Weighting Cache Replace Algorithm for Storage System

Transcription

1 Weghtg Cache Replace Algorthm for Storage System Yhu Luo 2 Chagsheg Xe 2 Chegfeg Zhag 2 School of mathematcs ad Computer Scece, Hube Uversty, Wuha , P.R. Cha 2 Natoal Storage System Laboratory, School of Computer Scece, Huazhog Uversty of Scece ad Techology, Wuha , P.R. Cha Abstract Usual cache replace algorthms are based o the assumpto that the hgh cache ht rato ca brg lower average access tme, whch s rght as storage system has the same devce access tme. By aalyzg the performace of storage system, a cocluso s draw that storage system ca get lower average access tme oly whe the cache ht ratos of some objects wth log devce access tme are hgher. Based o ths, some weghtg cache replace algorthms such as Weghtg LFU (WLFU), Weghtg LRU (WLRU) ad Weghtg LFRU (WLFRU) are proposed. These algorthms are desged to mmze average access tme ad algorthm overhead. Expermet proved that WLFU ad WLRU had better performace tha usual algorthms such as LRU, ad WLFRU had the best performace. Keywords: Cache replace algorthm, Average access tme, Algorthm overhead, Weghtg value. Itroducto Wth processor speed creasg dramatcally over the last few years ad ma memory desty doublg every two years, I/O appette cotues to grow, especally wth the developmet of applcatos such as multmeda ad etwork, whch place a evercreasg demad o the storage subsystem. Although the storage devce I/O speeds have creased greatly, t caot satsfy the demad of computer. As a result, storage systems become the bottleeck of computer system ad the performace of computer system s ot the optmzato. There are may methods to mprove the performace of storage system ad oe of the most effectve methods s to place a cache storage system. The cache devces are usually fast storage devces but have less capacty, so the sutable replace algorthms must be used cache to mprove the performace of storage system. There are may cache replace algorthms such as FIFO, LFU, LRU, ad some varetes of them. All of them mprove the cache performace by creasg the cache ht rato based o the localty of data referece. Must the hgher cache ht rato brg the better I/O performace the storage system? If the speeds of storage devces are the same storage system the cocluso s rght. However, storage devces usually have dfferet I/O speeds storage system, at the case the cocluso s o more rght, so the usual algorthms are ot the optmzato algorthms for the storage system. Based o ths stadpot, we propose a ew cache replace algorthm amed Weghtg Least Frequetly/Recetly Used (WLFRU) algorthm, whch s desged ot to crease the cache ht rato but to mmze the average access tme of the storage system. I order to do so, WLFRU s desged to crease the cache ht ratos of objects wth loger devce access tme, whch cosders ot oly I/O localty but the dfferece of devce access tme. The rest of ths paper s orgazed as the followg: after aalyzg the related works, we frst aalyze the I/O performace of storage system wth cache, through whch we prove that the hgher cache ht ratos does t result to hgher I/O speeds, at the same tme, we ca get a cocluso that the hgher I/O speeds are obtaed oly whe t s hgher to the cache ht ratos of objects wth loger devce access tme. Based o the cocluso, we the gve the Weghtg Least Frequetly Used algorthm (WLFU), Weghtg Least Recetly Used algorthm (WLRU) ad WLFRU. Afterwards, we gve the expermet to prove our cache algorthm rght. At last, we gve a cocluso ad the future work. 2. Related Works There are may researches about cache replace algorthm. The algorthm LRU always replaces the least recetly used objects. Varous approxmatos ad mprovemets to LRU aboud, see, for example, ehaced clock algorthm []. If the workload or the

2 request stream s draw from a LRU Stack Depth Dstrbuto (SDD), LRU s the optmal polcy. LRU has several advatages, for example, t s smple to mplemet ad respods well to chages the uderlyg SDD model. However, whle the SDD model captures rececy, t does ot capture frequecy. The algorthm LFU replaces the least frequetly used objects. A relatvely recet algorthm LRU-2 [2] approxmates LFU, whch remembers the last two tmes for each object, whe t s requested, ad to replace the object wth the least recet peultmate referece. Algorthms, whch cosder both rececy ad frequecy, are Frequecy-based replacemet (FBR) [4], Least Recetly/ Frequetly Used (LRFU) [5], mult-queue replacemet (MQ) [6]. Based o those, a algorthm amed Adaptve Replacemet Cache (ARC) was proposed [7]. The basc dea behd ARC s to mata two LRU lsts of objects. Oe lst, say L, cotas objects that have bee see oly oce recetly, whle the other lst, say L 2, cotas objects that have bee see at least twce recetly. L s thought as capturg rececy whle L 2 capturg frequecy. Although ARC captures both frequecy ad rececy, t does t cosder the access cost of objects. Addtoally, the sze of L s reszed very frequetly, whch may crease the algorthm overhead. Ekow