Adaptive Power-Aware Prefetch in Wireless Networks

Transcription

1 Adaptve Power-Aware Prefetch n Wreless Networks Langzhong Yn, Student Member, IEEE, and Guohong Cao, Member, IEEE Abstract Most of the prefetch technques used n the current cache management schemes do not consder power constrants of the moble clents and other factors such as the sze of the data tems, the data access rate, and the data update rate. In ths paper, we address these ssues by proposng a poweraware prefetch scheme, called adaptve value-based prefetch (A) scheme. The A scheme defnes a value functon whch can optmze the prefetch cost to acheve better performance. Also, A dynamcally adjusts the number of prefetches to get better tradeoff between performance and power. As stretch s wdely adopted as a performance metrc for varable-sze data requests, we show by analyss that the proposed approach can ndeed acheve the optmal performance n terms of stretch when power consumpton s consdered. Smulaton results demonstrate that our algorthm sgnfcantly outperforms exstng prefetchng algorthms under varous scenaros. Index Terms Cache management, prefetch, nvaldaton report, power conservaton, stretch. I. INTRODUCTION BROADCASTING has been shown to be an effectve data dssemnaton technque n wreless networks by many studes [2], [3], [13], [14]. Wth ths technque, clents access data by smply montorng the broadcast channel untl the requested data appear n the channel. The broadcastng model explots the asymmetrc nature of the wreless channel, where more bandwdth s avalable for the downlnk (serverto-clent), but less bandwdth for the uplnk (clent-to-server). Further, the model s scalable snce the bandwdth consumpton ndependent of the number of clentn the system. Although data broadcastng has many advantages, t also ntroduces some problems. For example, watng for the data to appear n the broadcast channel may ncrease the query latency. One way to allevate ths problem s to cache frequently accessed data on the clent sde [3], [7], [19], [20]. In ths way, the clent can serve many requests from the local cache wthout sendng uplnk requests. Ths not only reduces the average data access delay but also reduces the uplnk and downlnk bandwdth consumpton. To further reduce the access latency and mprove the cache ht rato, prefetchng technques can be used. Prefetchng has many advantagen moble envronments snce wreless networks such as wreless LANs or cellular networks support broadcastng. When the server broadcasts data on the broadcast channel, clents can prefetch nterested data wthout ncreasng the bandwdth consumpton. Note that f the requested data The authors are wth the Department of Computer Scence & Engneerng, The Pennsylvana State Unversty, Unversty Park, PA Emal: fyn, gcaog@cse.psu.edu tem s not prefetched earler, the clent has to send an uplnk request when recevng the query. Ths not only ncreases the query delay but also ncreases the uplnk bandwdth requrement. Snce the uplnk bandwdth s very expensve n wreless networks, prefetchng should be used frequently. However, prefetchng consumes a large amount of system resources such as battery power on the clent sde. Although prefetchng can make use of the broadcast channel, clents stll need to consume power to receve and process the data. Further, they cannot power off the wreless network nterface, whch consumes a large amount of power even when t n the dle mode [18]. Snce most moble clents are powered by battery, t mportant to prefetch the rght data when desgnng prefetchng schemes. Unfortunately, most of the prefetch technques used n the current cache management schemes [7], [12] do not consder power constrants of the moble clents and other factors such as the data sze, the data access rate, and the data update rate. To address these ssues, we frst propose a value-based () scheme, whch makes prefetch decsons based on the value of each data tem consderng varous factors such as access rate, update rate, and data sze. As stretch [1], [19] s wdely adopted as a performance metrc for varable-sze data requests, we show by analyss that the scheme can ndeed acheve the optmal performance n terms of stretch. Then, we extend the scheme and present two adaptve value-based prefetch (A) schemes, whch can acheve a balance between performance and power based on dfferent user requrements. Extensve smulatons are provded and used to justfy the analyss. Compared to prevous schemes, the proposed schemes can reduce the energy consumpton and mprove the system performance n terms of stretch under varous scenaros. The rest of the paper s organzed as follows. Secton II descrbes the system model and the performance metrcs. In Secton III, we present the and A schemes. Secton IV evaluates the performance of the and A schemes. Related work s provded n Secton V. Secton VI concludes the paper. II. PRELIMINARIES A. The System Model We use a pull-based broadcastng model, whch conssts of a sngle server and a number of clents. At the server sde, there s a database of n data tems: d 1, d 2,..., d n.theserver s responsble for mantanng the database and servng the requests of the moble clents. At the clent sde, caches are used to save frequently accessed data. When a clent needs to

