IEEE TRANSACTIONS ON COMPUTERS, VOL. 56, NO. 12, DECEMBER On-Bound Selection Cache Replacement Policy for Wireless Data Access

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1 IEEE TRANSACTIONS ON COMPUTERS, VOL. 56, NO. 12, DECEMBER On-Bound Selecton Cache Replacement Polcy for Wreless Data Access Hu Chen, Member, IEEE, and Yang Xao, Senor Member, IEEE Abstract Cache can be used for moble devces to reduce the usage of lmted bandwdth n wreless networks. Ideally, frequently accessed and nfrequently updated data tems should be cached and nfrequently accessed and frequently updated data tems should be evcted or not cached at all. Most of the exstng cache replacement polces adopt only access nformaton so that frequently updated data tems are also cached. As a remedy, we propose a cache replacement polcy, called On-Bound Selecton (OBS), that uses both data access and update nformaton. The proposed OBS s nspred by an analytcal analyss for a server-based Poll-Each-Read (SB-PER) and a revsed Call-Back (R-CB). The OBS provdes an upper bound for effectve ht rato and a lower bound for communcaton cost. The proposed scheme s evaluated and compared wth a least frequently used (LFU) replacement polcy through extensve smulatons. Smulaton results show that the OBS outperforms LFU n terms of both effectve ht rato and communcaton cost. Index Terms Cache, replacement polcy, wreless networks, access, update, effectve ht rato, communcaton cost. Ç 1 INTRODUCTION MOBILE Termnals (MTs) have been used to access nformaton stored n remote servers through wreless communcaton channels. However, wreless channels are the scarcest and most expensve resource n entre networks. Cache mechansms have been ntroduced to reduce the bandwdth usage of wreless channels [3], [7], [8], [13], [15], [20], [27], [29]. In general, a cache mechansm conssts of a cache access algorthm and a replacement polcy. A cache access algorthm defnes how a clent and ts server exchange messages and data to acheve a certan degree of data consstency. Examples of cache access algorthms are Poll- Each-Read (PER) [20], [21], Call-Back (CB) [14], [20], [31], and Invaldaton Report (IR) [3]. Many applcatons use strong consstent cache access algorthm [3], [7], [8] to prevent usng stalled data. A replacement polcy decdes whch cached data tem s evcted when an uncached data tem s accessed and the cache s full. Replacement polces affect the overall cache performance. They are more mportant to wreless MTs than to wred termnals snce wreless termnals generally have less cache space than wred ones. Many cache replacement polces have been proposed for wred and wreless networks [2], [26], [29], [30]. However, most of these replacement polces use only data access nformaton and gnore data update nformaton. Update nformaton s crtcal and should not be gnored because an update makes a cached data tem nvald and a cache ht becomes useless. Two replacement polces [29], [30] have. H. Chen s wth the Department of Mathematcs and Computer Scence, Vrgna State Unversty, Petersburg, VA E-mal: huchen@eee.org.. Y. Xao s wth the Department of Computer Scence, Unversty of Alabama, 101 Houser Hall, Box , Tuscaloosa, AL E-mal: yangxao@eee.org. Manuscrpt receved 22 Jan. 2006; revsed 17 Oct. 2006; accepted 13 June 2007; publshed onlne 9 July Recommended for acceptance by A. Me. For nformaton on obtanng reprnts of ths artcle, please send e-mal to: tc@computer.org, and reference IEEECS Log Number TC Dgtal Object Identfer no /TC been proposed to use both access and update nformaton wth IR schemes. However, ther desgn goal s to reduce the stretch, a normalzed delay, whch s not the scarce and expensve resource n entre networks and s, at least sometmes, not the best desgn goal. Furthermore, as ponted out n [20], IR schemes requre broadcastng n entre networks and are not sutable for mplementaton n realstc wreless networks. IR schemes may also requre low layer functons (for example, data lnk layer) of wreless network protocols, whch may not be avalable for mplementng cachng n upper layer applcatons (for example, applcaton layer). Ths paper studes cache replacement polces. Our goal s to desgn a replacement polcy for ncreasng effectve cache ht rato and decreasng communcaton cost as much as possble. Two update-based strong consstent cache access algorthms, a server-based PER (SB-PER) and a revsed CB (R-CB), are ntroduced and they provde both access and update hstores to replacement polces. They can also be run n applcaton layers and do not rely on lower layer functonaltes of wreless network protocols. Intutvely, a good replacement polcy should evct nfrequently accessed but frequently updated data tems. We analytcally analyze access and update processes n the SB-PER and the R-CB. The analyss provdes an upper bound of effectve ht rato and a lower bound of communcaton cost. The analytcal analyss nspres us wth how nfrequently accessed but frequently updated data tems can be chosen. We hence desgn a replacement polcy, called On-Bound Selecton (OBS), to evct nfrequently accessed but frequently updated data tems whle keepng frequently accessed but nfrequently updated data tems accordng to the defned bounds. Our proposed OBS replacement polcy s a frequency-based replacement polcy. It s not lmted to wreless data access and t s also applcable to wred networks such as Internet clentserver applcatons and Web cachng. The rest of ths paper s organzed as follows: Secton 2 shows the network archtecture, the data access model, and /07/$25.00 ß 2007 IEEE Publshed by the IEEE Computer Socety

2 1598 IEEE TRANSACTIONS ON COMPUTERS, VOL. 56, NO. 12, DECEMBER 2007 Fg. 1. Wreless network archtecture. several examples of wreless data applcatons. The SB-PER and the R-CB access algorthms are ntroduced n Secton 3. We propose the update-based replacement polcy n Secton 4. The analytcal model of cache access and update s presented n Secton 5. In Secton 6, we brefly present our motvaton and comments on cache replacement polces. Performance evaluaton and comparson are gven n Secton 7. We conclude the paper n Secton 8. 2 NETWORK ARCHITECTURE AND APPLICATIONS 2.1 Network Archtecture Overvew Wreless data applcatons and servces have been provded on personal communcaton servce (PCS) networks [25]. In current PCS networks, a servce area s dvded nto a number of locaton areas (LAs). An LA s further parttoned nto a number of cells. Each cell has a base staton (BS), whch controls many MTs wthn the cell va wreless lnks. All of the BSs wthn one LA are connected to a moble swtchng center (MSC). All of the MSCs are fnally connected to a publc swtched telephone network (PSTN). A PCS can be connected to the Internet n many ways, such as wreless carrers propretary networks and PSTN. An MT can access data servers resdng n ether PCS networks or the Internet va ts correspondng BS. Fg. 1 shows an example of a wreless network archtecture for wreless data access. In general, as shown n Fg. 1, wreless data access follows clent-server models. Databases are hosted at remote servers, whch are usually n the wred networks. In ths paper, we do not dstngush among clents, MTs, and users. A clent accesses data tems n a database n a remote server through wreless lnks when the data tem s not n cache or s cached but not vald. The server updates data tems when requested by clents or others. 2.2 Wreless Data Applcatons We brefly show several examples of wreless network applcatons whch can beneft from the proposed cache access algorthms and replacement polces. Wreless Web applcatons are partcular examples of such applcatons. Many network protocols can be used to support wreless network data applcatons. The Wreless Applcaton Protocol (WAP) s desgned to enable easy, fast delvery of relevant nformaton and servces to moble users n wreless cellular networks. WAP applcatons run n clent-server models. Cache operatons have been proposed for WAP applcatons [18]. In [20], a busness card applcaton s proposed for SMS, a platform that ntegrates the IP network wth the Short Message Servces (SMS) n a moble telephone network. A subscrber can store a phone book consstng of a number of busness cards n a remote server. Ths server-based applcaton has many advantages. Frst, the subscrber can access the phone book through dfferent MTs. Second, the applcaton server may provde drectory servces such as yellow pages and whte pages. In [16], an onlne aucton Web applcaton s proposed. An aucton tem s assocated wth ts descrpton, prce, and revews. Some of the tems change more frequently than others do. For example, prce may change every few mnutes and the descrpton remans the same durng the aucton. Ths applcaton s not necessarly mplemented as a Web applcaton and t s benefcal to mplement ths applcaton on wreless networks because a user may have a desre to start an aucton anytme and anywhere. A wreless applcaton called a real-tme stock prce montor can be used to check stock prces and a user can make a transacton by usng the MT based on the stock nformaton obtaned from a server. In ths applcaton, the data sources may or may not be located outsde the cellular networks. Stocks are updated and accessed at dfferent rates. Some stocks may be traded n a huge volume. Ther prces may change very frequently. These examples show that update and access frequences can be dfferent among dfferent data tems. In fact, as shown n [5], many data tems stored n remote databases and accessed through Web applcatons change frequently. Therefore, t s mportant to accommodate both update and access nformaton nto cache mechansm desgn. Furthermore, t s generally mpossble to cache all server-kept data tems such as the busness cards of all subscrbers, the prces of all aucton merchandse, and the prces of all stocks n local clent caches. Inevtably, cache replacement polces need to be taken nto account. Nevertheless, as we wll dscuss n Secton 7.5, t s not necessarly good for the overall system performance to maxmze clent cache space n networks wth updates, especally heavy updates. Consequently, replacement polces are better as an ntegral part of the network system archtecture. 3 CACHE ACCESS ALGORITHMS PER and CB are two wdely used fundamental cache access algorthms for a clent-server data access model [20], [21]. In PER, a clent attempts to read a data tem from a server at each access and the server only reples to t wth an acknowledgment when the data tem s cached and vald, where a vald data tem means that the data tem has not been updated snce t was cached, and, f the data tem s nvald, the server sends the data tem to the clent. In CB, the server sends an nvaldaton message at each update to the clent, whch caches the updated data tem. The detals of these two schemes can be found n [20]. In ths secton, we ntroduce an SB-PER and an R-CB sutable for usng both update and access nformaton n replacement polces. Both of these cache access algorthms have the capablty of