Otoo etc gave a replace algorthm for storage source maager data grds [4], whch defed a utlty fucto for each object to express ts use status. Ths fucto relate to referece frequecy, object sze ad devce access speed, but t has several drawbacks: t pays almost o atteto to recet hstory, ad does ot adapt well to chagg access patters sce t accumulates stale objects wth hgh frequecy couts that may o loger be useful, moreover, t requres logarthmc mplemetato complexty cache sze. Ulrch Hah etc offered a replace algorthm called ObjectLRU, whch take to accout fluece to replace algorthm by varous object propertes [8]. Ths uses a weghtg fucto to evaluate combatos of object propertes, whch provdes a more flexble approach. But ts weght values are dffcult to select. Furthermore, the cost of algorthm realzato s ot low. 3. The Performace Formula of Storage System The basal goal s to mprove the I/O performace usg cache storage system. So we frst calculate performace ga of storage system wth cache after descrbg the model of herarchcal storage system. Wth the performace ga, we ca get a few of coclusos that s the base of desgg cache replace algorthm order to optmze ts I/O performace. 3.. The Model of Herarchcal Storage System The herarchcal storage system s descrbed as fgure that cossts of cache ad storage devces. The cache s a small storage devce wth hgh speed, whch maybe the server memory or ts local dsk. The storage devces clude dfferet devces such as dsk, CDROM, tape or other storage devces, whch may have dfferet access speeds. The lks betwee cache ad devces may be bus or etwork, ad ther commucato speeds maybe dfferet. If t s etwork, ts speed may vary as the etwork load vares. I order to smplfy calculato, we suppose that the commucato tme s cotaed access tme of devces ad the speeds do t vary wth the etwork load vares. The access data maybe data blocks or fles the storage system ad ther szes maybe the same or dfferet, so we call the access data as data object, whch meas that ther szes are dfferet. Storage devce Server Cache Storage devce 2 Storage devce 3 Fg : The Model of Herarchcal Storage System The Performace Formula of Storage System The performace ga s defed to be the rato of access tmes wthout ad wth cache [8]. access tme wthout cache g = () access tme wth cache The factors fluecg the I/O performace are the I/O latecy of devces, the ht rato of cache ad data szes. I order to smplfy calculato, we suppose that data objects have the same szes. O the assumpto that the accessed data objects are {O, O 2,, O }, ad ther access frequeces are {m,

3 m 2,, m}, the total access frequeces of storage system s as the followg: M = m = (2) Wthout cache, accessed data comes from dfferet storage devces, ther access tme are {t, t 2, t 3,,t }, so the total access tme s as followg: T o = m t = (3) If the storage system cofgures cache, suppose the cache ht ratos of objects are {p, p 2,,p }, the total cache ht rato s as followg: P = p = (4) Suppose access tme of data object cache s t c, the total access tme wth cache s as followg: c = M p tc + = = T ( m M p ) t Thus performace ga s as the followg: To g = = T c = M = = M p t = c = = p( t t ) m t c + m t ( m M p) t (5) (6) From the formula (6), the followg coclusos are draw. It s ot the hgh total cache ht rato but the hgh cache ht rato of the data objects wth log access tme from devces that result to hgh performace ga. The usual cache replace algorthms are used to crease the total cache ht rato, so they are o more rght the case. If the access tme from dfferet devces s the same, the formula (6) ca express as the followg: g = = ( t tc) P M ( t tc) p = t ( m ) t = (7) I ths case, the hgher total cache ht rato meas the hgher I/O performace ga. So the usual cache replace algorthms such as LFU, LRU ad OPT are based o ths cocluso. 4. The Cache Replace Algorthms There are usually two goals to desg cache replace algorthms, oe s to make the cache ht rato hgher to obta least access tme, ad the other s to smplfy the cache algorthms order to mmze the overhead [9]. As descrbed secto 3, the usual replace algorthms are based o the formula (7), so they are ot the optmzato algorthms for storage system. I ths secto, we propose some algorthms based o the formula (6), whch are desged order to obta least access tme but ot hghest cache ht rato. I addto, we also try to smplfy the cache replace algorthms order to mmze the algorthm overhead. 4.. The WLFU algorthm As descrbed above, the hgh cache ht rato of the data objects wth log access tme from devces result to hgh performace ga. We defe a weghtg ht rato for each object cache as the followg: t p = p = c p (8) t m Iput: The request stream x, x 2,, x, For every, the followg two cases must occur. Case : If = the: t m =t Otherwse: If t < t m the {k= t m / t ad t m =t ad for every O j cache p = p *k ad c = c *k} Case 2: If x s cache the: p =p +c ad sort the p queue Otherwse: The followg two cases must occur. : If cache s full the: delete object wth mmal p 2: c = t / t m ad p =c ad sert p queue Fg 2: The Weghtg Least Frequetly Used algorthm. where, t m s the mmal devces access tme, t s the object s devce access tme, c s a teger to express the relatve access tme of O. We use c to replace t order to make the weghg value smple. t m s gve as the followg: whe the frst data object s accessed, ts devce access tme s set as t m, afterwards, f the devce access tme of data objects s ot less tha t m, t s ot chaged; otherwse, the ew devce access tme s set as t m, at the same tme, the weghtg ht ratos of all objects cache are multpled by the rato of old ad ew t m. I the case,