2 access a data tem that cannot be found locally, t sends out a query to the server through the uplnk channel. On recevng the request, the server sends the reply through the common broadcast channel. Smlar to most prevous work [7], [5], [19], [20], data can only be updated by the server. B. The Cache Invaldaton Model Cached data may become nvald due to server update. To ensure cache consstency, the server broadcastnvaldaton reports (IRs) every L seconds. The IR conssts of the current tmestamp T and a lst of tuples (d x ;t x ) such that t x > (T w Λ L), whered x s the data tem d, t x s the most recent update tmestamp of d x,andw s the nvaldaton broadcast wndow sze. In other words, IR contans the update hstory of the past w broadcast ntervals. However, any clent who has been dsconnected longer than w IR ntervals cannot use the report, and t has to dscard the cached tems. Every clent, f actve, lstens to the IRs and nvaldatets cache accordngly. To answer a query, the clent lstens to the next IR and uset to decde whether ts cache s vald or not. Snce the clent has to wat for the next IR before answerng a query, the average query delay s the sum of the actual query processng tme and half of the IR nterval. If the IR nterval s long, the delay may not be able to satsfy the requrements of many clents. In order to reduce the query latency, Cao [7] proposed to replcate the IRs m tmes wthn an IR nterval. As a result, a clent only needs to wat at most ( 1 m )th of the IR nterval before answerng a query. Hence, latency can be reduced to ( 1 m )th of the latency n the prevous schemes. Snce the IR contans a large amount of update hstory nformaton, to save the broadcast bandwdth, after one IR, m 1 updated nvaldaton reports (s) are nserted wthn an IR nterval. Each only contans the data tems that have been updated after the last IR was broadcasted. In ths way, the sze of the becomes much smaller compared to that of the IR. Although ths approach can reduce the query latency when there s a cache ht, clents stll need to wat for the data to be delvered f there s a cache mss. To mprove the cache ht rato, the approach also actvely prefetch data that are avalable n the broadcast channel. All the cached data are marked as prefetchable and whenever a data tem s broadcasted t wll be prefetched f the cached copy has expred. In ths paper, the approach s used for cache management. C. Performance Metrcs One wdely used performance metrc s the response tme,.e., the tme between sendng a request and recevng the reply. It s a sutable metrc for homogeneous settngs where dfferent data requests have the same sze. However, the data requrements of users and applcatons are nherently dverse, and then to encapsulate all responsento a snglesze broadcast would be unreasonably wasteful. Therefore, unlke some prevous work [6], [12], we do not assume that the data tems have the same sze. When data requests are heterogeneous, response tme alone s not a far measure gven that the ndvdual requests sgnfcantly dffer from one another n ther servce tme, whch s defned as the tme to complete the request f t was the only job n the system. In ths paper, we adopt an alternate performance measure, namely the stretch [1] of a request, defned to be the rato of the response tme of a request to ts servce tme 1. The ratonale behnd ths choce s based on our ntuton;.e., clents wth larger jobs should be expected to be n the system longer than those wth smaller requests. The drawback of mnmzng response tme for heterogeneous workloads that t tends to mprove the system performance of large jobs (snce they contrbute the most to the response tme). Mnmzng stretch, on the other hand, s more far to all job szes. III. THE ADAPTIVE VALUE-BASED PREFETCH (A) SCHEME The proposed A scheme conssts of two parts. The frst part s the value-based prefetch () scheme, whch dentfes valuable data tems for prefetchng. The second part s the adaptve value-based prefetch (A) scheme, whch determnes how many data tems should be prefetched. A. The Value-based Prefetch () Scheme In ths subsecton, we present a value-based functon whch allows us to gauge the worth of a data tem when makng a prefetch decson. The followng notatons are used n the presentaton: ffl n : the number of data temn the database ffl u : the mean update arrval rate for data tem ffl a : the mean access arrval rate for data tem ffl x : the rato of update rate to access rate for data tem,.e., x = u =a ffl p a : the access probablty of data tem, p a = a = np a k k=1 ffl p u : the probablty of nvaldatng cached data tem before next access. ffl l : the access latency for data tem ffl f : the delay of retrevng data tem from the server ffl : the sze of data tem ffl v : the cache valdaton delay ffl D : the set of all the data temn the database ffl C k : the set of cached data tems after the k th access ffl U k : the set of data tems updated between the k th and the (k +1) th access ffl P k : the set of data tems prefetched after the k th access The value functon s used to dentfy the data to be prefetched. Intutvely, the deal data tem for prefetchng should have a hgh access probablty, a low update rate, a small data sze, and a hgh retreval delay. Equaton (1) ncorporates these factors to calculate the value of a data tem. value() = p a (f v p u f ) (1) 1 Note that n broadcast systems, the servce tme for a request s the requested data sze dvded by the bandwdth. For smplcty, n ths paper we remove the constant bandwdth factor and use the data sze to represent the servce tme.