3 CHEN AND XIAO: ON-BOUND SELECTION CACHE REPLACEMENT POLICY FOR WIRELESS DATA ACCESS 1599 Fg. 2. (a) The SB-PER and (b) the R-CB. mantanng full access and update hstores and thus can use any replacement polcy usng both data access and update nformaton. 3.1 Server-Based Poll-Each-Read As shown n Fg. 2a, the SB-PER uses a stateful server, whch stores access (Step 1.3) and updates (Step 4.2) the hstores of all data tems. The server becomes the most knowledgeable entty n the network and, thus, t s capable of makng the wsest decsons. Therefore, the server makes replacement decsons for a clent (Step 3.1) and sends decsons to the clent (Step 3.2). At the server, an object profle s used for storng the update hstores of all data tems. 3.2 Revsed Call-Back As shown n Fg. 2b, we revsed the orgnal CB algorthm such that the server records the access and update hstores of all data tems (Steps 2.5 and 3.5) and the access and update hstores of the cached data tems at clents are synchronzed through the messages. We shall call t the R-CB. Note that the server saves the access hstory of a cached data tem by sendng a message to the server (Step 2.5) when t s evcted to accommodate the accessed data tem. The access and update hstores of a data tem are sent to a clent wth the data tem by the server (Step 2.2). Therefore, the clent has the up-to-date access and update hstores of all of the cached and accessed data tems and, thus, t can make the wsest replacement decson (Step 2.3). As shown n Fg. 2b, the user profles and the object profle have the same usage as the SB-PER. 4 ON-BOUND SELECTION REPLACEMENT In ths secton, we propose an update-based cache replacement polcy, called OBS, whch uses both update and access frequences. The OBS tres to cache frequently accessed but nfrequently updated data tems and to evct nfrequently accessed but frequently updated data tems n the cache. In other words, the OBS tres to keep good data tems and evct bad data tems n the cache. Let fj a ðtþ denote the access frequency of data tem O j at clent and let fj u ðtþ denote the update frequency of data tem O j at the server up to tme t, respectvely. Note that fj uðtþ does not have a subscrpt, but fa j ðtþ does snce fu j ðtþ s a global statstc. Denote j and j as the access rate of data tem O j at the clent and the update rate at the server, respectvely. We expect that fj a ðtþ and fu j ðtþ approach the access rate j and the update rate j, respectvely, when tme t s sgnfcantly large, that s, j ¼ lm t!1 fj a ðtþ and j ¼ lm t!1 fj u ðtþ. We defne an On-Bound Selecton factor (OBS factor) as follows: OBSF j ðtþ ¼ 2 fj a ðtþ fj a ðtþþfu j ðtþ ; OBSF j ¼ lm OBSF j ðtþ ¼ 2 j : ð2þ t!1 j þ j In the OBS replacement polcy, the cache access algorthms mantan access and update hstores, whch can be used to compute the OBS factor defned n (1). The replacement polcy computes the OBS factors of all of the cache data tems and the newly accessed data tem and then looks for the data tem wth the least OBS factor. If the data tem wth the least OBS factor s not the newly accessed data tem, the correspondng data tem s replaced wth the newly accessed data tem; otherwse, the accessed data tem s not cached and there s no change n the cache. The OBS polcy s a frequency-based replacement polcy snce t uses access and update frequences. Frst, as we have dscussed n Secton 3, the SB-PER and the R-CB are the cache access algorthms that are capable of mantanng access and update hstores of all data tems. Therefore, the OBS polcy can be appled to the SB-PER and the R-CB. Second, the access and update frequences are measured by usng a movng wndow. For the rest of the paper, the performance of the OBS polcy s studed for these two cache access algorthms. However, the proposed replacement polcy should not be lmted to just these two cache access algorthms and t should be sutable for any cache ð1þ

4 1600 IEEE TRANSACTIONS ON COMPUTERS, VOL. 56, NO. 12, DECEMBER 2007 access algorthm that can provde both access and update frequences. 5 ANALYTICAL MODEL In ths secton, we provde an analytcal analyss that gves the reasonng behnd the OBS scheme. The network has a data server and many clents. All data accesses happen at clents and all updates happen at the server. We have the followng assumptons: 1. The server has N data tems. 2. A clent has a cache that holds up to K data tems. 3. Accesses to data tem O follow a Posson process wth rate. 4. Updates to data tem O follow a Posson process wth rate. An effectve cache ht s defned as an event where an access happens to a data tem that s cached and vald. The effectve ht rato of a cache access algorthm wth a replacement polcy s the probablty that an access causes an effectve cache ht when the cache access algorthm s exercsed wth the replacement polcy. Let p SBPER and p RCB denote the effectve ht ratos of the SB-PER and the R-CB wth a gven replacement polcy, respectvely. Defne the effectve ht rato of data tem O of a cache access algorthm wth a replacement polcy as the probablty that an access causes an effectve cache ht and the accessed data tem s O when the cache access algorthm s exercsed wth a replacement polcy. Let p SBPER; and p RCB; denote the effectve ht ratos of data tem O for the SB-PER and the R-CB wth a gven replacement polcy, respectvely. Snce wreless channels between MTs and ther BSs are the scarcest and most expensve resources, we only consder the bandwdth usage of messages and data transmtted between MTs and ther correspondng BSs. Defne communcaton cost as the average bytes transferred through wreless lnks between MTs and the BSs per data access. Let c SBPER and c RCB denote communcaton costs for the SB-PER and the R-CB wth a gven replacement polcy, respectvely. Let X denote the random varable of the number of accesses to data tem O occurrng between two consecutve updates to data tem O. Let pðx ¼ kþ denote the probablty that exactly k accesses to data tem O occurrng between two consecutve updates to data tem O. pðx ¼ kþ s ndependent of replacement polces. Let EðX Þ denote the average number of accesses to data tem O occurrng between two consecutve updates to data tem O. EðX Þ depends on both access and update processes, but s ndependent of replacement polces. Let EðX SBPER; Þ and EðX RCB; Þ denote the average numbers of effectve cache hts to data tem O between two consecutve updates to the same data tem when the SB-PER or the R-CB s exercsed wth a gven replacement polcy, respectvely. Let n U SBPER; and n U RCB; be upper bounds of the average numbers of effectve cache hts to data tem O between two consecutve updates to the same data tem when the SB-PER and R-CB are exercsed, respectvely, wth a gven replacement polcy. The message transmsson costs for a request message (Step 1.n Fg. 2a and Step 2.1 n Fg. 2b), an acknowledge message (Step 1.5 n Fg. 2a and Step 3.4 n Fg. 2b), and an nvaldaton message (Step 3.n Fg. 2b) are c req, c ack, and c nv, respectvely. Assume that the cost for transmttng any data tem s the same and s denoted as c obj, that s, we assume that the data tems are of the same sze. We assume that message headers have some extra felds that can be used for holdng access and update frequency nformaton and replacement decsons. Therefore, the access/update frequency nformaton n messages n Step 3.n Fg. 2a and Steps 2.2 and 3.4 n Fg. 2b s not counted, only the message n Step 2.5 of Fg. 2b s counted and ts cost s denoted as c a. Lemma 1. The followng nequaltes always hold for both the SB-PER and the R-CB wth any replacement polcy: p SBPER; 1 ; p RCB; 1 : Proof. Accordng to [28], pðx ¼ kþ ¼ k ; ð5þ EðX Þ¼ X1 k¼0 kpðx ¼ kþ ¼ : There are three cases n total: 1) There s no access to data O between two consecutve updates to O, 2) there s only one access to data O between two consecutve updates to O, and 3) there are n 2 accesses to data O between two consecutve updates. When an access to data tem O happens, O may be cached f t s the frst access between two consecutve updates to O and, then, subsequent accesses can be cache hts. Note that replacements make the number of cache hts fewer than the number of subsequent accesses, that s, cases 1 and 2 do not contrbute to any effectve cache ht defntely and only case 3 contrbutes at most n 1 effectve cache hts no matter whch replacement polcy s used. Therefore, regardng data tem O, from (5), we can derve an upper bound of the number of effectve cache hts to data tem O between two consecutve updates to data tem O for the SB-PER for a gven replacement polcy, that s, n U SBPER; ¼ X1 ðk 1ÞpðX ¼ kþ and k¼2 ¼ X1 k¼2 k ðk 1Þ ¼ EðX SBP ER; Þn U SBP ER; EðX Þ: Because access and update are two Posson processes, accordng to (6), (7), and (8), ð3þ ð4þ ð6þ ð7þ ð8þ

