λ * λ. This is du to th softwaraging hnomnon whn an SS taks a full workload aftr it rlacs th rimary on. Basd on Fig., w now considr two disjoint aths that lad to th failur of th gat, which ar fails bfor calld ath vnt and fails bfor calld ath vnt. Fig.. An gat with a rimary comonnt and a SS ath : fails bfor fails, dnotd as. Lt and b th failur tims of and, rsctivly. In this cas, it is imossibl for to fail during 0, ]. nc, th robability of failing bfor fails, i.., r, can b calculatd using doubl intgrations as in Eq. 4. r t t + * f. f * 0 * 4 t t + * λ * λ * λ * 0 * whr * [h /h * ] λ /λ *. ath : fails bfor fails, dnotd as. In this cas, it is imossibl for to fail during 0, ], whr is th failur tim of. nc th robability of failing bfor fails, i.., r, can b calculatd as in Eq. 5. r t t λ λ λ λ 0 Th rliability function Rt for a gat with -SS is givn in a gnral form as Rt - Ut, whr Ut is givn as in Eq. 6. Rfr to th dtaild drivation of Eq. 6 in rvious work [9]. 5 U t r + r 6 B. An Gat for Cloud-Basd Systms with -SSs Figur shows a gat with on rimary comonnt and two SS comonnts and. Similar to th rvious cas with a singl SS, is initially owrd on. Whn fails, it is rlacd by on of th SSs dnding on thir numration ordr. An gat fails whn th rimary comonnt and all th altrnat inuts fail. Whn taks th lad to rlac, it bcoms *, with λ * λ, du to th softwar aging hnomnon whn it taks th full workload. In this cas, * srvs as a rimary on, and srvs as its hot softwar sar. Similarly, whn * fails, rlacs *, and bhav as *, with λ * λ. Fig.. An gat with a rimary comonnt and two SSs Lt, and b th failur tims of comonnt, and, rsctivly. W now idntify all th ossibl aths that lad to th failur of a gat according to th comonnt failur squnc. To calculat th rliability function of an gat, w invstigat six disjoint aths dnotd as to 6, rsctivly as follows. ath : Th comonnts fail in th squnc of,, and, dnotd as. In this cas, it is imossibl for to fail during 0, ] and for to fail during 0, ]. Th SS taks ovr th workload and bcoms * right aftr 577