3 (1- p u ) Access data pa Data tem n cache? v Y Consstent? Y Return data tem Fg. 1. N N pu f f Fetch data tem Fetch data tem The data access cost model Ths value functon can be further explaned by the data access cost model shown n Fgure 1. If tem s not n the cache, n terms of the stretch value, t takes f = to fetch tem nto the cache. In other words, f s prefetched to the cache, the access cost can be reduced by f =.However,t also takes ((v + P u f ))= to valdate the cached tem, and update t f necessary. Thus, prefetchng the data can reduce the cost by ((f v p u f ))= for each access. Snce the access probablty s p a, the value of prefetchng tem s p a s (f v p u f ). The scheme decdes whch data tem should be prefetched based on the value functon. The scheme s defned as follows. Suppose a clent can prefetch N p data tems, the scheme prefetches the N p tems whch have the hghest value based on the value functon. Note that s not responsble for determnng how many tems (N p ) should be prefetched. N p s determned by the adaptve scheme, whch wll be dscussed n Secton III-D. B. Analyss of the Value Functon In ths subsecton, we prove that the value-based prefetch scheme can mnmze the access cost gven that the number of prefetches lmted. We assume that the arrvals of data update and data access follow Posson dstrbuton. Then, the nter-arrval tme (t a ) of data access for tem, and the nterarrval tme (t u ) of the update follow exponental dstrbutons wth means of a and u. The update event (U )foradata tem durng the perod from the current tme to the arrval tme of the next query can be probablstcally wrtten as: p u = Pr(U )=Pr(t u <ta Z ) 1 Z t a = f (t a )g(tu )d t u t a=0 t u=0 = d t a u u + a (2) Therefore the value functon can be rewrtten as value() = p a (f v u f ) a + u = p a a (f v) a + u = p a f ( v) (3) 1+x We evaluate the access cost by calculatng the stretch of the k th access, whch can be defned as: S k = 1»»n p a : l (4) Equaton (4) can be rewrtten consderng cache hts and cache msses. S k = 2C k p a l + 2(D C k ) p a l (5) In case of a cache ht, there are two cases: cache ht wth an up-to-date copy and cache ht wth an obsolete copy. Thus, Equaton (5) can be rewrtten as: S k = 2C k + p a l p a l p u + (1 p u ) 2C k 2(D C k ) p a l (6) The access latency l s equal to f when there s a cache mss. When there s a cache ht, l = v when the cache ht s an up-to-date copy, and l = v + f when the cache ht s an obsolete copy. Combnng Equatons (2) and (6), we get S k = = 2C k ( + ( 2C k 2C k ( p a (v + f ) u ) u + a p a p a v u (1 ( ))) + u + a (v + f u u +a ) )+ 2(D C k ) 2(D C k ) p a f p a f (7) Theorem 1: Prefetchng tems wth hgh value can acheve lower stretch than any other prefetch schemes gven that the number of prefetches lmted. Proof. Let U k represent the data that have been modfed snce the last nvaldaton report and P k represent the data that are prefetched after the k th access. Then, C k+1 = C k U k + P k. S k+1 = 2C k+1 ( p a (v + f u u +a ) )+ p a f = S k + ( ( v)) 1+x 2U k 2(D C k+1 ) p a f p a f ( ( v)) (8) 1+x 2P k

4 P In Equaton (8), 2U k ( pa s ( f 1+x v)) cannot be reduced because t s caused by the server update. Equaton (8) mples that the cost can P be reduced by prefetchng those tems that can maxmze 2P k ( pa s ( f 1+x v)). Ths exactly what the proposed scheme tres to do: prefetchng those tems wth the maxmum sum of value. For any other prefetch scheme that prefetch the same number of data tems, let the set of prefetched data tems be P 0 k and the cost of the (k +1)th access be S 0 k+1, accordng to the proposed scheme, Thus p a f ( ( v)) > 1+x 2P k 2P 0 k S k+1 <S 0 k+1 ( p a f ( v)) 1+x Ths proves that the proposed scheme can mnmze the cost among all prefetch schemes that prefetch the same number of data tems. The proposed value-based functon s calculated n terms of stretch snce the performance metrc s stretch. Actually, ths value-based functon can be easly extended for other performance metrcs. For example, f the performance metrc s query delay, the value functon wll be changed to value() = p a (f v p u f ). Smlar technques can be used to prove that ths value functon can mnmze the query delay. C. Parameter Estmaton To mplement the A scheme, we need to estmate parameters f ; a,andu snce they are not constant. To estmate f, we adopt the exponental agng method, whch has been used n TCP to estmate the round-trp delay. It combnes both the hstorcal data and the currently measured data to estmate the parameters. Whenever a data tem s fetched from the server, f s re-calculated as followng: f = ff f new +(1 ff) f where f new s the currently measured data retreval delay, f on the rght sde of the formula s the calculated f before the last retreval of tem. Although ths formula can be used to estmate f, t s not sutable for estmatng a and u snce the access rate and the update rate should be aged n the absence of data access. That s, the values of a (u ) should be decreased even f there s no data access (update) over some perod of tme. We apply technques, whch have been used n [17], to estmate a and u. Ths method uses K most recent samples to estmate a and u as follows. K a = T T a (K) K u = T T u (K) where T s the current tme, T a (K) and T u (K) are the tme of the K th most recent access and update. If there are less than K samples, all the avalable samples are used to estmate the value. As shown n [17], the best performance can be acheved wth small value of K (2 or 3). Thus, the spatal overhead to store these samples very small. The estmaton of a should be done at the clent sde snce dfferent clents may have dfferent access pattern. However, t mpossble for clents to estmate u snce the data updates occur at the server sde. Therefore, the server estmates u of each data tem and pggybackt to clents when the data tem s broadcast. D. The Adaptve Value-based Prefetch (A) Scheme Due to lmtatons of battery technology, the energy avalable for a wreless devce s lmted and must be used prudently. If the prefetched data tem s not accessed or s nvaldated before t s accessed, the energy spent on downloadng thtem wll be wasted. To avod wastng power, t s mportant that clents only download the data wth hgh value, but such a strct polcy may adversely affect the performance of the system and ncrease the query delay. Each clent may have dfferent avalable resources and performance requrements, and these resources such as power may change over tme. For example, suppose the battery of a laptop lasts for three hours. If the user s able to recharge the battery wthn three hours, power consumpton may not be an ssue, and the user may be more concerned about the performance aspects such as the query latency. However, f the user cannot recharge the battery wthn three hours and wants to use t a lttle bt longer, power consumpton becomes a serous concern. Snce N p controls the number of data to be prefetched and then affects the tradeoff between performance and power, we propose adaptve schemes to adjust N p to satsfy dfferent clent requrements. 