5 CHEN AND XIAO: ON-BOUND SELECTION CACHE REPLACEMENT POLICY FOR WIRELESS DATA ACCESS 1601 p SBPER; ¼ EðX SBPER; Þ EðX Þ ¼ Smlarly, we have p RCB; ¼ EðX RCB; Þ EðX Þ n U SBPER; EðX Þ 2. ¼ 1 : n U RCB; EðX Þ ¼ 1 : ð10þ tu Theorem 1. The followng nequaltes always hold for both the SB-PER and the R-CB wth any replacement polcy: p SBPER 1 p RCB 1 ; : ð9þ ð11þ ð12þ Proof. Accordng to Lemma 1, when the SB-PER s exercsed wth a gven replacement polcy, we have p SBPER ¼ XN Smlarly, p RCB ¼ XN p SBP ER; XN p RCB; XN 1 ¼ 1 1 ¼ 1 : : ð13þ ð14þ Theorem 1 ndcates that we have found an upper bound for the effectve ht rato of the SB-PER and an upper bound for the effectve rato of the R-CB. Denote them as p U SBPER and p U RCB, respectvely, that s, p U SBPER ¼ pu RCB ¼ 1 : Corollary 1. The followng nequalty always holds for the SB-PER wth any replacement polcy: c SBPER c req þ 1 p U SBPER cobj þ p U SBPER c ack: ð15þ Proof. Accordng to our algorthm llustrated n Fg. 1a, the communcaton cost of the SB-PER wth a gven replacement polcy s c SBPER ¼ c req þ ð1 p SBPER Þc obj þ p SBPER c ack : ð16þ Then, dc SBPER ¼ c ack c obj : ð17þ dp SBPER Wthout loss of generalty, assume that c ack <c obj. Then, tu dc SBPER < 0: ð18þ dp SBPER Equaton (18) ndcates that c SBPER s a monotoncally decreasng functon of p SBPER. Snce p U SBPER s an upper bound, p SBPER p U SBPER. Therefore, c SBPER c req þ 1 p U SBPER cobj þ p U SBPER c ack: ð19þ tu Corollary 2. The followng nequalty always holds for the R-CB wth any replacement polcy: c RCB 1 p U RCB creq þ c obj : ð20þ Proof. Accordng to our algorthm llustrated n Fg. 1b, the communcaton cost of the R-CB s c RCB ¼ ð1 p RCB Þ c req þ c obj þ pnv ðc nv þ c ack Þþp rep c a ; ð21þ dc RCB ¼ c req þ c obj < 0; ð22þ dp RCB dc RCB dp nv ¼ ðc nv þ c ack Þ > 0; ð23þ dc RCB ¼ c a > 0: ð24þ dp rep Equatons (22), (23), and (24) ndcate that c RCB s a monotoncally decreasng functon of p RCB, a monotoncally ncreasng functon of p nv, and a monotoncally ncreasng functon of p rep, respectvely. We know that p nv 0 and p rep 0. Gven that p U RCB s an upper bound of the effectve ht rato, that s, p RCB p U RCB, we have c RCB ¼ ð1 p RCB Þ c req þ c obj þ pnv ðc nv þ c ack Þþp rep c a ð1 p RCB Þ c req þ c obj þ pnv ðc nv þ c ack Þþ 0 c a ð1 p RCB Þ c req þ c obj þ 0 ð cnv þ c ack Þ ð1 p RCB Þ c req þ c obj 1 p U RCB creq þ c obj : ð25þ Corollares 1 and ndcate that we have found a lower bound for the communcaton cost of the SB-PER and a lower bound for the communcaton cost of the R-CB. Denote them as c L SBPER and cl RCB, respectvely, that s, c L SBPER ¼ c req þ 1 p U SBPER cobj þ p U SBPER c ack and c L RCB ¼ð1pU RCB Þðc req þ c obj Þ. Theorem 2. The SB-PER and the R-CB (wth any replacement polcy) reach ther effectve ht rato upper bounds p U SBPER and p U RCB gven n Theorem 1, respectvely, when K N. Proof. Snce K N, there s no replacement. Wthout loss of generalty, assume that the cache s dvded nto N slots, and each slot can hold a data tem. Assocate each data tem wth a partcular slot. A data tem s tu

6 1602 IEEE TRANSACTIONS ON COMPUTERS, VOL. 56, NO. 12, DECEMBER 2007 always cached at a certan slot. Therefore, cachng dfferent data tems becomes dsjont events. We have p SBPER ¼ p RCB ¼ XN that s, ¼ 1 ; ð26þ p SBPER ¼ p RCB ¼ p U SBPER ¼ pu RCB : ð27þ tu Corollary 3. The SB-PER (wth any replacement polcy) reaches ts communcaton cost lower bound c L SBPER gven n Corollary 1 when K N. Proof. Accordng to Corollary 2 and Theorem 2, c L SBPER ¼ c req þ 1 p U SBPER cobj þ p U SBPER c ack ð28þ ¼ c req þ ð1 p SBPER Þc obj þ p SBPER c ack ¼ c SBPER : tu Corollary 4. When K N, the communcaton cost of the R-CB (wth any replacement polcy) s c RCB ¼ ð1 p RCB Þ c req þ c obj þ c nv þ c ack ; ð29þ whch s larger than c L RCB, gven n Corollary 2 wth no more than two message costs. Proof. Snce K N, there s no replacement, that s, p rep ¼ 0. We also have p nv ¼ XN c RCB ¼ ð1 p RCB ¼ 1 ¼ 1 p L RCB ; ð30þ Þ c req þ c obj þ pnv ðc nv þ c ack Þþp rep c a : ð31þ Therefore, when K N, we have c RCB ¼ 1 p L RCB creq þ c obj þ c nv þ c ack : ð32þ Accordng to Corollary 2 and Theorem 2, c RCB ¼ 1 p U RCB creq þ c obj þ c nv þ c ack ð33þ 1 p U RCB creq þ c obj ¼ c L RCB : tu 5.1 Remarks on the OBS Replacement Polcy Accordng to the defnton of the OBS factor and Lemma 1, we have the followng observatons about the effectve ht ratos of data tem O for the SB-PER and the R-CB, respectvely, at clent k: 2 k p U SBPER; ¼ pu RCB; ¼ 1 þ k 1 fk a ¼ lm ðtþ 2 t!1 fk a ðtþþfu ðtþ ¼ 1 lm t!1 OBSF k: ð34þ Furthermore, accordng to Theorem 1, we have the followng observaton about the effectve ht ratos for the SB-PER and the R-CB, respectvely: p U SBPER ¼ pu RCB ¼ 1 2 k ¼ 1 þ k lm OBSF k : t!1 ð35þ Therefore, the OBS factor actually defnes an upper bound of the effectve ht rato of a partcular data tem. Theorem 2 suggests that the upper bounds of the effectve ht ratos can actually be reached when there s no replacement. The proposed replacement polcy OBS always tres to keep the data tems wth larger OBS factors n the cache and to evct the data tem wth the least OBS factor. Therefore, the data tems wth larger OBS factors tend to stay n the cache longer than those wth smaller OBS factors and ther effectve ht ratos (p SBPER; and p RCB; ) approach ther upper bounds n Lemma 1. Ths clam s verfed through smulatons and shown n Secton 7. The above analyss can also be appled to the communcaton cost of the SB-PER due to Corollares 1 and 3. Accordng to Corollares 1 and 3, we have c L SBPER ¼ c req þ 1 p U SBPER cobj þ p U SBPER c ack ¼ c req þ c obj 1 c obj c ack lm ðobsf k Þ: t!1 ð37þ It mples that the communcaton cost lower bound of the SB- PER becomes less when data tems wth larger OBS factors are n the cache. Ths s also confrmed by Corollary 3. When there s no replacement, the communcaton cost s exactly the lower bound gven n Corollary 1. The OBS always tres to keep data tems wth large OBS factors n the cache and to evct data tems wth small OBS factors. The actual communcaton cost of the data tems wth large OBS factors tends to be small. As to the R-CB, we have the followng observatons accordng to Corollary 2: c L RCB ¼ 1 pu RCB creq þ c obj þ c nv þ c ack ¼ c req þ c obj þ c nv þ c ack 1 c req þ c obj þ c nv þ c ack lm OBSF k : t!1 ð38þ Though the lower bound cannot actually be reached, the dfference s no more than two message costs. Consderng that the data tem szes are large, we can have a smlar argument as the SB-PER. In summary, the OBS replacement polcy favors cachng the data tems wth good bounds, that s, the OBS has the capablty of keepng good data tems and evctng bad data tems n the cache. When these data tems are cached, the actual effectve ht ratos of the data tems actually gradually approach the found bounds. The sum of the effectve ht ratos of these data tems must be larger than those of the data tems otherwse chosen. The performance evaluaton presented n Secton 7 confrms the effectveness of the OBS replacement polcy.