4 the weghtg cache ht rato s used to replace the cache ht rato, ad the objects havg lttle p ' cache are frst replaced, whch makes the object wth log devce access tme cache log tme ad mprove ts cache ht. So the average access tme of storage system s lttle accordg to formula (6). I order to make algorthm smple, the LFU algorthm usually replaces ht rato wth frequecy, the WLFU algorthm also use the same techque. The WLFU algorthm uses a queue to record the weghtg frequecy of all objects cache. If a object s ot accessed cache, whe t s put cache, ts weght value s calculated ad weghtg frequecy s set as weght value, at the same tme, the t m may be chaged, ad all of the weghtg frequecy ad weght value maybe reewed. If a object s accessed cache, ts weghtg frequecy s added by weght value. So the WLFU algorthm selects the data object wth the least weghtg frequecy as the replaced object whe the cache eeds storage space to cache ew data object. The WLFU s descrbed as fgure 2. Ths algorthm s desged based o the assumpto that all data objects have the same sze storage system, but t s also suted to the storage system that has dfferet object szes. As descrbed the above, all data objects have the same sze storage system, whch meas that the devce access tme s the oes of ut data object. Although the larger object ca make ts weghtg frequecy creases, t also mproprates more cache space. So storage system wth dfferet object szes, the devce access tme s replaced wth the oes of ut data object. I the case the same algorthm s used. As ths algorthm s used, there are may objects that have the same weghtg frequecy but dfferet szes, how to select the replaced object? Our scheme s to select the large object to be replaced because the wrte of large object ca reduce the replace latecy. The followg algorthms are also desged for storage system wth same object sze, but they are all sutable to storage system wth dfferet object szes for the above reasos The WLRU algorthm The WLFU algorthm captures the oto of frequecy, but t pays almost o atteto to recet hstory, ad does ot adapt well to varyg access patters sce t accumulates stale objects wth hgh frequecy couts that may o loger be useful. The WLRU algorthm s desged to capture rececy. I order to desg t, we frst have a look at the LRU algorthm. LRU algorthm uses rececy to replace frequecy, whch ca reduce algorthm overhead. LRU uses a rececy stack to realze object queue, the top object of the LRU stack s accessed recetly ad the bottom object s least recetly accessed. LRU selects the object at the bottom of stack to be replaced as storage system eeds cache space to cache ew object. Iput: The request stream x, x 2,, x, Italzato: wdow= For every, The followg four cases must occur. Case : If = the: t m =t max = t Otherwse: oe ad oly oe of the followg two cases must occur. : If t < t m the t m =t 2: If t > t max the for every O j cache, k j = k j * t / t max ad t max =t Case 2: k= t max / t m ad f k>wdow the wdow=k Case 3: If x s t cache the: The followg two cases must occur. : If stack s full the: delete object at the bottom of stack ad replace the object cache 2: k = t max / t Otherwse: delete x the stack Case 4: If the k ter s ot empty the move all serate O j, whose local k, dow to the ext ter Put x the k ter of the stack Fg 3: The Weghtg Least Recetly Used algorthm. Cosderg the devce access tme dfferet, the WLRU algorthm gves a weght value k to the rececy of each object. Precsely, f some object has log devce access tme, ts rececy s multpled by a small weght value; otherwse, ts rececy s multpled by a bg weght value. k s teger calculated as (9). tmax r = r = kr (9) t I order to make a queue wth weghted rececy, WLRU set a wdow at the top of the LRU stack. I the wdow, the ew object ca sert aywhere; out the wdow, the order of objects s o chaged uless some objects are deleted. The wdow sze s set as the teger rato of the maxmal ad the mmal devce access tme. Whe a object s frst put cache, ts devce access tme s recorded as both the maxmal ad the mmal devce access tme ad the wdow sze s set as. Afterwards, whe some ew object s put cache, f ts devce access tme s more(or less) tha the maxmal(or mmal) devce access tme, the maxmal(or mmal)s set as the ow devce access tme ad the wdow sze value s reewed, otherwse the wdow sze value s ot chaged.