1) The Value of N p : When N p reduces to 0, there wll be no prefetch. As N p ncreases, the number of prefetchencreases and the power consumpton also ncreases. Snce the maxmum number of data tems to be prefetched s lmted by the cache sze, N p s also lmted by ths number. Intutvely, the query delay decreases as the number of prefetchencreases. However, ths not always true consderng the overhead to mantan cache consstency. In our cache nvaldaton model, a clent needs to wat for the next IR to verfy the cache consstency. Ths watng tme may ncrease the query delay compared to the approaches wthout prefetch. The cost has been quantfed n Equaton 1, where v s the cache nvaldaton delay. Due to the cost of v, the value of a data tem may be negatve. If value() s negatve, prefetchng tem not only wastes power but also ncreases the average stretch. Therefore, N p should be bounded by Np max, whch s lmted by the clent cache sze and the data value;.e., a clent wll not prefetch tems wth negatve values. The tradeoff between performance and power can be acheved by adjustng N p. In the followng subsectons, we present two adaptve schemes: the A T(TforTme)scheme whch dynamcally adjusts N p to reach a target battery lfe tme, and the A P (P for Power) scheme whch dynamcally adjusts N p based on the remanng power level. 2) A T: Adaptng N p to Reach a Target Battery Lfe: A commuter normally knows the amount of battery energy and the length of the trp between home and offce. Wth these resource lmtatons, the commuter wants to acheve the lowest

5 Notatons: ffl E: the amount of ntal energy. ffl T : the target battery lastng tme. ffl P avg: the estmated average power consumpton. ffl T old ;E old : the tme to obtan the last P avg, and the energy levelatthattme. ffl T new;e new: the current tme and the current energy level. ffl Np max : the maxmum N p. The A T scheme s as follows: P avg = ff Pavg +(1 ff) (E old E new)=(tnew Told ); f ( jp avg E=Tj=(E=T) > 0:05 )) then N p = nt(max(1;np) (1 2 (P avg E=T)=(E=T))); else f f (P avg E=T > 0) then Np ++; else N p ; g f (N p < 0) then N p =0; else f (N p >Np max ) then N p = N max p ; Fg. 2. The A T scheme query delay. Ths equvalent to the problem of adaptng N p to reach a target battery lfe and mnmze the average stretch. Suppose a battery wth E joule lasts T 1 seconds when,andt 2 seconds when N p =0. It s possble to adjust N p to reach a target battery lfe tme T 2 [T 1 ;T 2 ].In A T, the clent montors the power consumed n the past. If t consumes too much power n the past and cannot last T seconds, N p s reduced. On the other hand, t ncreases N p when t found that t has too much power left. Certanly, N p N p = N max p s bounded by Np max. Fgure 2 shows the detals of the A T scheme. 3) A P: Adaptng N p based on the Power Level: When the energy level s hgh, power consumpton s not a major concern and then tradng off energy for performance may be a good opton f the user can recharge the battery soon. On the other hand, when the energy level s low, the system should be power-aware to prolong the system runnng tme to reach the next battery recharge tme. Based on thntuton, the A P scheme dynamcally changes N p based on the power level. Let a k be the percentage of energy left n the clent. When a k drops to a threshold, the number of prefetches should be reduced to some percentage, say f (a k ), of the orgnal value. Some smple dscrete functon can be as follows: f (a k )= 8 >< >: 100% 0:5 <a k» 1:0 70% 0:3 <a k» 0:5 50% 0:2 <a k» 0:3 30% 0:1 <a k» 0:2 10% a k» 0:1 At regular nterval, the clent re-evaluates the energy level a k.ifa k drops to a threshold value, N p = N p f (a k ).The clent only marks the frst N p temn the cache, whch have the maxmum value, as prefetchable. In ths way, the number of prefetches can be reduced to prolong the system runnng tme. Because ths a dscrete functon, N p does not need to be frequently updated and the computaton overhead s low. Note that a smple polcy whch s nether too aggressve (9) nor conservatve mght result n smlar average stretch and lfetme as the VAP P scheme f the battery runs out before recharge. However, f the user recharges the battery frequently, ths smple polcy may not be a good opton snce t saves power at the cost of delay, but power consumpton s not a concern at ths tme. In contrast, our adaptve scheme tres to tradeoff power for performance at the begnnng, and become power-aware when the clent cannot recharge n tme. IV. PERFORMANCE EVALUATION To evaluate the performance of the proposed methodology, we developed a smulaton model smlar to that employed n [7], [19]. We compare the value-based prefetch () approach and the adaptve value-based prefetch (A) approaches wth the prefetch scheme used n [7] under varous workload and system settngs. A. Smulaton Model and Parameters 1) The Clent Model: Each clent generates a sngle stream of read-only queres. The mean query generate tme for each clent s T query. The access pattern follows a Zpf lke dstrbuton [4] whch has been frequently used to model nonunform dstrbuton. In the Zpf lke dstrbuton, the access probablty of the th ( 1»» n) data tem s represented as follows. p a = 1 P n k=1 where 0»» 1. When = 1, t s the strct Zpf dstrbuton. When =0, t becomes the unform dstrbuton. 