7 CHEN AND XIAO: ON-BOUND SELECTION CACHE REPLACEMENT POLICY FOR WIRELESS DATA ACCESS COMMENTS ON REPLACEMENT POLICIES OF NETWORK DATA APPLICATIONS Cache replacement polces play an mportant role when the cache sze s very lmted. Many MTs have small memory when compared wth the data tems beng accessed. Therefore, replacement polces are mportant aspects of moble/wreless data cachng. The least recently used (LRU) replacement polcy s popular n operatng systems and computer archtecture areas because data and programs are often stored contnuously n memory or hard dsks. The access pattern forms the so-called localty. Moreover, the LRU can be regarded as the smplest replacement polcy. For data applcatons where the data access pattern s not bound wth ther locaton (n memory or hard dsks), the LRU s not necessarly a good choce. As shown n [22], bursty access patterns make the LRU perform nadequately. Furthermore, t could be the worst choce, as shown n [11], for some database systems queres. It wll be benefcal to study dfferent replacement polces for network data applcatons where a busty access pattern s not uncommon. Many frequency-based replacement polces have been desgned, studed, and even mplemented for real systems, for example, the SQUID Web proxy cache system [2], [10], [12], [22], [23], [26], [29], [30]. An example of such a replacement polcy s the LFU. The goal of ths paper s to use both update and access frequences to desgn a smple and effectve replacement polcy. Many cache replacement polcy evaluatons use network traces, whch are representatons of real data collected from real networks. However, network traces are only samples and the performance evaluatons of dfferent traces can vary from trace to trace, as shown n [5]. In ths paper, we use Posson dstrbutons to model the network data accesses and updates. Posson dstrbuton may not be a precse model but t s ndeed a generalzaton of network data accesses and updates. It has been used qute often n research of ths knd [17], [29], [30]. In our study, we assume that data tems are of the same sze. Frst, as observed n [5], the effectveness of data tem sze used n replacement polces dmnshed for some network traces. Second, our paper s amed at network data applcatons, where memory pages can be regarded as a unt of data tem for a non-web applcaton. Thrd, the combnatoral optmzaton problem of multple data tems of dfferent szes for the cache replacements s NP-hard [30]. We leave ths problem to our future work. 7 PERFORMANCE EVALUATION In ths secton, we use dscrete-event smulaton to evaluate the performance of the proposed replacement polcy, the OBS, and also compare ts performance wth that of the LFU [23] by usng perfect access frequency nformaton [26]. We developed our smulaton programs n C Performance Metrcs The desgn goals of our replacement polcy are to ncrease the effectve ht rato and to reduce communcaton cost. Durng the smulatons, we collect the followng measurements to calculate the effectve ht ratos and the communcaton costs for both the SB-PER and the R-CB wth the OBS or the LFU. Let n a;j and n u;j denote the total number of accesses to data tem O j at the clent and the total number of updates to data tem O j at the server, respectvely. Let n mss be the total number of cache msses and n nvhts be the total number of cache hts to nvald data tems. Note that, whenever a cache mss or a cache ht to an nvald data tem happens, the accessed data tem s sent from the server to the clent. When the R-CB s exercsed, an nvaldaton message s delvered to clents, where the data tem beng updated s cached. Let n nvmsg represent the total number of nvaldaton messages. Let n rep denote the total number of cache replacements. Let n a denote the total number of accesses of all data tems. It s obvous that we have n rep n a and n mss n a. Smlarly to [20], we can compute the effectve ht ratos n the smulatons as follows: p SBPER ¼ p RCB ¼ 1 n mss þ n nvhts ; n a where n a ¼ XN n a;j : ð39þ We compute the communcaton cost for the SB-PER, that s, c SBPER, and that for the R-CB, that s, c RCB, by usng (16) and (21), respectvely. Note that, for the R-CB, we also have p nv ¼ n nvmsg n a ; ð40þ p rep ¼ n rep n a : ð41þ 7.2 Smulaton Setup The server has N data tems and a clent equps a cache whch can hold up to K data tems. Assume that access and update events are Posson processes. An access always happens at a clent and an update always occurs at the server. The rates of the access and the update to the data tem O j are j and j, respectvely. We denote total access rate and total update rate as and, respectvely, that s, ¼ P N, and ¼ P N. Two ssues are worth notng:. N s not necessarly the actual database sze because the database may contan data tems that are never accessed by a partcular clent n a certan tme frame n whch we are nterested. Therefore, N s actually an effectve database sze. For moble/wreless clents, N can be relatvely small, even though the actual database may be huge. To reflect ths fact n our smulaton studes, any access rate of the N data tems must be larger than 0 and N takes a relatvely small value.. Update frequences are global statstcs measured at the server, whereas access frequences are local statstcs collected for clents. Therefore, the update rate of a data tem can be larger than the access rate of a data tem because more than one clent can have updated the data tem between two consecutve accesses to the data tem at a clent.