3 fails; similarly, taks ovr th workload and bcoms * right aftr * fails. nc, th robability of th ath vnt r can b calculatd as in Eq. 7 with * [h /h * ] + *, which is a gnralizd form λ of th quation + for tim shifting Η * λ * * drivd in rvious work [6, 9]. r t t + * t [ + * ] + * 0 * * t t + * t [ + * ] + λ * 0 * * λ f f λ λ * * λ f λ * * * * λ * * ath : Th comonnts fail in th squnc of,, and, dnotd as. Similar to rvious work [9], th intgration of * rquirs to shift th intgration limit from * to *+, which lads to Eq. 8. r λ λ λ 8 t t t * 0 + * λ * λ λ * * λ ath : Th comonnts fail in th squnc of,, and, dnotd as. Not that this cas is a siml on similar to Eq. 4. Th robability that th gat fails can b calculatd as in Eq. 9. r λ λ λ 9 t t t * 0 * λ λ * λ * * λ ath 4: Th comonnts fail in th squnc of,, and, dnotd as. In this cas, it is imossibl for to fail during 0, ]. Th robability that th gat fails during 0, t] can b calculatd as in Eq. 0. r t t t 4 λ λ 0 0 λ λ λ λ λ ath 5: Th comonnts fail in th squnc of,, and, dnotd as. Similar to ath, this is whr fails first as a sar, thn fails bfor fails. In this cas, th robability that th gat fails can b calculatd as in Eq., whr * can b calculatd in a similar way to th calculation of * as in Eq t t t * λ λ * 0 λ * λ λ λ λ λ * * r ath 6: Th comonnts fail in th squnc of,, and, dnotd as. In this cas, th robability that th gat fails during 0, t] can b calculatd as in Eq.. 7 t t t r 6 λ λ 0 λ λ λ λ Th rliability function for a gat with -SSs is givn in a gnral form as Rt Ut, whr Ut is givn as in Eq.. U t r + r + r + r + r + r It is worth noting that thr ar major diffrncs btwn Eqs. 7- and th quations drivd in rvious work [9]. In Eqs. 7-, th robabilitis ar calculatd basd on nonconstant failur rats for th softwar comonnts; whil in rvious work [9], th drivd quations only work for constant failur rats. Though Eqs. 7- cannot b dirctly vrifid using Continuous Tim Markov Chain CTMC du to th non-constant failur rats, thy hav bn rovd corrct in rfrnc [9] for th scial cas whn th sha aramtr, i.., whn th failur rats ar constant valus. III. CASE STUDY In this sction, w show how to modl and analyz th rliability of a cloud-basd softwar systm with -SS and - SSs, whr all softwar comonnts hav th Wibull timto-failur distribution with incrasing failur rats du to softwar aging. Th softwar systm is modld using an xtndd DFT for softwar saring [6, 9], and th rliability analysis is conductd as dscribd in Sctions II.A and II.B. Our goal is to driv fasibl softwar rjuvnation schduls basd on rliability quantitativ analysis. Figur shows th xtndd DFT modl of two cloudbasd systms during th r-rjuvnation stag, i.., has. Th modl on th to contains a singl SS that is rady to rlac th rimary on whn it fails; whil th modl at th bottom contains -SSs to mak th systm mor rliabl and fault-tolrant. Th cloud-basd systm bing modld consists of an alication srvr A and a databas srvr B. In th - SS cas, A is st u for A, and B is st u for B to assur high rliability. Similarly, in th -SS cas, two SSs ar dloyd for ach rimary srvr. W assum th rliability thrshold to b 0.99 as a minimum constraint for systm rliability. In th cas study, w dfin th following scal aramtrs: λ A 0.004/day, λ A λ A 0.005/day, λ B 0.005/day, λ B λ B 0.00/day. For comarison uross, w st thm th sam valus as th constant failur rats of xonntial distribution usd in our rvious work [9] Th failur rat of an SS incrass aftr switching to th rimary-comonnt mod whn th rimary on fails. nc, h A h A* h A* and h B h B* h B*. In summary, th following Wibull aramtr valus ar usd for rliability analysis in th cas study: alication srvr sha.; scal λ A λ A * λ A * 0.004, and λ A λ A 0.005; and databas srvrs sha.; scal λ B λ B * λ B * 0.005, and λ A λ A

4 Fig.. DFT modl with -SS vs. -SSs has adatd from [9] Not that th rjuvantion rocss also involvs Cold Softwar Sar CSS comonnts, which ar imags of VM instancs that can b asily dloyd. Sinc a CSS is simly a cloud imag that is not running, its failur rat quals 0. As such, a CSS dos not aar in th DFT modl bcaus it dos not affct th systm rliability. W considr a CSS only whn it is activatd and dloyd as a rimary on or an SS. From Fig., w can s that th systm fails whn ithr th alication srvr or th databas srvr fails. W us th sum of disjoint roduct mthod to driv th rliability function for an OR-gat, which can b alid to both of th two DFT modls, as in Eq. 4. R t U t U t + U t * U 4 OR S S S t In Eq. 4, th unrliability functions U St and U St can b drivd using Eq. 6 and Eq. for th -SS and - SSs cass, rsctivly. Both systm-scific Scnario and comonnt-scific Scnario rjuvnation aroachs ar addrssd in th cas study. As dfind in rfrnc [6], a systm-scific rjuvnation schdul rstarts th whol systm whn th systm rliability rachs a safty thrshold. On th othr hand, a comonnt-scific rjuvnation schdul only rfrshs th most critical comonnt whn th systm rliability is blow th safty thrshold. A S A A A A S A A B S S A A B Fig. 4. DFT modl with -SSs - has Scnario adatd from [9] S S4 B B S S B B B B B Figur 4 rrsnts th DFT modl of th cloud-basd systm with -SSs in has basd on Scnario. Similar to th rliability analysis for has, w can analyz th DFT modl for has Scnario by dcomosing it into subtrs. Thus, th unrliability functions of th subtrs U St, U S t, U St and U S t can b comutd using Eq. 6 for - SS and Eq. for -SSs. As for U St and U S4t, sinc thy ar AND-gats, thir unrliability can b calculatd using th sum of disjoint roduct mthod as shown in Eqs Finally, th rliability of th whol systm can b drivd as in Eq. 4, similar to th cas of has. U S t U S t* U S' t 5 US 4 t US t* US' t 6 Onc w hav drivd th rliability function for Scnario in has, w can us th sam aroach to dal with Scnario in has. Th DFT modl for Scnario in has is illustratd in Fig. 5, in which th alication srvr is rjuvnatd. Not that whn th databas srvr is rjuvnatd, th DFT modl can b drivd in a similar way. A S S S A A A A Fig. 5. DFT modl with -SSs - has Scnario adatd from [9] In Fig. 5, th subtrs U St, U S t, U St and U St can b calculatd as w did for Scnario in has. In othr words, w can calculat U St, U S t and U St according to Eq. 6 and Eq. for th cass of -SS and -SSs, rsctivly. As nod S rrsnts th outut of an ANDgat, U St is drivd using th sum of disjoint roduct mthod for an AND-gat as in Eq. 5. Finally, th rliability function of th whol systm is dfind as in Eq. 4. Diffrnt from rvious work [9], all softwar comonnts dfind in th DFT modls ar subjct to non-constant failur rats as thir tim-to-failur follows th Wibull distribution. Th nxt st is to show th analysis rsults and visualiz th diffrncs and th imacts of mloying -SSs vs. -SS on rjuvnation schduls in a cloud-basd systm. In addition, w study th imact of using Scnario vs. Scnario for rjuvnation schduling in a cloud-basd systm with multil SSs subjct to th softwar-aging hnomnon. Tabl shows th rliability analysis rsults for th alication srvr subsystm in both of th -SS and -SSs cass. It is asy to s that th -SSs cas is mor rliabl than th -SS cas sinc th systm dsign mloys two SSs for ach rimary on, and thus it is mor fault-tolrant. A S B B B 579