2) The Server Model: The server broadcasts IRs and s perodcally to the clents. The IR/ broadcast messages are assgned the hghest prorty whereas the rest of the messages are of equal prorty. Ths ensures that IRs and s can be broadcast regularly over the wreless channels wth the broadcast nterval specfed by L. The IR nterval s set at 20 seconds and the s replcated 4 tmes wthn each nterval. The other messages are served on a frst-come-frst-serve bass. Should the server be n the mddle of a transmsson when an IR or has to be sent, the IR/ broadcast s deferred tll the end of the current packet transmsson. There are n data tems at the server sde. The sze ( )oftem grows lnearly from s mn to s max a ncreases. As a result of jont dstrbuton of access pattern and data sze, the tem wth smaller sze wll be accessed more frequently than bgger ones. Ths has been commonly observed n traces [4], [11]. The server generates a sngle stream of updates separated by an exponentally dstrbuted update nterval tme. The whole database s dvded nto two subsets: the frequently-updated subset whch contans the frst 20% of the data tems (d from 0 to n Λ 20% 1) n the database, and the rarelyupdated subset whch contans the rest of the data. 80% of the updates are randomly dstrbuted nsde the frequently-updated subset. The rest of the updates are randomly dstrbuted n the rarely-updated subset. It s assumed that the bandwdth s fully utlzed for broadcastng IRs and s and servng clent requests. The server processng tme s consdered to 1 k

6 Energy consumed per query (joule) (Np=10) (Np=50) (Np=200) Mean update arrval tme (seconds) Average stretch (a) Energy consumpton Fg (Np=10) (Np=50) (Np=200) Mean update arrval tme (seconds) (b) Average stretch (c) The energy-stretch Performance under varyng update arrval tme (Np=10) (Np=50) (Np=200) Mean update arrval tme (seconds) TABLE I SIMULATION PARAMETERS Number of data tems (n) 2000 Number of clents 100 smn 0.5k smax 10k Mean update tme (Tupdate) 100 seconds Broadcast nterval (L) 20 seconds Broadcast wndow (w) 10 nterval Broadcast bandwdth 144Kbps Uplnk bandwdth 14.4Kbps Relatve cache sze 20% of total database sze Mean query generate tme (Tquery) 100 seconds Zpf dstrbuton parameter 0.9 be neglgble. Most of the system parameters and ther default values are lsted n Table I. The energy consumpton model adopted n ths paper s smlar to the model used n [6], where the transmsson power dsspaton s 0.5 watt and the recevng power dsspaton s 0.2 watt for the wreless network nterface. In order to focus on the energy consumpton of data transmsson and recevng, we do not consder the energy consumed by other components. In order to better understand the overall performance of the system, we ntroduce a new metrc called energy-stretch, whchsdefnedas energy-stretch = stretch Λ energy-consumed The energy-stretch value gves a better ndcaton of the system performance because t consders two mportant parameters: energy consumpton and stretch. The smulaton results consst of two parts: one to evaluate the performance of the scheme and the other to evaluate the performance of the A schemes. B. Smulaton Results: 1) The Effects of the Mean Update Arrval Tme: Fgure 3 shows the effects of the mean update arrval tme on the energy consumpton, the average stretch, and the energystretch. The fgure shows varous approaches wth dfferent N p value. As we know, the number of prefetchencreases as N p ncreases. As a result, the energy consumpton ncreases and the average stretch drops. Ths has been verfed by the smulaton resultn Fgure 3(a) and (b). The N p = 10 approach has the lowest power consumpton, but t has the hghest stretch. Fgure 3(c) shows ther energy-stretch value. Although (N p = 10) has the lowest energy-stretch when T update = 10s, t has hgher energy-stretch than (N p = 50) when T update > 40s, and t has a very hgh average stretch. Generally speakng, (N p = 50) has low stretch whle consumng smlar power as (N p = 10) when T update > 40s. WeuseN p =50n the followng experments when scheme s used unless specfed otherwse. Compared to the approach, the approach saves a large amount of power snce the approach aggressvely prefetches data to fll up the clent cache. From Fgure 3(a), we can also see that four approaches have smlar power consumpton when T update = 10000s, because only lmted number of data temn the cache are nvaldated when T update s very large and hence the clents only need to prefetch a few data tems. As the mean update arrval tme drops, many data tems are updated, and the number of prefetchencreases. As a result, the power consumpton ncreases. However, the ncreasng trend s dfferent. The approach has the largest power consumpton ncrease whereas (N p =10)hasthe lowest. Ths due to the fact that (N p =10) lmts the number of prefetches to 10. From Fgure 3(b), we can see that the approach does not follow the same trend as other approaches. When the mean update arrval tme s low, has lower stretch than (N p = 10) and (N p =50) snce allows aggressve prefetchng, whle only prefetches N P tems wth hgh access rate and low update rate (based on the value functon). When the update arrval tme s low, data tems are frequently nvaldated. Due to aggressve prefetch, acheves better performance at the cost of hgh energy consumpton as shown n Fgure 3(a). As the mean update tme ncreases, varous approaches outperform, snce only prefetches the data wth hgh value. Comparng (N p = 200) wth, we can see the advantage of. Although (N p = 200) only prefetch 200 data tems, whch s much less that of the approach, t stll outperforms n terms of energy, stretch, and energy-stretch. 2) Comparsons wth Smple Prefetch Schemes: A prefetch scheme may utlze the fact that the Zpf-lke dstrbuton favortems wth small d. One smple and reasonable prefetch