5 The WLRU algorthm s realzed wth a stack as fgure 3. Case s used to revse the maxmal ad mmal devce access tme. At the same tme, the weght values of all objects cache are reewed f the maxmal devce access tme s revsed. Case 2 chages the sze of the wdow as the maxmal/mmal devce access tme s revsed. Case 3 deletes ht object or replace the weghtg least recetly access object the stack. Case 4 serts recetly access object the wdow accordg to weght value The WLFRU algorthm The WLFU algorthm captures frequecy ad the WLRU algorthm captures rececy, whch utlze oe part of I/O localty to mprove the performace of storage system. The WLFRU algorthm s a comprehesve oe that uses both frequecy ad rececy to select the replaced object. Iput: The request stream x, x 2,, x, Italzato: L=C/2, wdow = wdow 2 =, k=0 For every, oe ad oly oe of followg two cases must occur. Case: x s Q or Q 2 : Cache ht, sert x accordg to WLRU Q 2 Case2: x s ether Q or Q 2, Cache mss. Oe ad oly oe of followg two cases must occur. : Q =L, the a) Replace the WLRU object wth x Q, ad k=k+ b) f k>0 the L=L+ 2: Q <L, the a) If Q + Q 2 =C, the delete the WLRU object Q 2, ad k=k- b) Isert x accordg to WLRU Q c) If k<-0 the L=L- Fg. 4: The Least Frequetly/Recetly Used algorthm. I order to utlze the frequecy localty, we use two varable-szed stacks Q ad Q 2 to record the hstory of the cached object. The frst holds objects that have bee accessed oly oce recetly ad the secod holds objects that have bee accessed at least twce recetly, so the objects Q (or Q 2 ) may be least (or frequetly) accessed. I order to utlze the rececy localty, objects both Q ad Q 2 are orgazed accordg to the WLRU. Suppose the cache sze s C ad the maxmal sze of Q s L, Q ad Q 2 satsfy the followg: 0 Q L,0 Q 2 C,0 Q + Q 2 C L s cotually revsed order to mprove the utlty of cache, at the same tme t ca reduce joucg Q. For example, f some objects are cotually accessed cycle ad the sze of Q s less tha the total sze of those objects, objects are frequetly replaced ad the cache ht s 0. I the case, L must be creased. However, f L s too bg, Q 2 s small, whch may result to objects frequetly accessed to be replaced. The algorthm revses L accordg to the accumulatg teger k. k s set as 0 at the begg, ad t crease (or decrease) as a replacemet s take place Q (or Q 2 ). L s chaged oly whe k s accumulated to some value (such as 0), whch ca reduce the revsg of L. The WLFRU algorthm s descrbed as fgure 4. L s set wth C/2 at begg, whch ca reduce L s revsg. I case, cache ht takes place, the ht object s serted Q 2 accordg to WLRU. I case 2, cache mss takes place, the object s serted Q accordg to WLRU. Cache replace may take place case 2. If Q =L, replace takes place Q regardless cache beg full or ot, so k creases, at the same tme, L may crease as k s more tha a threshold. If Q <L ad Q + Q 2 =C, whch meas that L s too bg, so cache replace takes place Q 2 ad k s reduced to reduce L. 5. Expermet ad Results Cache ht rato s usually used to evaluate the performace of cache, whch shows how cache ca reduce devce I/O. However, as descrbed above, the hgher cache ht rato does t mea the less average access tme storage system. Thus we use average access tme to evaluate the performace of storage system. At the same tme, we also measure cache-ht ratos to compare t wth average access tme. We used Dsksm smulator, whch was developed by Carege Mello Uversty, to smulate cache storage system. Dsksm s a effcet, accurate ad hghly cofgurable dsk system smulator developed to support research to varous aspects of storage subsystem archtecture [0]. Dsksm cotas a cache module that ca smulate cache replace algorthms such as LRU, ad we have programmed to realze algorthms such as WLFU, WLRU ad WLFRU. We used the sythetc traces cotaed Dsksm to smulate those algorthms order to compare ther performace. The storage system cofgured two dsks. The average devce access tme was costat but the rato of devce access tme was set as, 4 ad 6. We measured both cache ht ratos ad average respose tme of storage system wth LRU, WLFU, WLRU, ad WLFRU. The cache ht ratos are show as the fgure 5, WLFU ad WLRU have cache ht rato as much as LRU, ad WLFRU has the hghest cache ht rato.