5 Tabl. Alication svr rliability with -SS and -SSs Tim days -SS A. Srvr Rt -SS A. Srvr Rt Similarly, Tabl shows th rliability analysis rsults for th databas srvr subsystm in both of th -SS and - SSs cass. Again, th -SSs cas is mor rliabl than th -SS cas sinc th systm dsign mloys two SSs for ach rimary on, and thus it is mor fault-tolrant. Tabl. Databas srvr rliability with -SS and -SSs Tim days -SS DB Srvr Rt -SSs DB Srvr Rt Tabl shows how th systm rliability volvs in rjuvnation cycls and hass with duration of 5 days for th -SS cas in Scnario. Th rows highlightd in blu in Tabl indicat that systm rliability has rachd th rliability thrshold, and thrfor a softwar rjuvnation occurs as schduld. Comarativly, w illustrat th systm rliability with th -SSs cas in Scnario, as shown in Tabl 4, for th similar tim san. Figur 6 illustrats in dtails th diffrncs btwn th two cass, -SS vs. -SSs, basd on Scnario for systmscific rjuvnation. From Tabls and 4, w can s that th systm rliability rachs th thrshold aftr 5 days and 59 days for th -SS and -SSs cass, rsctivly. According to Scnario, th whol systm is rstartd whn th thrshold is rachd, and th systm rturns to its initial stat. As a rsult, th rjuvnization must b ratd rgularly vry 5 and 59 days for th -SS and -SSs cass, rsctivly. Such rjuvnization stratgis ar rflctd in Fig. 6 as rcurrnt rjuvnation schduls for th two cass in Scnario. On th othr hand, both Tabls and 4 show irrgular ocurrncs of rjuvnation in Scnario. This is bcaus in Scnario, w rjuvnat th comonnt that has th lowst rliability whn th systm rliability rachs thrshold Tabl. Systm rliability with rjuvnation -SS Scnario has Tim days Systm Rliability -SS Scnario Figur 7 shows th diffrncs btwn th two cass, - SS vs. -SSs, basd on Scnario for comonnt-scific rjuvnation. According to th figur, whn th rliability thrshold is rachd, th comonnt with th lowst rliability,.g., th databas srvr, is rjuvnatd first. It is worth mntioning that in Scnario with -SS, th databas srvr gts rjuvnatd for two conscutiv tims on day 80 and day 0, as shown in Tabl. W can s how this irrgularity affcts th rliability attrn in Fig

Tabl 4. Systm rliability with rjuvnation -SSs Scnario has Tim days Systm Rliability -SSs Scnario 0 0.999999985 5 0.99999686 0 0.999968858 0 0.9988777 59 0.9904855 59.0047 0.9976898 59.008 0.