7 Energy consumed per query (joule) SIMP-30 SIMP-50 SIMP-100 Average Stretch SIMP-30 SIMP-50 SIMP SIMP-30 SIMP-50 SIMP Mean query generate tme (seconds) (a) Energy consumpton Mean query generate tme (seconds) Mean query generate tme (seconds) (b) Average stretch (c) The energy-stretch Fg. 4. Comparsons wth smple prefetch schemes Energy consumed per query (joule) Cache sze (% of total database sze) Average stretch Cache sze (% of total cache sze) Cache sze (% of total cache sze) (a) Energy consumpton (b) Average stretch (c) The energy-stretch Fg. 5. Performance as a functon of the cache sze scheme s to prefetch those k hottest (frequently accessed) data tems. In ths subsecton, we evaluate ths smple prefetch scheme wth. In Fgure 4, SIMP-k represents the prefetch scheme whch prefetches k hottest data tems. As expected, smaller k resultn lower energy consumpton and hgher average stretch. Overall, the scheme has the best performance consderng both energy consumpton and average stretch. Although the smple prefetch scheme consders the access frequency factor, t does not consder other factors such as data sze, cache nvaldaton cost. Thus, t underperforms the scheme. From Fgure 4, we can also see that the energy consumpton of the approach and the approach both ncrease wth the mean query generate tme. Ths can be explaned as follows. When the mean query generate tme ncreases, f other parameters do not change, the update rate wthn the tme of two query nterval ncreases. In other words, ncreasng the mean query generate tme wthout changng the update arrval tme should have the same effect of reducng the update arrval tme wthout changng the mean query generate tme. As explaned n Secton IV-B.1, the energy consumpton ncreasef the update arrval tme drops, and then the energy consumpton ncreases as the mean query generate tme ncreases. 3) The Effects of the Cache Sze: Fgure 5 shows the effects of the cache sze on the average stretch and the energy consumpton of the approach and the scheme. As can be seen, and have smlar energy consumpton when the cache sze s small snce the number of tems to be prefetched s lmted by the cache sze n the approach. As the cache sze ncreases, the number of prefetchen the approach ncreases and ts energy consumpton also ncreases. Ths dfferent from. Snce N p s fxed, the data to be prefetched s also fxed n. Moreover, when the cache sze ncreases, the cache ht rato ncreases, and then more queres can be served from the cache wthout sendng requests and recevng data. Thus, the amount of energy consumed per query actually drops. Ths explans why the energy consumpton per query n drops as the cache sze ncreases. As shown n Fgure 5 (b), due to aggressve prefetchng, the average stretch of the approach drops below that of the approach when the cache sze ncreases to 25%. When consderng both power consumpton and stretch, always outperforms as shown n Fgure 5(c). 4) The Effects of the Zpf Parameter : The Zpf parameter determnes the skewness of the access dstrbuton. Fgure 6 shows the effects of the access pattern on the system performance. When = 0, the access pattern follows unform dstrbuton. That s, all the data tems have the same access probablty. At ths tme, prefetch s less effectve and the energy-stretch value s hgh. As ncreases, more data accesses are focused on tems wth small d and the energy-stretch drops. Fgure 6 demonstrates that our approach always outperforms the approach. Even when the access pattern follows unform dstrbuton ( =0), our approach stll performs better. It also shows that our approach works for a

8 Energy consumed per query (joule) Zpf parameter θ Average Stretch Zpf parameter θ Zpf parameter θ (a) Energy consumpton (b) Average stretch (c) The energy-stretch Fg. 6. The effects of the Zpf parameter Energy consumed per query (joule) Mean access pattern change nterval delta Average stretch Mean access pattern change nterval delta Mean access pattern change nterval delta (a) Energy consumpton (b) Average stretch (c) The energy-stretch Fg. 7. The effects of the access pattern varaton wde spectrum of access patterns. 5) The Effects of the Access Pattern Varaton: In practce, the clent access pattern may change. To model such envronments, we make the followng modfcatons. The data access dstrbuton s shfted one tem every ff IR ntervals. More specfcally, suppose tem s the data to be accessed accordng to the Zpf dstrbuton. An offset s added to after each ff IR ntervals so that + s the actual data tem that wll be accessed. ntalzed to 0, and ncreased by one every ff IR ntervals. The smaller ff s, the faster the access pattern changes. To make t reasonable, we also apply the same offset to the update so that the tems wth hgh update rate stll have hgh access rate. Fgure 7 shows the results when the access pattern changes. If the access pattern changes rapdly, the average energy consumpton s very hgh because clents need to spend more energy to prefetch and request data from the server. It can be seen that the approach always outperforms the approach. C. Smulaton Results: Adaptaton 1) Adaptng N p to Reach a Target Battery Lfe: Fgure 8 evaluates the performance of the A T scheme after the clents are assgned 5000 joule ntally. By smulaton, we found that the battery lfe s 190k seconds when (N p =0) s used. Although the cache sze s 20% of the database sze, consderng the data dstrbuton pattern and the data sze dfference, the clent cache can hold as many as 840 data tems. We set Np max to be 840, but we should know that clents wll not prefetch data tems wth negatve value. Based on smulaton results, the battery lfe s 110k seconds when (N p = 840) s used. To evaluate the performance of the A T scheme, we consder the followng target battery lfe (T ): ffl T = 100k seconds. In ths case, denoted as A T(100, 0), a very short battery lfe tme s expected, and N p has an ntal value of 0. ffl T = 200k seconds. In ths case, denoted as A T(200, 840), the battery lfe s too long to be reachable, and N p has an ntal value of Np max. ffl T = 140k seconds. There are two cases: N p has an ntal value of 0, denoted as A T(140, 0); N p has an ntal value of of Np max, denoted as A T(140, 840). As shown n the Fgure 8(a), the adaptve schemes can quckly adjust N p to reach the target battery lfe f t s possble. For AV P T (200; 840) and AV P T (100; 0), because the target battery lfe s not reachable, these two schemes can only adjust N p to reach the target as close as possble. The small dfference of the battery lfe tme between AV P T (200; 840) and (N p = 0) s caused by the aggressve ntal prefetch of the AV P T (200; 840) scheme. For the two adaptve schemes wth moderate target lfe, AV P T (140; 0) and AV P T (140; 840), both reaches the target battery lfe tme. The dfference between the actual battery lfe and the target battery lfe s less than 3%. Fgure 8(c) shows the cumulatve average stretch from the tme to

9 Np Cumulatve average stretch A_T(140, 840) A_T(140, 0) A_T(200, 840) A_T(100, 0) Tme (Thousand seconds) (a) The adaptaton of N p (Np=840) (Np=0) A_T(140, 840) A_T(140, 0) A_T(100, 0) A_T(200, 840) Tme (Thousand seconds) (c) Cumulatve average stretch Energy level (%) Average stretch (Np=840) (Np=0) A_T(140, 840) A_T(140, 0) A_T(100, 0) A_T(200, 840) Tme (Thousand seconds) (b) The energy level (Np=840) (Np=0) A_T(140, 840) A_T(140, 0) A_T(100, 0) A_T(200, 840) Tme (Thousand seconds) (d) Average stretch Fg. 8. A T: adaptng Np to reach a target battery lfe collect results. Fgure 8(d) shows the average stretch of every 2000 seconds, whch s the tme for N p to be re-evaluated. As can be seen from 8(c), the dfference between the fnal average stretch of AV P T (140; 0) and AV P T (140; 840) s less than 4%. Fgure 8(d) also shows that AV P T (140; 0) and AV P T (140; 840) have smlar stretch after the frst 60k seconds. 2) The Adaptaton of N p based on the Power Level: In A P, when the energy level becomes less than a threshold, the prefetch rate s reduced. When the energy level becomes crtcally low, the prefetch rate s further reduced. By reducng the prefetch rate, energy can be saved and the system can last longer. Fgure 9 compares the energy level and the system performance of three schemes:, (Np = 400), and A P. In A P, the ntal value of N p s also 400. As can be seen, the approach has hgher prefetch rate and consumes more energy, whereas our approaches have lower energy consumpton. Due to energy savng, our adaptve approach can last more than 20% longer than the approach. (Np = 400) and A P have the same amount of energy consumpton when there are abundant energy. As the energy level falls below 50%, AP reduces the prefetch rate to save energy. Fgure 9 (a) shows that A Pusesless energy because of the reducton of N p. As shown n the fgure, wthout adaptaton, contnues to use more energy and eventually runs out of power sooner than A P. On the other hand, the power savng of A P s at the cost of ncreasng the average stretch, although the ncrease s not that sgnfcant. As shown n Fgure 9(b), the average stretch of A P s only slghtly hgher than that of. Fgure 9(c) shows that A P manages to acheve low energy-stretch whle ncreasng the battery lfe. V. RELATED WORK Prefetchng has been wdely used to reduce the response tme n the Web envronment [8], [9], [15], [16]. Most of these technques concentrate on estmatng the probablty of each fle beng accessed n the near future. Snce these technques are desgned for the pont-to-pont communcaton envronment, they are not sutable for the broadcastng envronment n moble computng systems. Recently, prefetchng has been used n many cache management schemes for moble envronments [6], [10], [12] to reduce the query latency and the bandwdth consumpton. In Grass s scheme [12], a pushbased model s used. The system performance s optmzed usng ndexng technques to perodcally re-broadcast the hot data. In ther prefetch scheme, each data tem s assgned a calculated value fv(), whch s a functon of the access rate of tem. Based on ths value, the clent decdes whether to prefetch the tem or not when t appearn the broadcast channel. If there exsts an tem j n the clent s cache such that fv() > fv(j), tem j s removed from the cache and replaced by tem. Ths prefetch scheme fals to address a number of ssues such as data sze, data update rate, and power consumpton. In [6], Cao proposed an adaptve prefetch scheme. In ths scheme, clents record the number of tmes a cached tem beng accessed and prefetched, respectvely. The clent calculates the prefetch access rato (PAR), whch s the number of prefetches dvded by the number of accesses, for each tem.

10 Energy level (%) (NP=400) A_P Tme (Thousand seconds) Cumulatve average stretch (a) The energy level (b) Average stretch (Np=400) A_P Tme (Thousand seconds) (Np=400) A_P (c) The energy-stretch Tme (Thousand seconds) Fg. 9. The energy level and system performance as a functon of tme If PAR s less than one, prefetchng the data s useful snce the prefetched data may be accessed multple tmes. When power consumpton becomes an ssue, the clent marks those cache tems wth PAR > f as non-prefetch,wheref>1 s a system tunng factor, and should be dynamcally changed based on the energy consumpton. However, no clear methodology as to how and when f should be changed. Ths scheme, lke the prevous one [12], does not consder varyng data sze and the data update rate. Gtzens and Bambos [10] proposed a prefetch scheme consderng the qualty of the wreless channel. Clents prefetch aggressvely when the channel qualty s good but reduce the prefetch rate when the channel qualty becomes poor. Ther scheme assumes that the cost of accessng a data tem s already gven. Our value-base