8 1604 IEEE TRANSACTIONS ON COMPUTERS, VOL. 56, NO. 12, DECEMBER 2007 It has been observed that, n Web applcatons, dfferent data tems have dfferent populartes. To reflect ths observaton, we let access events of dfferent data tems follow cutoff Zpf-lke dstrbutons [4]. It s beleved to be a reasonable assumpton for Web applcatons and a representaton for dsparty of access popularty, though t may not hold for any network data applcaton. We let the update rates of dfferent data tems become dfferent. For smplcty, we assume that the update events also follow cutoff Zpf-lke dstrbutons. N data tems are always ranked as ¼ 1; 2;...; N. Thus, when an access or an update happens, the data tem O k whose rank s s chosen to be accessed or updated at probablty p ¼ 1=½ P N j¼1 1=j Š. Note the followng remarks:. We defne ð 0Þ as a Zpf exponent. When ¼ 0, p ¼ 1=N, that s, all data tems are chosen at the same probablty 1=N. The access and update events do not necessarly follow the same cutoff Zpf-lke dstrbuton. Let a denote the Zpf exponent of access events and u be the Zpf exponent of update events.. Data tem dentfer (ID) and data tem rank are dfferent concepts, that s, data tem O s not necessarly ranked as.. Data tems can be ranked ndependently for access and update events. A data tem wth rank for access events s not necessarly the data tem wth rank for update events. Thus, a data tem wth a larger access probablty s not necessarly a data tem wth a larger update probablty. Snce there are two dfferent Zpf-lke dstrbutons for access and update events, we categorze ther relatonshps nto fve cases:. Case 1. a > 0 and u ¼ 0, that s, the access frequences of dfferent data tems are dfferent and the update frequences of all data tems are the same.. Case 2. a ¼ 0 and u > 0, that s, the access frequences of all data tems are the same and the update frequences of dfferent data tems are dfferent.. Case 3. a > 0, u > 0, and the access and update rankngs to the same data tem are the same, that s, a more frequently accessed data tem s also a more frequently updated data tem. Furthermore, the access frequences of dfferent data tems are dfferent and the update frequences of dfferent data tems are dfferent.. Case 4. a > 0, u > 0, the access rankngs of data tems are n an ascendng order, and the update rankngs are n a descendng order, that s, a more frequently accessed data tem s also a less frequently updated data tem. Furthermore, the access frequences of dfferent data tems are dfferent and the update frequences of dfferent data tems are dfferent.. Case 5. a > 0, u > 0, and the access and update rankngs of data tems are totally ndependent, that s, f we order the data tems accordng to access probabltes, the update probabltes tend to be Fg. 3. Comparson of analytcal and smulaton results for both SB-PER and R-CB. (a) Effectve ht rato versus total update rate (). (b) Communcaton cost versus total update rate (). randomly dstrbuted. Furthermore, the access frequences of dfferent data tems are dfferent and the update frequences of dfferent data tems are dfferent. All of the above cases are studed n the smulatons. We let c req ¼ c ack ¼ c nv ¼ c a ¼ 60, whch s a reasonable value for many wreless systems such as General Packet Rado Servce (GRPS) and SMS [20]. Snce these message szes are the same, we use c msg ¼ 60 to denote the message sze. Unless otherwse stated, we choose c obj ¼ 10c msg ¼ 600, N ¼ 20, K ¼ 10, ¼ 1:0, ¼ 1:4, a ¼ 0:1, and u ¼ 1:8. Though these default parameters are chosen to capture the scenaro where data tems have dfferent access rates and a small porton of the entre data set has very hgh update rates, we vary each parameter n Secton 7.5 (for example, u from 0 to 1 and from 1 to 5) and study ther effects on the performance. We start the smulaton when the clent cache s empty. We obtan the metrcs measurements when the system has reached a stable state for a long tme. To meet ths requrement, we often run the smulaton for 10 7 arrval events. 7.3 Comparson of Smulaton and Analytcal Results We compare the analytcal and smulaton results for the SB- PER and the R-CB. We choose K ¼ 20 and a ¼ 0. Ths s Case 2 and there wll be no replacement. The effectve ht ratos and communcaton costs are obtaned accordngly for both the SB-PER and the R-CB. Fg. 3a shows the effectve ht rato upper bounds and the effectve ht ratos from smulatons for both the SB-PER and the R-CB. Fg. 3b shows the communcaton upper bounds and the communcaton costs from smulatons for both the SB-PER and the R-CB. We have the followng observatons:. Fg. 3a shows that the effectve ht ratos of the SB- PER and the R-CB are the same n the gven case and they match the effectve upper bounds defned n Theorem 1. It therefore confrms Theorem 2. Fg. 3b

9 CHEN AND XIAO: ON-BOUND SELECTION CACHE REPLACEMENT POLICY FOR WIRELESS DATA ACCESS 1605 Fg. 4. Effects of on-bound selecton. shows that the communcaton upper bounds of the SB-PER defned n Corollary 1 match the smulaton results obtaned n the gven case. Ths confrms Corollary 3. The communcaton upper bound of the R-CB defned n Corollary s less than both the analytc and smulaton results obtaned n the gven case, but the dfference s less than two message costs. Ths confrms Corollary 4.. Even though the cache s suffcently large to hold the entre database, the effectve ht ratos decrease, whereas the communcaton costs ncrease for both the SB-PER and the R-CB when ncreases, as shown n Fgs. 3a and 3b. Ths s because some cached data tems are nvaldated by updates. It mples that t s mportant to consoldate the update process nto replacement polces so that frequently updated but nfrequently accessed data tems wll not be cached. Our analytcal analyss provdes an understandng of what a frequently updated but nfrequently accessed data tem can be. 7.4 Effects of OBS The smulaton results shown n Fg. 4 demonstrate the effects of OBS. As an example, we only have the result obtaned for Case 3, where u ¼ 1:0. In Fg. 4, the data tems are assgned ID numbers accordng to ther upper bounds, that s, ther OBS factors. For example, the data tem wth the least ID has the least OBS factor. When the OBS s exercsed, K data tems wth the most upper bounds almost acheve the most, that s, the upper bound n the fgure. However, when the LFU s exercsed, the opposte result s observed. Ths fgure confrms that the OBS ndeed keeps a good data tem n the cache. Interestngly, none of the data tems has zero effectve ht ratos. Ths s due to the exstence of updates. A cached data tem always has a chance of beng nvaldated and ts cache space can be used to cache other data tems no matter what replacement polcy s used and what ts update and access rates are. 7.5 Frequency Measurement We adopt a sldng wndow scheme [10], [12], [30] for calculatng the access and update frequences n the Fg. 5. Performance of SB-PER+OBS versus sldng wndow sze. (a) Effectve ht rato versus sldng wndow sze. (b) Communcaton cost versus sldng wndow sze. algorthms. For each data tem, we measure the k most recent access tmes. We calculate the access frequency of data tem as follows: f a ¼ k tt, where the superscrpt a ;k a denotes access, t s the current tme, and t a ;k s the tme of the kth most recent access on data tem O. Smlarly, we calculate the update frequency of data tem as follows: f u ¼ k tt, where the superscrpt u u ;k denotes update. When k ¼ 1, f a s drectly related to the access recency of the data tem. Therefore, by adjustng k for access to data tem O, f a can be a measurement for both access frequency and access tme (that s, access recency). Smlarly, by adjustng k for updates to data tem O, f u can be a measurement for both update frequency and update tme (that s, update recency). Fg. 5 shows that the defned metrcs vary wth the sldng wndow sze. All fve cases descrbed n Secton 7.2 show smlar results. For demonstraton purposes, we only show the result of Case 3, n whch the performance slghtly vares wth dfferent wndow szes and the performance becomes almost nvarant wth wndow sze when the wndow sze s large enough. Denote the sldng wndow sze as k. It appears that the overall memory space needed for the above scheme s on the order of OðkNÞ to store most k recent access (or update) tmes of N data tems. The scheme seems to become prohbtve when k s large. The followng example shows that t s not dffcult to overcome t: From observaton of Fg. 5, when k s large enough, a smlar performance can be obtaned when we use k=2 as the wndow sze. We only keep two access stamps and two access counters for data tem O. We denote t a ;n a; ¼0 mod k as the access tmestamp of data tem O when n a; ¼ 0 mod k, where n a; s the total number of accesses on data tem O and mod s modular operaton. Let t a ;n a;¼0 mod k=2 be the access tmestamp of data tem O when n a; ¼ 0 mod k=2. We reset counter k ;na; ¼0 mod k at tme t a ;n a;¼0 mod k and counter k ;na; ¼0 mod k=2 at tme t a ;n a; ¼0 mod k=2 respectvely. We then calculate the access frequency as follows: f a ¼ k ;na;¼0 mod k t t a ;na; ¼0 mod k when