6 Tabl 4. Systm rliability with rjuvnation -SSs Scnario has Tim days Systm Rliability -SSs Scnario rjuvnation whil king th systm rliability wll abov th 0.99 thrshold. This rsult was as xctd bcaus using -SSs for ach rimary on surly maks th whol systm mor rliabl and dndabl. IV. CONCLUSIONS AND FUTURE WORK In this ar, w rform rliability analysis for cloudbasd systms with softwar sars subjct to non-constant failur rats. Th roosd work is basd on an analytical aroach for schduling a rvntiv maintnanc rocdur, calld softwar rjuvantion. W adotd an xtnsion of DFT, calld gat, to modl and valuat th rliability of a cloud-basd systm with multil hot softwar sars. W usd th Wibull distribution to mulat an incrasing failur rat du to th softwar-aging hnomnon. Th cas study showd that our aroach was fasibl and could roduc usful rvntiv maintanc schuduls. For futur work, in ordr to forcast incrasing failur rats for softwar comonnts, w will dvlo an -commrc alication, dloy it on rutabl cloud-basd latfroms, such as Amazon Wb Srvic AWS, Window Azur, and Googl A Engin, and collct mirical data rlatd to rsourc dgradation. Data fitting tchniqu will b usd to driv th most suitabl robability dnsity function for th systm timto-failur. Stochastic artial diffrntial quations may b considrd and alid to this fild of study to hl rdict how softwar aging affcts th failur rat. As such, mor accurat rsults for systm rliability can b usd to driv rvntiv maintncanc schduls for cloud-basd systms. REFERENCES Fig. 6. Rjuvnation schduling: -SSs vs. -SS Scnario Fig. 7. Rjuvnation schduling: -SSs vs. -SS Scnario Figur 7 also shows that rjuvnations ar ndd for Scnario with -SSs vs. 7 rjuvnations ndd for th - SS cas during 5 days. Thrfor, comard with Scnario with -SS, using Scnario with -SSs rsults in 7 /7 57% rduction in cost and managmnt for softwar [] M. Rausand and A. øyland, Systm Rliability Thory: Modls, Statistical Mthods, and Alications, Scond Edition, obokn, Nw Jrsy, USA, John Wily & Sons, Inc., 004. [] M. Grott, A. Nikoran, and K. S. Trivdi, An mirical invstigation of fault tys in sac mission systm softwar, in roc. of th Intrnational Confrnc on Dndabl Systms & Ntworks DSN 00, Jun 8-July, 09, Chicago, IL, USA, [] M. Grott, R. Matias, and K. S. Trivdi, Th fundamntals of softwar aging, in roc. of th First Intrnational Worksho on Softwar Aging and Rjuvnation WoSAR, in conjounction with th 9 th IEEE Intrnational Symosium on Softwar Rliability Enginring ISSRE, Sattl, WA, USA, Novmbr -4, 008,. -6. [4] Y. uang, C. Kintala, N. Kolttis, and N. Fulton, Softwar rjuvnation: analysis, modul and alications, in roc. of th Twnty- Fifth Intrnational Symosium on Fault-Tolrant Comuting FTCS 95, asadna, CA, USA, Jun 7-0, 995, [5] M. Lyu, Softwar rliability nginring: a roadma, in roc. of th 9th Intrnational Confrnc on Softwar Enginring, Futur of Softwar Enginring, Minnaolis, USA, 00, [6] J. Rahm and. Xu, A softwar rliability modl for cloud-basd softwar rjuvnation using dynamic fault trs, Intrnational Journal of Softwar Enginring and Knowldg Enginring IJSEKE, Vol. 5, Nos. 9 & 0, 05, [7]. Boudali,. Crouzn and M. Stolinga, Dynamic fault tr analysis using inut/outut intractiv markov chains, in roc. of th 7 th Intrnational Confrnc on Dndabl Systms and Ntworks DSN, Edinburgh, UK, Jun 5-8, 007, [8] R. B. Abrnthy, Th Nw Wibull andbook, nd Edition, Abrnthy, North alm Bach, FL, USA, 996. [9] J. Rahm and. Xu, Dndabl and Rliabl Cloud-Basd Systms Using Multil Softwar Sar Comonnts, To aar in roc. of th Intrnational Confrnc on Advancd and Trustd Comuting ATC- 7, San Francisco Bay Ara, CA, USA, Aug. 4-8,

The Application of Phase Type Distributions for Modelling Queuing Systems

The Application of Phase Type Distributions for Modelling Queuing Systems Th Alication of Phas Ty Distributions for Modlling Quuing Systms Eimutis VAAKEVICIUS Dartmnt of Mathmatical Rsarch in Systms Kaunas Univrsity of Tchnology Kaunas, T - 568, ithuania ABSTRACT Quuing modls