prefetch scheme actually gves a functon to dentfy the value of each data tem and prefetch those tems that can mnmze the overall access cost. Thus ther work complements our work. VI. CONCLUSIONS Prefetchng s an effectve technque to reduce the query latency. However, prefetchng consumes power. In wreless networks where power s lmted, t s essental to correctly dentfy the data to be prefetched n order to provde better performance and reduce the power consumpton. In ths paper, a value-based prefetch scheme was proposed. The proposed scheme evaluates the cost of prefetchng a data tem by takng nto account varous factors such as the data sze, the access rate, the update rate, and the cache valdaton delay. In addton to makng smarter prefetch decsons, the scheme s desgned to be adaptve, adjustng the prefetch rate based on the current energy level. Smulaton results verfed that the proposed schemes can reduce the energy consumpton and mprove the system performance n terms of stretch compared to the approach under varous system settngs. The major contrbuton of the paper s the value-based functon. Although we explored varous adaptve approaches, many ssues stll need further nvestgaton. For example, the channel state nformaton [10] can be used when makng prefetch decsons,.e., N p can be dynamcally adjusted based on the channel state. If the target battery lfe tme s not known or only known wth some probablty, A T needs to be extended to factor nto these uncertantes. If the battery recharge cycle or the user profle s known or known wth a hgh probablty, how to enhance A TandAP needs further nvestgaton. Acknowledgments We would lke to thank the edtors and the anonymous referees whose nsghtful comments helped us to mprove the presentaton of the paper. Ths work was supported n part by the Natonal Scence Foundaton (CAREER CCR and ITR ). REFERENCES [1] S. Acharya and S. Muthukrshnan, Schedulng on-demand broadcasts: New metrcs and algorthms, MobCom98, pp , Oct [2] S. Acharya, M. Frankln, and S. Zdonk, Dssemnaton-based Data Delvery Usng Broadcast Dsks, IEEE Personal Communcatons, pp , Dec [3] D. Barbara and T. Imelnsk, Sleepers and Workaholcs: Cachng Strateges for Moble Envronments, ACM SIGMOD, pp. 1 12, [4] L. Breslau, P. Cao, L. Fan, G. Phllps, and S. Shenker, Web Cachng and Zpf-lke Dstrbutons: Evdence and Implcatons, Eghteenth Annual Jont Conference of the IEEE Computer and Communcatons Socetes, [5] G. Cao, On Improvng the Performance of Cache Invaldaton n Moble Envronments, ACM/Baltzer Moble Networks and Applcaton (MONET), vol. 7, no. 4, pp , Aug [6] G. Cao, Proactve Power-Aware Cache Management for Moble Computng Systems, IEEE Transactons on Computer, June [7] G. Cao, A Scalable Low-Latency Cache Invaldaton Strategy for Moble Envronments, IEEE Transactons on Knowledge and Data Engneerng, vol. 15, no. 5, September/October 2003 (A prelmnary verson appeared n ACM MobCom 00). [8] K. Chnen and S. Yamaguch, An Interactve Prefetchng Proxy Server for Improvement of WWW Latency, Proc. INET97, June [9] C. Cuhna and C. Jaccound, Determnng WWW User s Next Access and ts Applcaton to Pre-fetchng, Proceedngs of ISCC 97: The Second IEEE Symposum on Computers and Communcatons, [10] Savvas Gtzens and Ncholas Bambos, Power-Controlled Data Prefetchng/Cachng n Wreless Packet Networks, INFOCOM, [11] S. Glassman, A Cachng Relay for the World Wde Web, Computer Networks and ISDN Systems, vol. 27, [12] Vncenzo Grass, Prefetchng Polces for Energy Savng and Latency Reducton n a Wreless Broadcast Data Delvery System, ACM MSWIM, [13] S. Hameed and N. Vadya, Effcent algorthms for schedulng data broadcast, ACM/Baltzer Wreless Networks (WINET), pp , May [14] T. Imelnsk, S. Vswanathan, and B.R. Badrnath, Data on Ar: Organzaton and Access, IEEE Transactons on Knowledge and Data Engneerng, vol. 9, no. 3, pp , May/June [15] Zhme Jang and Leonard Klenrock, An Adaptve Network Prefetch Scheme, IEEE Journal on Selected Arean Communcatons, Aprl [16] V. Padmanabhan and J. Mogul, Usng Predctve Prefetchng to Improve World Wde Web latency, Computer Communcaton Revew, pp , July [17] J. Shm, P. Scheuermann, and R. Vngralek, Proxy Cache Algorthms: Desgn, Implementaton, and Performance, IEEE Transactons on Knowledge and Data Engneerng, vol. 11, July/August [18] M. Stemm and R. Katz, Measurng and Reducng Energy Consumpton of Network Interfacen Hand-Held Devces, IEICE Trans. on Communcatons, vol. 80, no. 8, pp , Aug

11 [19] J. u, Q. Hu, W. Lee, D. Lee, An Optmal Cache Replacement Polcy for Wreless Data Dssemnaton under Cache Consstency, 2001 Int l conference on parallel processng, Sept [20] J. Yuen, E. Chan, K. Lam, and H. Leung, Cache nvaldaton scheme for moble computng systems wth real-tme data, ACM SIGMOD Record, Dec Langzhong Yn receved the B.E. degree and the M.E. degree n computer scence and engneerng from the Southeast Unversty, Nanjng, Chna, n 1996 and 1999, respectvely. He s currently workng toward the Ph.D. degree at the Pennsylvana State Unversty. From 1999 to 2000, he was an Engneer n the Global Software Dvson of Motorola. Hs research nterests nclude wreless/ad hoc networks and moble computng. Guohong Cao receved the B.S. degree from an Jaotong Unversty, an, Chna. He receved the M.S. degree and Ph.D. degree n computer scence from the Oho State Unversty n 1997 and 1999, respectvely. Snce Fall 1999, he has been an assstant professor of computer scence and engneerng at Pennsylvana State Unversty. Hs research nterestnclude wreless networks, moble computng, and dstrbuted fault-tolerant computng. He has served as an edtor for IEEE Transactons on Wreless Communcatons, and has served on varous conference program commttees. He was a recpent of the Presdental Fellowshp at the Oho State Unversty n 1999, and a recpent of the NSF CAREER award n 2001.