10 1606 IEEE TRANSACTIONS ON COMPUTERS, VOL. 56, NO. 12, DECEMBER 2007 LRU, and LRU-K [22], where K s taken to be 2 when R-CB s exercsed. The followng observatons are nterestng: Fg. 6. Performance of R-CB and replacement polces. (a) Effectve ht rato versus cache sze (K). (b) Communcaton cost versus cache sze (K). k ;na;¼0 modk k=2, and f a ¼ k ;na;¼0 mod k=2 t t a ;na;¼0 mod k=2 when k ;na;¼0 mod k=2 k=2. Then, the space complexty becomes OðNÞ, whch s the same as the LRU. The above sldng wndow approach can be regarded as a very smple agng method. Agng [10], [12] s a wellknown mechansm for consderng both access frequency and the age of a cached data tem (access tme or recency). A well-desgned agng method not only helps reduce the memory space requrement, but also helps cope wth the evolvng access (update) pattern. Many dfferent agng methods [10], [12] have been proposed. Some cache replacement polces, such as LRU-K [22], have bult-n agng mechansms. In our study, agng has to be consdered for both the access and update processes. Better agng methods can help our proposed replacement polcy better cope wth the evolvng access (update) pattern. They deserve dedcated study due to ther complexty. However, they are not the focus of ths paper and we leave t as our future work. 7.6 Comments on the Importance of Cache Replacement Polces MTs are gradually ganng more memory whch can be used for clent cachng. We am at reducng the overall network bandwdth usage. For ths purpose, cache replacement polces cannot be gnored, even for MTs wth large cache space. Ths argument holds true for cache mechansms whch nvolve CB procedures. We refer to the CB procedure as the procedure n whch the server nforms clents that cached data tems have become nvald due to updates. The CB (for example, R-CB n ths paper), Lease, and IR schemes use the CB procedure. Our argument s verfed n Fg. 6. We choose c req ¼ c ack ¼ c nv ¼ c a ¼ 60, c obj ¼ 2c msg ¼ 120, N ¼ 20, K ¼ 10, ¼ 1:0, ¼ 5. These 20 data tems are dvded nto four groups. The access rates (update rates) of the data tems wthn the same group are the same. The access rates and updates are drawn from two dfferent Zp-lke dstrbutons, wth a ¼ 0:1, and u ¼ 10; however, the rankngs of the four groups for access and update processes are of opposte drectons (smlar to Case 4 descrbed n Secton 7.2). Ths parameter settng ensures that some data tems are moderately frequently accessed but are updated very frequently and the cost of sendng nvaldaton messages s qute large. Fg. 6 compares four cache replacement polces, that s, OBS, LFU,. Fg. 6a shows that the effectve ht ratos of all four replacement polces ncrease wth the cache sze.. Fg. 6b shows that the mnmum communcaton cost s obtaned when K ¼ 10 for R-CB+OBS and R-CB+LFU when the cache sze s varyng. The server needs to send an nvaldaton message when an update happens to t. It s lkely that the clent has to fetch a data tem from the server due to frequent updates. Then, the cost of sendng an nvaldaton message may not be offset by usng the cached copy. In our parameter setup, when the cache space s larger than 10 data tems, such types of frequently updated data tems wll nevtably be cached. The total communcaton cost goes up whle more such data tems are cached. Fg. 6b also shows that R-CB+LRU and R-CB+LRU-K have larger costs when gven a small cache space. Ths can be explaned smlarly.. Fgs. 6a and 6b also show that R-CB+LFU/OBS has better performance than R-CB+LRU/LRU-K. Ths s due to 1) the nonexstence of the localty related to the adjacency of memory locaton where the data tems are stored (n other words, recency does not capture the data access pattern well) and 2) they do not consder updates. Ths has been dscussed n Secton 6. Due to page lmts, we wll not further compare our replacement polcy wth LRU and LRU-K n ths paper. In a nutshell, cache replacement polces are not necessarly good for the overall network bandwdth usage when maxmzng cache space. Nevertheless, cache replacement polces are essental to a network envronment wth the exstence of updates, even when memory capacty s abundant. 7.7 Case Studes: Comparson of OBS and LFU The followng smulatons wll show that the OBS outperforms the LFU n terms of both effectve ht rato and communcaton cost n all fve cases lsted n the prevous subsecton. Ths aspect s shown wth regard to dfferent parameters, that s, the Zpf-exponents, cache and database szes, and access and update rates Zpf Exponents The two schemes are compared when the Zpf exponents are varyng. The results are shown n Fg. 7.. Fgs. 7a and 7b show an example of Case 1, that s, a > 0 and u ¼ 0. In Fgs. 7a and 7b, (SB-PER)/ (R-CB)+OBS have the same effectve ht ratos and costs as (SB-PER)/(R-CB)+LFU, respectvely. It means that OBS and LFU perform the same n ths example. In fact, accordng to (1), the OBS s equvalent to the LFU f the update frequences of data tems are the same, whch has been confrmed by ths example, snce the update frequences of data tems are ndeed the same n ths case.. Fgs. 7c and 7d show an example of Case 2, that s, a ¼ 0 and u > 0. They show that (SB-PER)/ (R-CB)+OBS have consstently larger effectve ht ratos and consstently smaller costs than (SB-PER)/ (R-CB)+LFU, respectvely. In other words, the OBS outperforms the LFU.

11 CHEN AND XIAO: ON-BOUND SELECTION CACHE REPLACEMENT POLICY FOR WIRELESS DATA ACCESS 1607 Fg. 7. Performance of the OBS and the LFU at dfferent cases wth regard to the Zpf exponents. (a), (c), (e), (g), and () show effectve ht rato versus Zpf exponent of access events ( a ) for Cases 1, 2, 3, 4, and 5, respectvely. (b), (d), (f), (h), and (j) show communcaton cost versus Zpf exponent of access events ( a ) for Cases 1, 2, 3, 4, and 5, respectvely.. Fgs. 7e and 7f show an example of Case 3, that s, a > 0, u > 0, and the rankng of access and update to the same data tem are the same. We observe smlar results as n Case 2, that s, (SB-PER)/ (R-CB)+OBS have consstently larger effectve ht ratos and less costs than (SB-PER)/(R-CB)+LFU, respectvely. It means that the OBS chooses approprate data tems to evct from the cache so that better performance s acheved, even f the frequently accessed data tems are also frequently updated data tems.. Fgs. 7g and 7h show an example of Case 4, that s, a > 0 and u > 0 n whch the rankngs of data tems for accesses are n ascendng order and those for updates are n descendng order. For example, frequently accessed data tems are also nfrequently updated data tems. The OBS tends to cache frequently accessed data tems but not nfrequently updated data tems, whch s consstent wth the LFU n ths partcular case. Therefore, t s not surprsng that the OBS and the LFU perform the same.. Fgs. 7 and 7j show an example of Case 5, that s, a > 0 and u > 0, n whch the rankngs of data tems for both accesses and updates are totally ndependent. Because access and update probabltes are assgned randomly, every dfferent run possbly produces a dfferent result. Thus, the average performance should be more representatve than an ndvdual run. Fgs. 5 and 5j show the average performance out of 50 dfferent runs. It s clear that the (SB-PER)/(R-CB)+OBS have larger effectve ht ratos and less communcaton costs than (SB-PER)/(R-CB)+LFU, respectvely. All fve of these possble cases show the advantage of the OBS over the LFU, whch confrms that the OBS, ndeed, s capable of choosng the bad data tem to be evcted whle retanng the good data tem, regardless of the Zpf exponents. We also have the followng observatons:. As shown n Fgs. 7a, 7c, 7g, and 7, when u ncreases, the effectve ht rato ncreases as well. u s ncreasng means that fewer data tems take up most of the total update rate and others have smaller update rates, even though the total update rate s the same. The OBS tends to cache data tems wth smaller update rates. Those few data tems wth larger update rates are probably cached a smaller number of tmes. The most cached data tems have smaller update rates. Therefore, the cached data tems are less lkely to be made nvald by updates and the effectve ht rato s ncreased.. As shown n Fgs. 7b, 7d, 7h, and 7j, when u ncreases, the communcaton cost decreases. It s due to the same reason as the above.. Fg. 7e shows that the effectve ht rato decreases frst and then ncreases when u ncreases. Fg. 7f shows that the communcaton cost ncreases frst and then decreases when u ncreases. Bascally, the ncrease of the effectve ht rato and the decrease of the communcaton cost are caused by the reason above Cache and Database Szes Fg. 8 shows the comparson between the OBS and the LFU when we vary the cache sze and fx the database sze. As before, fve dfferent cases are studed. We have the followng observatons:. Fgs. 8a and 8b show an example of Case 1, that s, a > 0 and u ¼ 0. Both replacement polces have the same effectve ht ratos and costs, that s, OBS and LFU perform the same n ths example, regardless of the cache sze, due to the same reason presented for Fgs. 7a and 7b.