6 Sce WLRU ad WLFU ehace the ht ratos of some objects wth more devce access tme whle reduce the ht ratos of some objects wth less devce access tme, t does t mprove cache ht rato compare to LRU. However, WLFRU uses both frequecy ad rececy to capture localty, so ts cache ht rato s hgher tha the two oes. Cache Ht Rato LRU WLFU WLRU WLFRU 4 6 The Rato of Devce Access Tme Fg. 5: The cache ht ratos vary wth varyg of devce access tme. Average Access Tme (ms) LRU WLFU WLRU WLFRU 4 6 The Rato of Devce Access Tme Fg. 6: The average access tme vary wth varyg of devce access tme. The average respose tmes of storage system are descrbed as fgure 6, WLRU ad WLFU have less average respose tme tha LRU ad the WLFRU has the least average respose tme. Ths s because WLFU, WLRU ad WLFRU cosder ot oly access localty but also the dfferece of devce access tme. 6. Coclusos ad the Future Work Cofgurg cache storage system s a effectve meas to mprove ts performace. Cosderg the effect of devce access tme, the hgher cache ht rato does t mea the less average access tme. Based o ths cocluso, we propose WLFU, WLRU ad WLFRU algorthm, whch cosder ot oly the I/O localty but also the devce access tme, so they have hgher performace tha usual algorthm. However, these algorthms do t cosder the effect of etwork badwdth ad I/O load. Addtoally, WLFRU algorthm, although we use accumulated k to revse L, how to select the threshold wth I/O load varyg s ot cosdered. I the future, we wll research o cache replace algorthms adapted to the varyg of etwork badwdth ad I/O load. We also pla to mprove WLFRU algorthm to make t sut to dfferet I/O load. Addtoally, the cache algorthms about dstrbuted cache ad cooperato cache are our goal. Ackowledgemet Ths work s partally supported by Natoal Nature Scece Foudato of Cha (Grat No ). Refereces [] W. R. Carr ad J. L. Heessy, WSClock a smple ad effectve algorthm for vrtual memory maagemet. Proc. 8th Symp. Operatg System Prcples, pp , 98. [2] E. J. O Nel, P. E. O Nel, ad G. Wekum, A optmalty proof of the LRU-K page replacemet algorthm, J. ACM, 46: 92 2, 999. [3] J. T. Robso ad M. V. Devarakoda, Data cache maagemet usg frequecy-based replacemet, Proc. ACM SIGMETRICS Cof., pp , 990. [4] Ekow Otoo, Frak Olke ad Are Shosha. Dsk Cache Replacemet Algorthm for Storage Resource Maagers Data Grds. Proceedgs of the IEEE/ACM SC2002 Coferece, November, [5] D. Lee, J. Cho, J.-H. Km, S. H. Noh, S. L. M, Y. Cho, ad C. S. Km, LRFU: A spectrum of polces that subsumes the least recetly used ad least frequetly used polces, IEEE Tras. Computers, 50: , 200. [6] Y. Zhou ad J. F. Phlb, The mult-queue replacemet algorthm for secod level buffer caches, Proc. USENIX Aual Tech. Cof. (USENIX 200), Bosto, MA, pp. 9 04, Jue 200 [7] N. Megddo ad D. S. Modha. ARC: A self-tug, low overhead replacemet cache. I Proceedgs of the Secod USENIX Coferece o Fle ad

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