12 1608 IEEE TRANSACTIONS ON COMPUTERS, VOL. 56, NO. 12, DECEMBER 2007 Fg. 8. Performance of the OBS and LFU at dfferent cases wth regard to the cache sze. (a), (c), (e), (g), and () show effectve ht rato versus cache sze (K) for Cases 1, 2, 3, 4, and 5, respectvely. (b), (d), (f), (h), and (j) show communcaton cost versus cache sze (K) for Cases 1, 2, 3, 4, and 5, respectvely.. Fgs. 8c and 8d show an example of Case 2, that s, a ¼ 0 and u > 0. OBS has better performance than LFU, regardless of the cache sze.. Fgs. 8e and 8f show an example of Case 3, that s, a > 0, u > 0, and the rankng of access and update to the same data tem are the same. OBS has better performance than LFU, regardless of the cache sze.. Fgs. 8g and 8h show an example of Case 4, that s, a > 0:1, 1 > 0, and u > 0, n whch the rankngs of data tems for accesses are n ascendng order and those for updates are n descendng order. For example, frequently accessed data tems are also nfrequently updated data tems. It s not surprsng that the OBS and the LFU perform the same.. Fgs. 8 and 8j show an example of Case 5, that s, a > 0 and u > 0, n whch the rankng of data tems for both accesses and updates are totally ndependent. The results are the average performance out of 50 dfferent runs. It s clear that the (SB-PER)/(R-CB)+OBS have larger effectve ht ratos and less communcaton costs than (SB- PER)/(R-CB)+LFU, respectvely. Besdes the above observatons, t s clear that, from the smulaton results shown n Fg. 8, the effectve ht ratos of (SB-PER)/(R-CB)+OBS/LFU ncrease wth the cache sze. In our examples, the communcaton costs decrease when the cache sze ncreases. Ths s because, when the cache sze ncreases, more data tems are cached. However, no matter how the cache sze vares, we have shown that (SB-PER)/ (R-CB)+OBS have better performance than (SB-PER)/ (R-CB)+LFU. We study how performances of (SB-PER)/(R-CB)+OBS/ LFU vary wth the database sze when the cache sze s fxed. The results are shown n Fg. 9, where K ¼ 10:. Fgs. 9a and 9b show an example of Case 1 and Fgs. 9g and 9h show an example of Case 4. These two examples show that the OBS and the LFU have the same performance, whether the SB-PER or the R-CB s exercsed. It s due to an argument smlar to the one shown n Fgs. 7a, 7b, 7g, and 7h.. Fgs. 9c and 9d, 9e and 9f, and 9 and 9j show examples for Cases 2, 3, and 5, respectvely. Evdently, the OBS consstently outperforms the LFU, whether the SB-PER or the R-CB s exercsed. These observatons evdently show that the OBS s a better replacement polcy than the LFU n terms of effectve ht rato and communcaton cost. Fg. 10 shows the performance varyng wth N when K=N s a constant. For demonstraton purposes, only Case 3, where u ¼ 1:0, s shown. Evdently, Fgs. 10a and 10b show that OBS always performs better when the database and cache szes scale up Access and Update Rates In ths part, we study the effects of access and update rates, that s, and. Fg. 11 shows the smulaton results, where s fxed and s varyng. We can observe smlar results as before:. Fgs. 11a and 11b and 11g, and 11h correspond to Cases 1 and 4, respectvely. They show that the OBS and the LFU have almost the same performance, regardless of, when ether the SB-PER or the R-CB s exercsed. Fgs. 11c and 11d, 11e and 11f, and 11 and 11j show the results for Cases 2, 3, and 4, respectvely. They show that the OBS outperforms the LFU, regardless of, when ether the SB-PER or the R-CB s exercsed. The above two observatons show that the OBS s ether better than or equvalent to the LFU, regardless of. Besdes, no matter the case, the effectve ht ratos of (SB- PER)/(R-CB)+OBS/LFU decrease and the communcaton costs of (SB-PER)/(R-CB)+OBS/LFU ncrease when ncreases. When ncreases, a data tem has a greater chance of beng updated. If the data tem s cached, t has a greater chance of beng nvaldated. Therefore, the effectve

13 CHEN AND XIAO: ON-BOUND SELECTION CACHE REPLACEMENT POLICY FOR WIRELESS DATA ACCESS 1609 Fg. 9. Performance of the OBS and LFU at dfferent cases wth regard to the database sze when the cache sze s fxed. (a), (c), (e), (g), and () show effectve ht rato versus database sze (N) for Cases 1, 2, 3, 4, and 5, respectvely. (b), (d), (f), (h), and (j) show communcaton costs versus database sze (N) for Cases 1, 2, 3, 4, and 5, respectvely. ht ratos of (SB-PER)/(R-CB)+OBS/LFU become less and the communcaton costs of those become more. 7.8 Comments on the Server-Based Approach In order to reduce transmsson cost over wreless lnks, we have ntroduced the server-based cache access algorthm, that s, the SB-PER, to test our update-based replacement polcy, that s, the OBS. The SB-PER s capable of provdng up-to-date access and updated nformaton to the replacement polcy. In general, the SB-PER requres more powerful servers. Snce servers are much more nexpensve compared to wreless lnks, we assume that a server can be easly upgraded wth a more powerful machne or a cluster of machnes, that s, a vrtual server or a server farm. Furthermore, when compared wth the clent-based cache access algorthm, the SB-PER mproves the effectve ht rato Fg. 10. Performance of the OBS and LFU versus N (K=N s a constant). (a) Effectve ht rato versus sdatabase sze (N). (b) Communcaton cost versus database sze (N). sgnfcantly, that s, fewer data tems are fetched from the server. Therefore, our algorthm may perform even better n terms of response tme. Server response tme s related to many factors. CPU cycles are on the order of mcroseconds (s) or even less, and the hard dsk random-seek tme s on the order of a few mllseconds (ms). Therefore, the hard dsk random-seek tme s often a domnant factor for server response tmes [25]. We assume that the server stores object profles and update profles n the man memory; therefore, accesses to two of these profles do not result n a random seek on hard dsks. As shown n Fg. 2a, a random seek s performed to locate the data tem on the hard dsk only when the data tem s cached or the data tem s nvald (Steps 2.4 and 3.2). For a far comparson, we assume that metadata ncludng tmestamps of data tems can be loaded nto the man memory as well when the PER s exercsed so that the PER requres a random seek when the data tem s not cached or nvald too. Fg. 12 compares the random-seek count per access between the PER and the SB-PER (only Case 5 s shown). However, the PER s exercsed wth the LFU and the SB-PER uses the OBS. A dfferent replacement polcy s chosen for the PER because the PER does not provde update nformaton to the clents and the clents cannot use the OBS. Fg. 12 shows that the SB-PER has a much smaller random-seek count per access. In other words, the SB-PER outperforms the PER n terms of server response tme under our parameter settngs. 7.9 More General Network Traffc In our analytcal analyss n Secton 5, data access and update follow a Posson dstrbuton. In ths secton, we loosen the assumpton of Posson dstrbuton to demonstrate the performance of the proposed OBS under a more general network traffc model. Fg. 13 s obtaned when both access and update processes follow Gamma dstrbutons. Although smlar results can be obtaned for other cases, the fgure only shows Case 3, as defned n Secton 7.2. In Fgs. 13a and 13b, we vary the varance of access tme. The results show that 1) the effectve ht rato and the

14 1610 IEEE TRANSACTIONS ON COMPUTERS, VOL. 56, NO. 12, DECEMBER 2007 Fg. 11. Performance of the OBS and LFU at dfferent cases wth regard to the total update rate when the total access rate s fxed. (a), (c), (e), (g), and () show effectve ht rato versus total update rate () for Cases 1, 2, 3, 4, and 5, respectvely. (b), (d), (f), (h), and (j) show communcaton costs versus total update rate () for Cases 1, 2, 3, 4, and 5, respectvely. transmsson costs of SB-PER/R-CB+OBS/LFU do not vary sgnfcantly wth the varance and 2) the OBS replacement polcy consstently outperforms the LFU, regardless of whether the SB-PER or the R-CB s exercsed when the varance of access tme s varyng. Ths suggests that the proposed OBS can be appled to more general network traffc and consstently gve better performance even though t s based on a more strngent assumpton. 8 CONCLUSION An update can make a cached data tem obsolete and, thus, a cache ht becomes useless. Lttle research has consoldated the update process nto a cache algorthm desgn, especally the cache replacement polcy desgn. In ths paper, we proposed a replacement polcy, the OBS, whch uses both access and update frequences. We conducted an analytcal analyss of cache access and update. An upper bound of the effectve rato and a lower bound of communcaton cost are gven. We further show that the upper bound of the effectve ht rato and the lower bound of the communcaton cost can be reached when there s no replacement. Accordng to our understandng of these bounds, we show that the proposed replacement polcy tres to keep the good data tems n the cache and to evct the bad data tems from the cache n terms of ncreasng the effectve ht rato and reducng the communcaton cost. We studed ts performance wth two cache access algorthms, the SB-PER and the R-CB, through dscrete-event smulatons. The smulaton results show that the OBS outperforms the LFU n terms of both the effectve ht rato and the communcaton cost n all of the possble cases that we have studed. Therefore, we beleve that the OBS ndeed asymptotcally keeps the good data tems n the cache whle evctng the bad ones. In the smulatons, we further loosen the traffc assumpton wth Gamma dstrbutons and smlar results are observed. In our future work, we wll address the effects of dfferent data tem szes and extend update-based replacement polces to clent-based cache access algorthms. Fg. 12. Random-seek count per access versus u. Fg. 13. Metrcs of network traffc of Gamma dstrbuton. (a) Effectve ht rato versus the varance of acess tme. (b) Communcaton cost versus the varance of access tme.

15 CHEN AND XIAO: ON-BOUND SELECTION CACHE REPLACEMENT POLICY FOR WIRELESS DATA ACCESS 1611 REFERENCES [1] S. Acharya and S. Muthukrshnan, Schedulng On-Demand Broadcasts: New Metrcs and Algorthms, Proc. ACM MobCom 98, pp , [2] A. Balamash and M. Krunz, An Overvew of Web Cachng Replacement Algorthms, IEEE Comm. Surveys and Tutorals, vol. 6, no. 2, pp , [3] D. Barbará and T. Imelnks, Sleepers and Workaholcs: Cachng Strateges for Moble Envronments (Extended Verson), VLDB J., vol. 4, no. 4, pp , [4] L. Berslau, P. Cao, L. Fan, G. Phllps, and S. Shenker, Web Cachng and Zpf-Lke Dstrbutons: Evdence and Implcatons, Proc. IEEE INFOCOM 99, vol. 1, pp , Mar [5] P. Barford, A. Bestavros, A. Bradley, and M. Crovella, Changes n Web Clent Access Patterns: Characterstcs and Cachng Implcatons, World Wde Web J., vol. 2, pp , [6] J. Ca and K.-L. Tan, Energy-Effcent Selectve Cache Invaldaton, Wreless Networks, vol. 5, no. 6, pp , [7] G. Cao, Proactve Power-Aware Cache Management for Moble Computng Systems, IEEE Trans. Computers, vol. 51, no. 6, pp , June [8] G. Cao, A Scalable Low-Latency Cache Invaldaton Strategy for Moble Envronments, IEEE Trans. Knowledge and Data Eng., vol. 15, no. 5, Sept./Oct [9] B.Y.L. Chan, A. S, and H.V. Leong, Cache Management for Moble Databases: Desgn and Evaluaton, Proc. 14th Int l Conf. Data Eng. (ICDE 98), pp , Feb [10] L. Cherkasova and G. Cardo, Role of Agng, Frequency, and Sze n Web Cache Repalcement Polces, Lecture Notes n Computer Scence, vol. 2110, pp , [11] H. Chou and D. DeWtt, An Evaluaton of Buffer Management Strateges for Relatonal Database Systems, Proc. 11th Int l Conf. Very Large Data Bases (VLDB 85), pp , [12] J. Dlley, M. Arltt, and S. Perret, Enhancement and Valdaton of the Squd Cache Replacement Polcy, Proc. Fourth Int l Web Cachng Workshop (WCW 99), [13] C.C.F. Fong, J.C.S. Lu, and M.H. Wong, Quantfyng Complexty and Performance Gans of Dstrbuted Cachng n a Wreless Network Envronment, Proc. 13th Int l Conf. Data Eng. (ICDE 97), pp , Oct [14] J. Howard, M. Kazar, S. Menees, D. Nchols, M. Satyanarayanan, R. Sdebotham, and M. West, Scale and Performance n a Dstrbuted Fle System, ACM Trans. Computer Systems, vol. 6, no. 1, pp , Feb [15] Q.L. Hu and D.L. Lee, Cache Algorthms Based on Adaptve Invaldaton Reports for Moble Envronments, Cluster Computng, vol. 1, no. 1, pp , Feb [16] A. Iyengar, E. Nahum, A. Shakh, and R. Tewar, Web Cachng, Consstency and Content Dstrbuton, The Practcal Handbook of Internet Computng, M.P. Sngh, ed., Chapman & Hall/CRC Press, [17] R. Jan, The Art of Computer Systems Performance Analyss. John Wley & Sons, [18] J. Jng, A.K. Elmagarmd, A. Helal, and R. Alonso, Bt-Sequences: A New Cache Invaldaton Method n Moble Envronments, Moble Networks and Applcatons, vol. 2, no. 2, pp , [19] A. Kahol, S. Khurana, S.K.S. Gupta, and P.K. Srman, A Strategy to Manage Cache Consstency n a Dstrbuted Moble Wreless Envronment, IEEE Trans. Parallel and Dstrbuted Systems, vol. 12, no. 7, pp , July [20] Y.-B. Ln, W.-R. La, and J.-J. Chen, Effects of Cache Mechansm on Wreless Data Access, IEEE Trans. Wreless Comm., vol. 2, no. 6, pp , [21] M. Nelson, B. Welch, and J. Ousterhout, Cachng n the Sprte Network Fle System, ACM Trans. Computer Systems, vol. 6, no. 1, pp , Feb [22] E. O Nel, P. O Nel, and G. Wekum, The LRU-K Page Replacement Algorthm for Database Dsk Bufferng, Proc. ACM SIGMOD Int l Conf. Management of Data, pp , [23] J.T. Robnson and M.V. Devarakonda, Data Cache Management Usng Frequency-Based Replacement, Proc. ACM SIGMETRICS Conf., pp , [24] K.L. Tan, J. Ca, and B.C. Oo, An Evaluaton of Cache Invaldaton Strateges n Wreless Envronments, IEEE Trans. Parallel and Dstrbuted Systems, vol. 12, no. 8, pp , Aug [25] A.S. Tanenbaum, Computer Networks, fourth ed. Prentce Hall PTR, [26] J. Wang, A Survey of Web Cachng Schemes for the Internet, ACM SIGCOMM Computer Comm. Rev., vol. 29, no. 5, pp , [27] K.-L. Wu, P.S. Yu, and M.-S. Chen, Energy-Effcent Cachng for Wreless Moble Computng, Proc. 12th Int l Conf. Data Eng. (ICDE 96), pp , Feb [28] Y. Xao, Optmal Locaton Management for Two-Ter PCS Networks, Computer Comm., vol. 26, no. 10, pp , June [29] J. Xu, Q. Hu, D.L. Lee, and W.-C. Lee, SAIU: An Effcent Cache Replacement Polcy for Wreless On-Demand Broadcasts, Proc. Nnth ACM Int l Conf. Informaton and Knowledge Management (CIKM 00), pp , Nov [30] J. Xu, Q. Hu, W.-C. Lee, and D.L. Lee, Performance Evaluaton of an Optmal Cache Replacement Polcy for Wreless Data Dssemnaton, IEEE Trans. Knowledge and Data Eng., vol. 16, no. 1, pp , Jan [31] J. Yn, L. Alvs, M. Dahln, and C. Ln, Volume Leases for Consstency n Large-Scale Systems, IEEE Trans. Knowledge and Data Eng., vol. 11, no. 4, pp , July/Sept [32] J. Yuen, E. Chan, K.Y. Lam, and H.W. Leung, Cache Invaldaton Scheme for Moble Computng Systems wth Real-Tme Data, ACM SIGMOD Record, vol. 29, no. 4, pp , Hu Chen receved the MS and PhD degrees n computer scence from the Unversty of Memphs, Tennessee, n 2003 and 2006, respectvely. He was a geophyscst and worked as a software developer for AutoZone, Inc., from 2005 to He joned the faculty of the Department of Mathematcs and Computer Scence at Vrgna State Unversty n Although he retans hs nterests n studyng computatonal problems n Earth scences, he prmarly works on computer system and networkng research such as the desgn and analyss of personal communcaton servce systems, wreless LANs, wreless sensors, moble/wreless dstrbuted systems, and cache systems for wreless systems. He s servng as a guest edtor for the EURASIP Journal on Wreless Communcatons and Networkng specal ssue on wreless telemedcne and applcatons. He s the author of more than 30 scentfc papers and artcles. He s a member of the IEEE. Yang Xao was wth Mcro Lnear as a Medum Access Control (MAC) archtect nvolvng the IEEE standard enhancement work before he joned the Department of Computer Scence at the Unversty of Memphs, Tennessee, n From 2001 to 2004, he was a votng member of the IEEE Workng Group. He s currently wth the Department of Computer Scence at the Unversty of Alabama. He s currently the edtor-n-chef of the Internatonal Journal of Securty and Networks (IJSN), the Internatonal Journal of Sensor Networks (IJSNet), and the Internatonal Journal of Telemedcne and Applcatons (IJTA). He s an assocate edtor or on the edtoral boards of several journals, such as the IEEE Transactons on Vehcular Technology. He s also a referee/revewer for many fundng agences, a panelst of the US Natonal Scence Foundaton (NSF), and a member of the Telecommuncatons Expert Commttee, Canada Foundaton for Innovaton (CFI). He s a member of the techncal program commttees of more than 90 conferences, such as IEEE INFOCOM, ICDCS, ICC, Globecom, and WCNC. Hs research nterests are securty, telemedcne, sensor networks, and wreless networks. He has publshed more than 200 papers n major journals (more than 50 n varous IEEE journals/magaznes), refereed conference proceedngs, and book chapters related to hs research areas. Hs research has been supported by the NSF. He s a senor member of the IEEE and a member of the Amercan Telemedcne Assocaton.. For more nformaton on ths or any other computng topc, please vst our Dgtal Lbrary at